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1 European Journal of Personality, Eur. J. Pers. (2012) 65 2 Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/per.1865 66 3 67 4 68 5 69 6 70 7 OPEN PEER COMMENTARY 71 8 72 9 73 10 Bias due to Controlling a Collider: A Potentially Important Issue for Personality Research 74 11 75 12 76 JENS B. ASENDORPF 13 77 14 Department of Psychology, Humboldt University Berlin, Germany 78 15 [email protected] 79 16 80 17 Abstract: I focus on one bias in correlational studies that has been rarely recognised because of the current taboo on discussions of 81 fi 18 causality in these studies: bias due to controlling a collider. It cannot only induce arti cial correlations between statistically 82 19 independent predictors but also suppress or hide real correlations between predictors. If the collider is related to selective sampling, a 83 particularly nasty bias results. Bias due to controlling a collider may be as important as bias due to a suppressor effect. Copyright © 20 84 2012 John Wiley & Sons, Ltd. 21 85 22 86 23 In his stimulating paper that is unfortunately sometimes hard Self-efficacy is an important resource, so the association of im- 87 24 to read, Lee (this issue) touches a taboo topic in current migrant status with self-efficacy provides important 88 25 personality publications: causal relations among variables information. Do these immigrants have lower self-efficacy 89 26 that describe between-person differences. For many years, expectations than their Greek peers? The answer is yes (the 90 27 authors were educated by reviewers and editors to avoid zero-order correlation between dummy-coded immigrant 91 28 causal language because of the many pitfalls in causal inter- status in a sample of 969 adolescent immigrant students along 92 29 pretations of correlations. These pitfalls granted dismissing with their Greek classmates was .15, p < .001). 93 30 causality altogether are like throwing out the baby with the In studies of immigrant adaptation, skills in the host 94 31 bathwater. As humans, we cannot avoid thinking in terms language are often routinely controlled because they may 95 32 of causality, and therefore, tabooing this topic in publications already explain most or all effects of other predictors of 96 33 does not prevent readers and mass media from their own causal adaptation (although in many cases, suppressor effects may 97 34 interpretations guided by implicit rules such as ‘A correlates occur because the effect of language skills on adaptation is 98 35 with B’ means ‘A causes B’ but ‘B correlates with A’ means relatively strong). In the aforementioned case, if one controls 99 36 ‘B causes A’. the correlation between immigrant status and self-efficacy for 100 37 Although causality is a difficult concept in correlational the ability to speak Greek, the resulting partial correlation is 101 38 studies, scientists should and actually can do better than this .03 and not significant any more. The control of Greek speak- 102 39 if they can be pressed to explicate the causal model, or alterna- ing skills induces a bias due to a collider because these skills are 103 40 tive causal models, underlying their research questions. The very likely causally influenced by both immigrant status and 104 41 directed acyclic graph (DAG) method described by Lee (this self-efficacy. Indeed, the respective correlations were .37, 105 42 issue) is a valuable method of achieving such an explication p < .001 and .23, p < .001. Thus, controlling for host language 106 43 (see Foster, 2010, for an excellent discussion of causality based skills is highly problematic in studies of the adaptation of immi- 107 44 on DAGs for developmental psychologists). My comment here grants where a resource and/or an adaptation outcome influence 108 45 focuses on a key concept in the DAG approach: the collider. these skills because in such cases one controls a collider. 109 46 If one starts with explicit causal models before decisions 110 47 Bias due to explicit control of a collider: Example from are made on the statistical control of variables in the model, 111 48 research on adaptation one will rarely commit this kind of erroneous over control. 112 49 But if no causal analysis is made and the models involve many 113 50 A collider is an outcome of two joint predictors that may be variables, or variables where it is not clear whether they should 114 51 correlated or not. If one statistically controls for a collider, be considered a predictor or an outcome, researchers can easily 115 52 the resulting correlation between the predictors will be neces- be lost in covariation, relying on traditional routines designed 116 53 sarily biassed. Although this bias is most often discussed for the control of certain predictor variables although they 117 54 only for the case where two predictors are uncorrelated such might be outcomes in the present context. 118 55 that the bias consists of a spurious correlation, the bias is in 119 56 fact general: any correlation will be biassed by the adjust- Bias due to implicitly controlling a collider through 120 57 ment. As Lee (this issue) has correctly observed, the bias is sampling: Example from research on achievement 121 58 obvious but rarely noticed by researchers. 122 59 For an example, let us consider data on risks and resources If a collider is related to sampling such that the sample of 123 60 for adaptation of immigrant youth in Greece to the Greek participants is restricted in variation on the collider, this is 124 61 culture (Motti-Stefanidi, Asendorpf, & Masten, in press). equivalent to statistically controlling part of the variation of 125 62 126 63 127 64 Copyright © 2012 John Wiley & Sons, Ltd. 128 1 2 Discussion 65 2 66 3 the collider and therefore also introduces a bias. This is a Note that this bias is different from effects of restricted 67 4 particularly nasty case because the researcher did not variance that can inflate or suppress a correlation but cannot 68 5 explicitly control for the collider—the collider was implicitly induce a spurious correlation or change signs of a correlation. 69 6 controlled through selective sampling. Bias due to implicit control of a collider can do this and may 70 7 Asurprisingfinding from research on achievement may be even more common than bias due to explicit control of a 71 8 illustrate this bias (I am grateful to Marco Perugini who alerted collider. Many personality researchers are aware of biases 72 9 me to this case). Studies that relate IQ and conscientiousness to due to restricted sampling, and the possibility to correct for 73 10 achievement regularly find the expected positive correlations them, but there is no tradition to consider biases due to the 74 11 of IQ and conscientiousness with achievement but at the implicit control of a collider. 75 12 same time nonsignificant or even negative correlations 76 13 between IQ and conscientiousness (see, e.g. the meta-analysis Importance for personality research 77 14 by Ackerman & Heggestad, 1997), and authors who tried to 78 15 explain this unexpected result had difficulty finding post hoc Right now it is hard to judge the importance of biases in 79 16 explanations. A causal analysis suggests a bias introduced by personality research that are due to explicit or implicit 80 17 controlling a collider related to sampling. Most of these studies control of colliders because both biases are largely 81 18 used university students or samples biassed toward high unexplored. For the time being, a working hypothesis is 82 19 achievement, and this bias in sampling alone induced a that they may be as important as the better known 83 20 negatively biassed correlation because achievement is a suppressor effects between multiple predictors of the 84 21 collider of IQ and conscientiousness. same outcome. 85 22 86 23 87 24 88 25 89 26 What Kind of Causal Modelling Approach Does Personality Research Need? 90 27 91 28 DENNY BORSBOOM1, SOPHIE VAN DER SLUIS1,2, ARJEN NOORDHOF1, MARIEKE WICHERS3, NICOLE 92 29 GESCHWIND3, STEVEN H. AGGEN4,5, KENNETH S. KENDLER4,5 AND ANGÉLIQUE O. J. CRAMER1 93 30 94 31 1 Department of Psychology, University of Amsterdam 95 32 2 Complex Trait Genetics, Department of Functional Genomics and Department of Clinical Genetics, Centre for Neurogenomics and 96 33 Cognitive Research (CNCR), FALW-VUA, Neuroscience Campus Amsterdam, VU University Medical Centre (VUmc) 97 34 3 European Graduate School for Neuroscience, SEARCH, Department of Psychiatry and Psychology, Maastricht University Medical Centre 98 35 4 Virginia Institute for Psychiatric and Behavioural Genetics 99 36 5 Department of Psychiatry, Virginia Commonwealth University 100 37 101 38 [email protected] 102 39 103 40 Q1 Abstract: Lee (2012) proposes that personality research should utilise recent theories of causality. Although 104 41 we agree that such theories are important, we also note that their empirical application has not been very 105 42 successful to date. The reason may be that psychological systems are frequently characterised by feedback, 106 43 nonlinearity and individual differences in causal structure. Such features do not preclude the application of 107 44 causal modelling but do limit the usefulness of the approach for the analysis of typical personality data. To 108 45 adequately investigate personality, intensive time series of repeated measurements are needed. Copyright © 109 46 2012 John Wiley & Sons, Ltd. 110 47 111 48 112 49 We agree with Lee that recent theories of causality (Pearl, to showing that there is a problem in either the causal 113 50 2000) are important additions to the methodological litera- assumptions or the data, or both. This prompts the question 114 51 ture and deserve more widespread study in psychology. In whether the data currently at our disposal, which typically 115 52 addition, as will be clear from our own paper (this issue), concern individual differences at a single time point, are 116 53 Lee’s conceptualisation of personality in terms of (causal) adequately suited for the application of causal modelling in 117 54 networks is closely related to our own. However, although the context of personality. In our view, there are two aspects 118 55 the theoretical value of Pearl’s work stands beyond doubt, of psychological systems in general, and personality research 119 56 it is not as clear that the methodology is invariably fruitful in particular, that hamper causal modelling of the data we 120 57 in psychological applications. typically have in personality research. First, personality pro- 121 58 In our experience with the kind of analysis that Lee cesses are likely to involve feedback. Feedback is optimally 122 59 attempts in his empirical data example, such analyses often analysed in time series, which are not often available. 123 60 fail to return readily interpretable results. Lee’s analysis suf- Second, when applied to one-shot test data (i.e. when a large 124 61 fers the same fate, and its illustrative value is thereby limited number of people answer questionnaire items at one specific 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 Discussion 3 65 2 66 3 moment in time), causal modelling requires that the system this assumption is viable. For instance, some people react to 67 4 analysed is invariant over the units of observation; that is in stress by eating less; some by eating more. Some people 68 5 psychology, it requires that people are homogeneous in their become agitated when they lose sleep; some become slow. 69 6 organisational and causal structure. This is, in our view, Some people react to fear by fighting, some by fleeing and 70 7 unlikely (see also Molenaar, 2004). others by freezing. It is not even established that such 71 8 Regarding the first point, although there have been patterns remain stable over development. Although such 72 9 some stabs at modelling cycles in graphs, the main individual differences do not rule out the application of 73 10 power of the graphical approach to causality lies in the causal models if these are fitted to individual time series 74 11 analysis of directed acyclic graphs. Note that directed (e.g. Dahlhaus & Eichler, 2003; Eichler, 2007), it does call 75 12 acyclic graphs may be used to model feedback (e.g. into question the patterns of conditional independencies 76 13 Dahlhaus & Eichler, 2003), but that is not possible if the that are required for the sort of individual differences data 77 14 data are not sampled from the time domain. However, that Lee analyses. 78 15 feedback is likely to play a very important structural role Both feedback and individual differences can be 79 16 in developing and sustaining personality. As we argued addressed within the casual framework of Pearl (2000) if 80 17 in our own paper (this issue), feedback is likely to operate one is willing to invest in gathering sufficiently long time 81 18 through the selection of situations where the individual series that can be analysed at the level of the individual. 82 19 can express behaviour that is in some sense rewarding. Such data are becoming more frequent, and it is to be 83 20 However, it also pops up in the basic regulation of the body hoped that researchers are willing and able to make a 84 21 through homeostatic couplings between properties (e.g. large-scale transition in its research practice towards 85 22 sleep and fatigue, mood and activity, etc.). It is likely gathering such data. However, we live in a time when 86 23 that such feedback processes, which are instrumental in many researchers still interpret personality traits as forces 87 24 controlling the most fundamental aspects of human that operate at the level of the individual person, which 88 25 functioning, are also important in shaping and maintaining leads to the inaccurate impression that personality 89 26 personality features. psychology is already studying the mechanisms of 90 27 In many practical cases, the causal modelling approach individual behaviour. Lee does not commit to this 91 28 (which is in principle nonparametric in nature) is not only interpretation. However, although we agree that factor 92 29 limited to the analysis of directed acyclic graphs but also models need not necessarily be causally interpreted in all 93 30 supplemented with linearity assumptions (a primary and applications, it is unclear to us what his alternative 94 31 well-known example of this involves typical applications conceptualisation of factors comes down to. We note that 95 32 of structural equation modelling). However, in the case of the application of the theory of McDonald (2003), which 96 33 homeostasis, we almost always see variables that are Lee invokes, relies on the interpretation of factor scores as 97 34 bounded from below and from above (e.g. one cannot scores on infinite unidimensional item domains (tail 98 35 sleep less than zero or more than 24 h a day, eat less measures; see Ellis & Junker, 1997; Markus & Borsboom, 99 36 than nothing, etc.), which means that relations between 2011). It is, in our view, unlikely that this interpretation is 100 37 such variables cannot be linear. Thus, feedback must be satisfactory in personality theory, which does not even have 101 38 coupled with nonlinearity. It is not clear that if one samples finite unidimensional item domains. 102 39 the result of such processes at a single time point across In conclusion, we agree with Lee that recent theories 103 40 individuals (the typical data-gathering setup in personality of causality deserve more widespread dissemination. 104 41 research), anything reasonable and coherent can be However, it is still unclear whether the empirical methods 105 42 expected from applying standard causal modelling using associated with these theories will bear fruit in the area 106 43 directed graphs. of personality research. In our view, it is more likely that 107 44 Second, the approach that Lee utilises is predicated on the a redirection of research towards the study of the dynamic 108 45 assumption that the people studied can be described by the structure of individuals will better move the field of 109 46 ‘same’ causal organisation. In personality, it is not clear that personality research forward. 110 47 111 48 112 49 113 50 Scale Issues in Causality 114 51 115 52 DAVID M. CONDON, ASHLEY BROWN-RIDDELL, JOSHUA WILT AND WILLIAM REVELLE 116 53 117 54 Northwestern University 118 55 119 56 [email protected] 120 57 121 58 122 59 Abstract: Elaboration of the manner by which graphical frameworks of causality can benefit personality research is a 123 60 much-needed contribution. We argue that attempts to apply these frameworks in personality will benefit from consid- 124 61 eration of two concepts related to scale. The first is that the appropriate scale on which to evaluate causality depends 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 4 Discussion 65 2 66 3 upon the level of analyses on which the research is conducted. Second, the distal scale between typical expressions of 67 4 personality and their possible causes limits discussion of causality to probabilistic rather than mechanistic factors. 68 5 Copyright © 2012 John Wiley & Sons, Ltd. 69 6 70 7 71 8 By virtue of even attempting to integrate Judea Pearl’s of extraversion. An example of zooming in still further 72 9 innovative work on causality (Pearl, 2009) into the personality might include recent theoretical work relating an individual’s 73 10 psychology literature, James Lee is to be commended for desire to engage in prototypically extraverted behaviours to 74 11 initiating a conversation that is—in truth—uncomfortable for physiological measures of dopamine (Smilie, Cooper, Wilt, 75 12 a field of ‘correlators’ (Cronbach, 1957). But it is Lee’s & Revelle, in press). 76 13 concise elaboration of so many nuances of the graphical ‘Fictional factors’ play an integral role at each of these 77 14 framework that makes the target article an invaluable contri- levels of analysis in the form of latent behavioural trait 78 15 bution to the field, particularly for those unfamiliar with constructs. Admittedly imprecise at all levels, factors 79 16 Pearl’s work. To the extent that personality psychologists enable researchers to delineate continuous streams of 80 17 increasingly focus on the development and evaluation of observable behaviours into chunks that can be reasonably 81 18 predictive causal models, we consider it likely that the well measured and organised. The speculative proposition 82 19 influence of this work by Lee will grow over time. Although to map each of the hypothetical relationships between 83 20 many aspects of Lee’s review merit further exploration, our low-level biology and long-term, multiply determined 84 21 commentary primarily focuses on two aspects of the outcomes such as extraverted behaviours that affect career 85 22 relationship between the causal framework that Lee describes outcomes would seem to neglect this tension between 86 23 and considerations of scale. precision and efficacy. To be clear, we do not argue 87 24 The first point of note pertains to Lee’s comments on against the merits of model specificity but rather for the 88 25 the role of psychometric factors in graphical conceptualisa- merits of appropriate model scaling. Whereas it is 89 26 tions of psychological causality. We agree with Lee that invaluable to be reminded that the factor analytic approach 90 27 one of the goals of personality research should be to can only inform a subset of the questions personality 91 28 recursively ‘expand a directed edge in one graph into psychologists hope to explore, it is also true that the 92 29 an entirely new subgraph’ (p. 47) to understand the parsimonious chunking of data that factoring allows will 93 30 mechanistic relationship between two nodes, an endeavour likely justify its continued application. Lee stops short of 94 31 that would ideally result in richly detailed causal offering psychological researchers a metric for identifying 95 32 diagrams similar to those found in biology texts. Achieving and pursuing the appropriate levels of analysis. 96 33 this level of mechanistic detail may well resolve Our second point is to emphasise that the scale on 97 34 debates about the causal status for many psychometric which personality unfolds requires acknowledgement of 98 35 factors, but it would not mitigate the functional utility that the distinction between mechanistic and probabilistic 99 36 factors provide. causality. Intuitively speaking, the complexity of pathway 100 37 By analogy, a graph is something like an online navigation is a function of proximity. To be more precise, 101 38 geographic map. Psychometric factors, like many carto- the number of intermediate nodes is the variable that 102 39 graphic features, are not physically observable; researchers determines the number of alternative pathways, but it is 103 40 would no more benefit from ‘discarding the convenient effectively true that outcomes that are temporally or 104 41 fictions of folk psychology’ (p. 48) than travellers would physically proximal to their causes are predicted with 105 42 if the town, state and nation labels were stripped from higher probability than those that are distal. In other 106 43 maps. The familiar experience of ‘zooming’ an online words, the pursuit of mechanistic causality is a reasonable 107 44 map to the appropriate viewing level illustrates the contex- aspiration on a small scale because outcomes and their 108 45 tual utility of complexity, which is itself a function of purported causes are relatively proximal. 109 46 scale. Practically, infinite detail is possible in mapping of Most outcomes under study by personality psycholo- 110 47 both human behaviour and geography, but this would gists, however, are multiply determined over long periods 111 48 rarely be functional. Conceptual relationships are more of time. This suggests that the majority of causal factors 112 49 easily grasped and manipulated when they are manageable are probabilistic rather than mechanistic. Conditioning 113 50 in number and roughly similar in scale. discussions of causality on this distinction is vital as the 114 51 For example, it is common for trait psychologists to very basis for researching personality and cognitive ability 115 52 lament the broad imprecision of factors like the Big Five would be altered if these constructs were found to be 116 53 that are borne out of data reduction, yet most would agree mechanistically determined by genetics. The distinction is 117 54 that this is the appropriate level of analysis for evaluating also sobering in that it forces us to acknowledge that 118 55 topics such as the differential relationships on career personality is determined by the cumulative influence of 119 56 outcomes of extraversion and cognitive ability (Roberts, thousands of genes, a nearly infinite variety of environmen- 120 57 Kuncel, Shiner, Caspi, & Goldberg, 2007). More narrow tal variables, and multiple types of gene by environment 121 58 organisational frameworks such as the Big Five Aspect interplay (Johnson, 2007; some of which may occur more 122 59 Scales (DeYoung, Quilty, & Peterson, 2007) or the 30 commonly than the rare incident of mutation claimed 123 60 NEO facets (Costa & McCrae, 1992) would be appropriate by Lee as justification for general temporal restriction 124 61 for exploring the differential relationships of various facets [p. 40]). These genetic and environmental inputs do not 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 Discussion 5 65 2 66 3 directly cause behaviour but are rather mediated through typical manners of behaving across a wide variety of con- 67 4 their effect on proteins and subsequent neural systems that texts. We take this to mean that future knowledge regarding 68 5 lead to differential environmental sensitivities resulting in gene-trait associations would only allow for probabilistic 69 6 different cognitive, affective and motivational values. estimates, for example, of a given individual’s typical desire 70 7 Lee acknowledges this complexity and clearly explains to attend lively parties as an opportunity to express the 71 8 why the proximity of cause and outcome is less relevant for extraverted tendencies that result from the dopaminergic 72 9 gene-trait association studies. However, this does not imply effects on their wanting system (Smilie et al., ). Although this 73 10 mechanistic causality for the expression of the trait in any type of knowledge will someday constitute an impressive 74 11 given context. Unlike the examples made of height, hair contribution to the field, it will not reflect ‘causality’ as 75 12 Q2 morphology and Parkinson’s, personality constructs describe traditionally defined. 76 13 77 14 78 15 79 16 The Wright Stuff: Genes in the Interrogation of Correlation and Causation 80 17 81 18 GEORGE DAVEY SMITH 82 19 83 20 MRC Centre for Causal Analyses in Translational Epidemiology, University of Bristol 84 21 85 22 [email protected] 86 23 87 24 Abstract: The contemporary use of what are now called causal diagrams can be traced back to Sewall Wright’s 88 25 introduction of path coefficients in the early 1920s. Wright was explicit that causal evidence was required to formulate 89 26 such diagrams and that these schema did not alone provide evidence for or against causality. In population sciences, 90 27 germline genetic variation can provide required anchors for the separation of causal from (mere) correlational associa- 91 28 tions. Advances in biological and other material sciences offer more for improved causal understanding than new ways 92 29 of conceptualising and representing associations. Copyright © 2012 John Wiley & Sons, Ltd. 93 30 94 31 95 32 For most branches of science, the distinction between the now triumphant directed acyclic graph. I must admit to 96 33 (mere) correlation and causation is a central issue. My disci- being pleased that structural equation models largely failed 97 34 pline, epidemiology, is one prone to over interpretation—by to penetrate epidemiology; their (sometimes) manner of 98 35 the media, by researchers or both—of associations observed presentation as a form of alchemy can isolate causal 99 36 in data sets that are most plausibly explained by chance, bias pathways in an intercorrelated morass of data being 100 37 or confounding (Davey Smith & Ebrahim, 2002). James Lee scarcely credible. In the epidemiological setting, underlying 101 38 muses on these issues in the context of behavioural traits within social and biological processes, combined with reverse 102 39 the psychological literature and promotes the graphical causation (outcome influencing apparent exposure, rather 103 40 approach (in particular, directed acyclic graphs) now beloved than vice versa), leads to association being the norm rather 104 41 of many working within the epidemiological tradition. His than the exception (Davey Smith et al., 2008). Levels of Q3 105 42 clear presentation merits a close reading and raises issues of measurement error that exist in most domains simply cannot 106 43 general relevance. I will focus on the opportunities offered by be disciplined, and the confident production of coefficients 107 44 his statement that ‘the soundness of any causal conclusion that apparently have meaning seems chimeral. Thus, coming 108 45 depends on both conforming data and the correctness of the across Wright, authoring a paper in 1921 with the exact 109 46 requisite assumptions. Our substantial prior knowledge of same title as Lee, setting out his stall for his form of path 110 47 genetics justifies many powerful assumptions which lead to analysis was enlightening: 111 48 correspondingly powerful results.’ (p. xx). Indeed, leveraging 112 49 the power of germline genetic variation transforms our ability The ideal method of science is the study of the direct 113 50 to elucidate the causal chains within the networks of associa- influence of one condition on another in experiments 114 51 tions within the biological realm (Zhu et al., 2007), and in which all other possible causes of variation are 115 52 whereas graphical presentations may help, it is the biological eliminated. Unfortunately, causes of variation often seem 116 53 realities, rather than new ways to draw these on paper, that to be beyond control. In the biological sciences, especially, 117 54 contain the most promise, and which are only beginning to one often has to deal with a group of characteristics or 118 55 yield findings that will transform how we approach causality conditions which are correlated because of a complex of 119 56 in the population sciences. interacting, uncontrollable, and often obscure causes. The 120 57 Lee invokes the evolutionary biologist and population degree of correlation between two variables can be calcu- 121 58 geneticist Sewall Wright, the progenitor of path anal- lated by well-known methods, but when it is found it gives 122 59 ysis (and, through that, structural equation modelling, merely the resultant of all connecting paths of influence. 123 60 the structural equation models beloved more of the psycho- The present paper is an attempt to present a method of 124 61 logical than epidemiological literature) in the prehistory of measuring the direct influence along each separate path 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 6 Discussion 65 2 66 3 in such a system and thus of finding the degree of Lee, this issue; Sheehan, Didelez, Burton, & Tobin, 67 4 which variation of a given effect is determined by each par- 2008) and are reflected in Lee’s discussion of the 68 5 ticular cause. The method depends on the combination distinction between Fisher’s notion of the as-observed 69 6 of knowledge of the degrees of correlation among the ‘average excess’ associated with a genetic difference and 70 7 variables in a system with such knowledge as may be the ‘average effect’ that would be seen with a gene 71 8 possessed of the causal relations. In cases in which the substitution. That confounding can exist in genetic 72 9 causal relations are uncertain the method can be used to find association studies is of course widely recognised, with 73 10 the logical consequences of any particular hypothesis in ancestral population differences in both gene frequency 74 11 regard to them. (Wright, 1921, p. 557) and disease risk (‘population stratification’) being the 75 12 most likely culprit. There are well-established methods 76 13 Wright’s famous path analyses (Figure; Wright, 1920) of accounting for this using genome-wide data as 77 14 required prior causal knowledge to make sense. With this, indices of such population stratification, and with 78 15 they introduced important new understanding, not the least established genetic variant-phenotype links, it is remark- 79 16 of which was the identification of what Wright termed able how homogeneous the associations seen within 80 17 ‘intangible variance’—induced by what we may call different populations generally are, despite allele 81 18 stochastic or chance events—that lead to group level, frequency often varying between populations (Hindorff 82 19 rather than individual trajectory, understanding, which is et al., 2012). Empirical data also demonstrate that 83 20 the best that can ever be hoped for in the population confounding of genetic variants with social, behavioural 84 21 sciences (Davey Smith, 2011a). and physiological factors that plague conventional 85 22 To an extent, known biological relationships in quanti- observational studies are conspicuous by their absence 86 23 tative genetic analyses in the behavioural genetics field (Davey Smith et al., 2008). 87 24 provide a form of reliable prior information on the pres- Lee considers at length the possibility that selection bias 88 25 ence and direction of causation. However, in the molecular related to participation in studies could bias findings. Thus, 89 26 genetics era, the most powerful source of prior causal if a genetically influenced trait was related to willingness to 90 27 knowledge that can, and is, now being leveraged comes participate in a study, and this was differential for cases 91 28 from germline genetic variants that have established and controls, a spurious association could be generated. This 92 29 associations with particular traits. R.A. Fisher explicitly is in principle true, but common control groups have been 93 30 referred to the essentially randomised nature of genetic used for various diseases (e.g. the Wellcome Trust Case 94 31 perturbations (Fisher, 1952), as Lee mentions and as others Control Consortium, 2007), and unless the participation 95 32 directly associated with Fisher have written about effect was condition specific, such bias would generate 96 33 (Bodmer, 2003; Box, 2010), although the possibility that similar associations for all the diseases, which were not 97 34 Mendelian randomisation came before experimental seen. Even if such a participation effect was disease 98 35 randomisation in Fisher’s intellectual biography has been specific, it would only influence case-control studies, not 99 36 little recognised (Davey Smith, 2006). That genetic prospective studies, and generally, genetic associations 100 37 variation inducing a group-level difference in a potentially have been similar across study designs (Hindorff et al., 101 38 modifiable phenotype can provide evidence of the 2012). More complex hypotheses could be advanced 102 39 downstream causal effect of this phenotype, free of the involving interactions of genetic variants influencing 103 40 influence of confounding or reverse causation, is now participation and condition-specific disease risk, but 104 41 widely recognised and implemented in epidemiological plausibility decreases with increasing elaboration of the 105 42 studies (Timpson, Wade, & Davey Smith, 2012). To give hypothesis in this regard. Again, the fact that similar 106 43 just one example of relevance to the study of behavioural effects for established variants tend to be seen in designs 107 44 traits—the topic of Lee’s paper—such ‘Mendelian with widely differing participation rates, from high response 108 45 randomization’ (as the method is generally termed; Davey rate general population cohorts to what are essentially 109 46 Smith & Ebrahim, 2003) has been applied to the effects volunteer studies, is reassuring in this regard. 110 47 of smoking. As proof of principle, such studies have Graphical approaches to causal inference are certainly 111 48 demonstrated that a genetic variant robustly associated of value in forcing investigators to be explicit about 112 49 with smoking behaviour relates to lung cancer risk to the their assumptions and can help in the identification of 113 50 degree expected by the association of the variant with unrecognised potential biases. There are also often 114 51 appropriately ascertained smoking behaviour (Munafo unrecognised drawbacks to formulaic or mechanical 115 52 et al., 2012; Wang, Broderick, Matakidou, Eisen, & imposition of such approaches (Dawid, 2008). In epidemi- 116 53 Houlston, 2011), and associations with several other ological circles, it is now not uncommon to receive peer 117 54 smoking-related diseases have been made. Such studies review comments that focus on the possible adjustment 118 55 have also shown that smoking lowers body mass index for a collider in model 3 of Supplementary Table 4 rather Q4 119 56 (Freathy et al., 2011; despite naive observational associa- than an informed overview of the totality of evidence 120 57 tions sometimes being in the opposite direction, given provided. ‘Inference to the best explanation’ (Lipton, 121 58 confounding by socioeconomic position and various other 2004), which is surely what any attempt at causal 122 59 socially patterned exposures). reasoning is aiming at, can go out of the window as the 123 60 The various assumptions of such Mendelian randomisa- d-connected nodes, rather than how the world actually is, 124 61 tion studies have been reviewed (Davey Smith, 2010; become the focus of attention. 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 Discussion 7 65 2 66 3 Wright opined that ‘great refinement in statistical 67 4 treatment is often a waste of effort’ (Wright, 1917). 68 5 William Provine (1986), in his unsurpassable intellectual 69 6 biography of Wright, discusses the development of path 70 7 analysis and how, working with methods that tried to 71 8 hold other factors constant through statistical manipulation, 72 9 ‘Wright was still dissatisfied. He saw clearly that by 73 10 itself the partial correlation coefficient, like the correlation 74 11 coefficient, was a mathematical quantity not tied or 75 12 leading by itself to any causal interpretation of the relations 76 13 under examination. Wright wanted to minimise correla- 77 14 tional statistics and maximise the quantitative causal 78 15 interpretation of the variables’ (p. 127). This can only be 79 16 carried out when causal anchors—that come from how 80 17 the material world is, not how we draw diagrams on 81 18 paper—are introduced into the mix. Germline genetic 82 19 variants provide precisely such anchors and open up vast 83 20 new vistas of possible causal understanding generated from Diagram illustrating the casual relations between litter mates 84 21 observational data (Davey Smith, 2011b). (O, O’) and between each of them and their parents. H, H’,H" 85 22 and H"’ represent the genetic constitutions of the four indivi- 86 23 duals; G, G’,G"andG"’ represent that of four germ cells. E 87 ACKNOWLEDGEMENTS 24 represents such environmental factors as are common to litter 88 25 Thanks to Dave Evans for discussion of selection bias in mates. D represents other factors, largely ontogenetic irregu- 89 26 genome-wide association study. larity. The small letters stand for the various path coefficients. Q5 90 27 91 28 92 29 93 30 Causing a Shift in Causal Thinking 94 31 95 32 JOSHUA J. JACKSON1 AND SETH M. SPAIN2 96 33 97 34 1Washington University in St. Louis 98 35 2Binghamton University and State University of New York 99 36 100 37 [email protected] 101 38 102 39 Abstract: We concur that the difficulties of causal analysis are especially problematic for personality psychologists. 103 40 We suggest that this stems from both historical and methodological reasons. Additionally, we note that the Pearl 104 41 model is not completely adequate for some questions pertinent to personality psychologists and mention the existence 105 42 of underutilised methods that provide stronger causal inference. It is important to remember that many hypotheses are 106 43 causal in nature and that designs other than randomised experiments exist to estimate causal effects. However, no 107 44 single design can guarantee the identification of causality. Copyright © 2012 John Wiley & Sons, Ltd. 108 45 109 46 110 47 Discussions of causality within personality psychology are (Almund et al., 2011). Moreover, in the interest of conducting Q6 111 48 usually relegated to a research methods class or the occasional better science, it is important to be open about causal hypotheses 112 49 methods chapter and rarely (ever?) make their way into journal as our theories drive the way in which we conduct and analyse 113 50 introductions or discussion sections. Of course, this is despite our research. 114 51 many of our hypotheses being causal hypotheses (Pearl, 115 52 2000). Most likely, this is due to personality psychologists How do we think about causality? 116 53 knowingthateachresearchdesignweemployisimperfect 117 54 and, thus, incapable of producing strong causal conclusions. Currently, psychologists (and other related fields) tend to 118 55 Instead of openly discussing causal hypotheses, it is easiest to have a relatively narrow and unified view of causality 119 56 err on the side of caution. Therefore, we omit direct reference (White, 1990). This causal framework was built out of the 120 57 to causal relationships and instead speak in safe terms of philosophical discussion of causality first championed by 121 58 ‘associations’ or ‘prediction’. One of the highlights of the current Hume and Mill and then developed into formal statistical 122 59 article is to appreciate that we are often interested in causal models. This model, the Rubin model of causality (proposed 123 60 questions. If personality psychologists desire to provide input by Holland but based on ideas introduced by Neyer and 124 61 to policy, wrestling with issues of causality is a necessary task Rubin, thus also called the Neyer–Rubin or Holland–Rubin 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 8 Discussion 65 2 66 3 Q7 model; Holland, 1986; Rubin, 1980; 1991) focuses on through the inclusion of covariates in a standard linear model. 67 4 providing a framework to make the strongest causal inference In contrast, propensity score matching offers a much stronger 68 5 possible, whose ‘gold standard’ is the randomised experimental way to control for selection bias in observational data by simul- 69 6 design (Campbell & Stanley, 1963). Unfortunately, the taneously controlling for many covariates (Thoemmes & Kim, 70 7 observational and correlational designs employed by personality 2011). In this approach, each participant receives an estimated 71 8 psychologists do not usually fit this model given that individual propensity score, which is the conditional probability that a 72 9 differences are not readily manipulable, and certain questions given participant would be exposed to the treatment condition, 73 10 necessitate observational or correlational designs because of given certain values on observed covariates. By matching 74 11 ethical, temporal or financial reasons. Given this purview, participants that have or have not been exposed to the treatment 75 12 causality is not discussed when these less than optimal designs on this estimated propensity score, pairs of participants are cre- 76 13 are employed. Rather, a cautious and agnostic approach is taken ated that are balanced on all observed covariates—a situation 77 14 in this instance because the design is not the gold standard that would be expected under a randomised experiment. This 78 15 randomised experimental design. We believe that this prevailing matching process creates two distributions that are balanced 79 16 model of causality has become so prevalent that what is causal is with regard to observed background variables that may bias 80 17 solely defined by the method endorsed by this model. In other our findings. Accordingly, these two distributions only differ 81 18 words, it is assumed one cannot find causal associations unless in terms of the treatment that they received. This approach is 82 19 a manipulation occurs (Holland, 1986). slowly being integrated into psychology (e.g. Jackson et al., Q8 83 20 This purview is unfortunate because not only it limits our 2012; Kendler & Gardner, 2010) but has yet to fully utilised. 84 21 ability to speak in causal terms but also because there exist Another major threat to causal inference is endogeneity 85 22 other approaches to think about causality and test causal (Antonakis, Bendahan, Jacquart, & Lalive, 2010). Endogene- 86 23 relationships (Goldthorpe, 2001). In psychology, structural ity occurs when a predictor or set of predictors is correlated 87 24 equation modelling is often brought up as an obvious with the error term in a model (Kennedy, 1985). Endogeneity 88 25 candidate. Of course, the structural models are simply is especially problematic for personality researchers because 89 26 covariance matrices that in and of themselves do not it can occur when important variables are omitted from the 90 27 necessarily capture many of the agreed upon requirements for model or if there is reciprocal causation between outcome 91 28 causality (Bollen & Pearl, ). The Pearl model nicely builds and predictor(s). The result of endogeneity is a biassed esti- 92 29 upon this framework and provides a way to think about mate of model coefficients. 93 30 causality that does not necessarily rely on manipulation of Instrumental variables are one method to safeguard 94 31 variables. The positives of this model are many, but a few against endogeneity. An IV is a variable correlated with the 95 32 difficulties exist, especially for personality psychologists. regressor but independent of the error term. Two-stage least 96 33 One major challenge for the Pearl causal approach is that squares is used to estimate the effect of a ‘purified’ regressor, 97 34 it cannot, generally, handle issues of reciprocal causation or, cleansed of its error-correlated variance. Say we have a model 98 35 more specifically, nonrecursive models. Within Pearl’s of the type, Y = b0 +b1X+e, where cov(X,e) 6¼ 0. In such a 99 36 approach, causal models must take the form of directed case, the estimate of b1 will not be equal to the ‘true’ 100 37 acyclic graphs. So, X ! YorX Y, but X ! Y is not population value and is thus a biassed estimate. IV methods 101 38 generally allowed (where ! represents mutual causation, are used to ‘clean’ the variance of X association with e.In 102 39 not correlation). Cycles, such as reciprocal causation, will essence, IV methods first regress X on an instrument, Z, to 103 40 typically result in a breakdown in the mathematical logic that obtain a purified X*, and then Y is regressed on X* to obtain 104 41 leads to causal knowledge. Within personality psychology, an unbiased estimate (Gelman & Hill, 2007). 105 42 many different theories posit that two variables may affect For example, consider the hypothesis that extra schooling 106 43 each other across time and thus would not be applicable to increases IQ. A policy change that would lead to a greater 107 44 the type of analysis presented in the current paper. Other number of years of education, such as some states providing 108 45 causal modelling traditions directly deal with these difficul- a large number of scholarships, could serve as an instrument, 109 46 ties, such as some econometric models (Heckman, 2005). provided that scholarships were not based on IQ. This policy 110 47 change would not directly affect the outcome, IQ, and thus 111 48 How can we test causal relationships? could act as an instrument to better test the causal effect of 112 49 whether schooling leads to increases in IQ. 113 50 As mentioned before, we believe that a number of designs 114 51 other than randomised experiments can provide causal Summary 115 52 inferences. These designs do so by safeguarding against many 116 53 biases that arise in observational studies. One common It must be remembered that no single design can definitively 117 54 technique is to use heredity to our advantage (e.g. Davey Smith identify a causal relationship. For all of the positives of 118 55 & Ebrahim, 2003; Rutter, 2007). Two relatively new—for randomised experiments, there exist shortcomings that do not 119 56 psychologists—methods of causal analysis are propensity guarantee causal inference. In the end, the best way to 120 57 score matching and instrumental variables (IVs). understand causality is by growing a nomological net— 121 58 Because observational designs are not randomised, testing and retesting, ruling out alternative hypotheses and 122 59 selection biases exist. As a result, it is necessary to control replicating findings. Personality psychologists, however, can 123 60 for any confounding pre-existing differences that could bias do this as well as any other discipline and thus should not be 124 61 the estimation of causal effect. Typically, this is carried out coy about their causal hypotheses. 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 Discussion 9 65 2 66 3 Petard 67 4 68 5 WENDY JOHNSON 69 6 70 7 Department of Psychology, University of Edinburgh 71 8 Centre for Cognitive Ageing and Cognitive Epidemiology, University of Edinburgh, Edinburgh, UK 72 9 73 10 [email protected] 74 11 75 12 Abstract: Lee has made an important contribution in introducing personality psychologists to Judea Pearl’s rigorous 76 13 conceptual approach to thinking about causality. The approach makes clear the dangers in applying commonly used 77 14 statistical controls without considering all alternative causal mechanisms. Ironically, Lee chose gene-trait 78 15 association as a likely ultimately causal model. He was likely hoist with his own petard when he omitted the path from 79 16 environmental circumstances to gene expression. No abstract conceptual approach can be a complete substitute for 80 17 clear and objective thought about alternative explanations. Copyright © 2012 John Wiley & Sons, Ltd. 81 18 82 19 83 20 In warfare, a siege takes place when an army attacks a especially when collider variables are statistically con- 84 21 fortress that cannot easily be taken and refuses to withdraw. trolled. As he noted, such control can and too often does 85 22 Personality psychology has long been engaged in a siege take place unintentionally through sample selectivity and 86 23 against the fortress of complexity surrounding the emergence also intentionally but unwittingly through application of 87 24 and application of personality traits in the lives of indivi- statistical control that disregards alternative pathways. 88 25 duals. The siege’s progress ebbs and flows: occasionally, These examples play to the strength of the approach, 89 26 we stumble on a crack in the fortress walls through which which is to bring to light mistakes in causal attribution 90 27 we can hurl a bomb, but often, it seems that the better our resulting from overly simplistic causal models. The 91 28 weapons, the higher those walls grow. Lee, however, has approach can certainly be used actively to prevent such 92 29 introduced personality psychologists to an important new mistakes through examination of all possible alternatives, 93 30 weapon in the elegant and revealing conceptual approach to but the thoroughness of this process, and thus its effective- 94 31 causality of Pearl (2009). ness, lies completely in the hands of the researcher. The 95 32 Pearl’s weapon reminds me of the petard. In mediaeval approach itself cannot ensure the necessary objectivity 96 33 and Renaissance siege warfare, a petard was a small bomb. and independence of mind. Perhaps unintentionally, Lee 97 34 It was used to breach fortifications by blowing up specific made this instructively clear in Section 4. He selected 98 35 gates or walls. Petards were often placed inside tunnels gene-trait association as one of the most likely direct 99 36 under walls or directly upon gates. Like Pearl’s approach examples of ultimate causality. R. A. Fisher’s model of 100 37 to understanding causality, when it worked, the petard additive genetic variance and heritability was considered 101 38 was a sophisticated, targeted tool with considerable power a substantial contribution in its day, but it is becoming 102 39 to accomplish a much larger goal. Also like Pearl’s clearer by the moment that that pesky environment, 103 40 approach, however, successful use of the petard meant broadly construed as circumstances both external and 104 41 keeping track of the interconnections among many internal to the organism (including other genes in the 105 42 different contributing factors. For example, it was common genotype), repeatedly gets in the way, not only by making 106 43 for the attacker to dig a shallow trench close to the fortress it hard to avoid genetically selected samples as Lee 107 44 gate. The engineer would then erect a small hoisting discussed but also by altering the very nature of gene 108 45 engine of wood, ropes and pulleys from this trench. The expression. 109 46 engine was designed to lift the petard, once lit by And it is gene expression, well beyond gene presence 110 47 the engineer, out of the trench and to hurl it at the gate, in the genotype, that likely matters most for genetic 111 48 where it would detonate, destroying the gate. Sometimes, influences on the patterns of behaviours that personality 112 49 however, in activating the system, the engineer would psychologists explore. To date, evidence for this is 113 50 become entangled in the ropes and hoisted out along with generally indirect in humans, and specific examples come 114 51 the petard and blown up himself, ‘hoist by his own petard’. primarily from model organisms (see Johnson, Penke, & 115 52 In Hamlet, Shakespeare used this occurrence as a metaphor Spinath, 2011 last year’s target article in this journal and 116 53 for the position in which Hamlet found himself: bearer of its associated comments for more complete discussion of 117 54 sealed letters from his Uncle Claudius to the King of this). Nevertheless, disregarding the relevance of these 118 55 England, instructing the King to execute him. Fans of examples to human personality development is to trip over 119 56 Shakespeare have made the expression a commonly used the guide rope just as you light and hoist the petard. 120 57 figure of speech in English, meaning much the same as 121 58 ‘shooting oneself in the foot.’ 122 ACKNOWLEDGEMENTS 59 Lee has made Pearl’s approach relevant to personality 123 60 psychologists through several apt examples, pointing out I thank Tom Booth and Rene Mottus for the comments on an 124 61 clearly the potential for misattributions about causality, earlier draft. 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 10 Discussion 65 2 66 3 Causality: Populations, Individuals and Assumptions 67 4 68 5 ROGIER A. KIEVIT1, LOURENS J. WALDORP1, KEES-JAN KAN2 AND JELTE M. WICHERTS1 69 6 70 7 1Faculty of Social and Behavioural Sciences, University of Amsterdam 71 8 2Biological Psychology Department, Free University of Amsterdam 72 9 73 10 [email protected] 74 11 75 12 Abstract: We side with Lee on the importance and potential use of graphical causal modelling in personality research but 76 13 raise three issues crucial to its validity. First, causal relations obtained at the inter-individual level should not be confused 77 14 with intra-individual causal relations. Second, it is difficult to explicate all assumptions about which variables are measured, 78 15 their causal relations and the possibility of co-occurring events when applying graphical modelling to personality data. 79 16 Third, multiple testing complicates assessing (in)dependencies. Conclusions and inferences should always be drawn with 80 17 appropriate attention to the underlying assumptions. Copyright © 2012 John Wiley & Sons, Ltd. 81 18 82 19 83 20 We agree with Lee (this issue) that the graphical makes up some population, and therefore distinct from 84 21 framework as set out by Pearl (2009); Lauritzen (1996); the inter-individual pattern (e.g. Hamaker, Nesselroade, & 85 22 Spirtes, Glymour, and Scheines (2000) and others provides Molenaar, 2007). This confirms Lee’s suggestion that a 86 23 a rich account of causality much needed in the social well-fitting model at the group level does not necessarily 87 24 sciences. However, we would like to point out three issues capture all causally relevant dynamics. 88 25 in causal modelling that we believe were not given sufficient The distinction between within-subject and between- 89 26 attention by Lee. First, causal relations obtained at the subject explanations is crucial (e.g. Penke et al., 2011), 90 27 population level (inter-individual differences) are often especially for biological explanations. In behaviour genet- 91 28 applied to, and confused with, intra-individual causal ics and cognitive neuroscience, inter-individual findings 92 29 relations. Second, to infer a causal relation, strong assump- are often interpreted as being causally operative at the level 93 30 tions are required about which variables are measured, their of the individual. For instance, as Figure 1 in Lee illus- 94 31 causal relations and the possibility of co-occurring events. trates, the links between genes, brains and cognition are 95 32 Third, when testing (in)dependencies, one is faced with the often assumed to be causal and one way. Recent studies 96 33 multiple testing issue. suggest that psychological activities such as intense mem- 97 34 In Lee’s discussion, within-subject and between-subject ory training can affect brain structure within individuals 98 35 analyses are often confounded. This is especially relevant over time (e.g. Draganski et al., 2004). This can occur 99 36 for personality research, as personality dimensions are regardless of cross-sectional correlations between brain 100 37 generally studied as inter-individual dimensions. Consider and behaviour. The biological phenomena that explain 101 38 Lee’s Figure 2, which is a description of a sequence of events differences between people may differ from phenomena 102 39 unfolding over time under different settings. It entails a that explain changes within people over time. Or, in 103 40 ‘within-pavement’ causal explanation. Imagine if instead of the do-syntax:(grey matter|do(differences in memory 104 41 repeatedly observing this pavement over time (e.g. seasons), performance)) 6¼ (grey matter|see differences in memory 105 42 we were to observe the same indicators for different performance). Similarly, the heritability of certain psycho- 106 43 pavements across the world. This dataset will include logical traits is a variable that explains differences between 107 44 pavements from rich and poor countries (where they can or people, not the process (or inevitability of the outcome) 108 45 cannot afford good sprinklers) with pavements in areas with within individuals. This distinction is essential yet often 109 46 4, 3 or 2 distinct seasons, with differing building materials, overlooked. Thus, we suggest that extra attention be paid 110 47 and a host of variables that will affect their inter-pavement to distinctions between inter-individual and intra-individual 111 48 wet-becoming behaviour. Such a model will tell a different causal explanations and causal explanations that cross 112 49 causal story, as it is concerned with differences between explanatory levels. 113 50 pavements. For instance, building materials may be a Our second point concerns the assumptions of estimating 114 51 relevant factor in explaining the causal chain from raining causal effects. Our view is that causal analyses are very power- 115 52 to wetness between pavements but not within pavements. ful, but that assumptions should be made explicit so that 116 53 These are two distinct causal explanations, and both are researchers can properly evaluate the strength of the 117 54 relevant for personality research. Although the conventional conclusions. Consider the example in Lee’sFigure3.Toinfer 118 55 Big Five model represents individual differences, it can be a causal effect of IQ on SES, we are required to use the back- 119 56 extended to include intra-individual data, by actually measur- door criterion that assumes that (i) all direct causes of IQ (i.e. 120 57 ing differences in behaviour and attitudes within people over have an arrow into IQ) are controlled for, (ii) no effects of IQ 121 58 time (Molenaar & Campbell, 2009). Structural equation are controlled for and (iii) the probability of the direct causes 122 59 modelling of time-series personality data reveals that the of SES and IQ is almost nowhere zero. 123 60 intra-individual pattern, and therefore the nature of the causal Condition (i) implies that the set of measured variables 124 61 explanation, may be different within each individual that is sufficient to block all paths to IQ. In general, this is 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 Discussion 11 65 2 66 3 difficult to maintain or test. It is often unclear which vari- to test. We are in favour of graphical modelling, but users 67 4 ables are involved and/or there may be a lack of consensus should be aware of the meaning of these crucial assumptions 68 5 about the direction of arrows. In the example, could educa- before applying such techniques. 69 6 tion be a relevant variable, and if so, will it have a direct A final issue concerns the analysis of complex graphi- 70 7 arrow into SES or will it be an effect of SES? If cal models that are often encountered in personality 71 8 education is considered a cause of SES, then it should be research. Consider a simple example with five nodes in a 72 9 controlled for; if education is considered an effect of graph. To test all (in)dependencies implies that for each 73 10 SES, then it should not be controlled for. Such prior combination of nodes, we have six tests, and so for all 74 11 knowledge is crucial. The application of the formula of 5*(51)/2 = 20 combinations, we have 120 tests. This 75 12 the back-door (Pearl, 2000) requires that the distribution raises the question of how to deal with multiple 76 13 is positive almost everywhere (Lauritzen, 1996). If this is comparisons. Should we use Bonferroni, False Discovery 77 14 not the case, the adjustment cannot be applied. In the example, Rate (FDR) or local FDR? 78 15 condition (iii) entails that, for instance, there should be families Overall, Lee’s arguments for the better incorporation of 79 16 with low parent SES and high offspring SES, and vice versa. graphical models and causal inference are timely and 80 17 Is this likely? And if these combinations do not co-occur, well taken. However, for the aforementioned reasons, 81 18 should we censor distributions? So assumptions of applying conclusions and inferences should always be drawn with 82 19 the back-door adjustment are quite strong and often difficult appropriate attention to the underlying assumptions. 83 20 84 21 85 22 86 23 Correlation and Causation—The Logic of Co-habitation 87 24 88 25 JUDEA PEARL 89 26 90 27 Computer Science Department, University of California, Los Angeles 91 28 92 29 [email protected] 93 30 94 31 Abstract: Recent advances in graphical models and the logic of causation have given rise to new ways in which scientists 95 32 analyse cause–effect relationships. Today, we understand precisely the conditions under which causal relationships can 96 33 be inferred from data, the assumptions and measurements needed for predicting the effect of interventions (e.g. treatments 97 34 on recovery) and how retrospective counterfactuals (e.g. ‘I should have done it differently’) can be reasoned about 98 35 algorithmically or derived from data. The paper provides a brief account of these developments. Copyright © 2012 99 36 John Wiley & Sons, Ltd. 100 37 101 38 102 39 James Lee’s paper, Correlation and Causation, would Although the do-operator and expressions of the type 103 40 probably raise a few eyebrows among readers of the P(mud|do(rain)) may appear to be an unnecessary, if not 104 41 European Journal of Personality. ‘Again?’ Some will ask, offensive infringement on probability theory, the causal 105 42 ‘Haven’t we heard enough about this subject? and isn’tit diagrams that encode such expressions appear infinitely more 106 43 an established fact that even seasoned experts cannot agree friendly, especially to researchers familiar with path analysis 107 44 on the definition of cause and effect or on how one should and structural equation models (SEMs). I strongly recom- 108 45 estimate such relationships from observational studies?’ mend therefore that researchers invest the time in acquiring 109 46 Things have changed in the past two decades. Today, the few fundamental graphical tools necessary for causal 110 47 experts agree (some unwittingly) on almost every aspect of analysis. D-separation is one such tool, without which one 111 48 causal analysis; controversies have given way to theorems, is at a loss as to what the testable implications are of a given 112 49 paradoxes have been resolved, and estimation problems have model, whether a variable Z qualifies to serve as an 113 50 been algorithmitised. instrumental variable or whether two proposed models are 114 51 James Lee is right in starting the discussion by introducing statistically indistinguishable. The back-door criterion is 115 52 new notation. Most controversies of the past have originated another, with the help of which one can tell immediately 116 53 with notational confusion, and most mistakes today stem whether a causal effect can be estimated by adjustment on 117 54 from the belief that probability calculus is sufficient for observed covariates. 118 55 handling causal relations. The insufficiency of probability However, the theory of causal diagrams differs in two 119 56 (and statistics) is traumatic to most researchers in the field of fundamental aspects from conventional SEM. First, no com- 120 57 data analysis because our schooling has given us the illusion mitment is made to linearity or to any parametric represen- 121 58 that, first, a joint density function of all variables is the ultimate tation of the equations—they remain totally nonparametric. 122 59 source of all knowledge and, second, everything that can be Second, the causal assumptions that go into the diagram 123 60 inferred from data can be inferred using the mathematical are precisely defined and, contrary to conventional practice, 124 61 machinery of probability and statistics. are not conflated with their statistical surrogates. 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 12 Discussion 65 2 66 3 In the sequel, I will summarise the tools that the new to both continuous and categorical variables, linear as 67 4 theory of causation offers to researchers: For details, please well as nonlinear interactions. 68 5 see Pearl (Pearl, 2009; Pearl, 2010; Pearl, ). 69 6 The mediation formula 70 7 Summary of capabilities 71 8 This last result deserves further discussion because the 72 9 1. Tools for reading and explicating the causal assumptions problem of mediation is extremely important in personality 73 10 embodied in SEM models as well as the set of assumptions research for it unveils the mechanisms that mediate between 74 11 that support each individual causal claim. causes and effects. 75 12 2. Methods of identifying the testable implications (if any) The analysis of mediation has long been a thorny issue in 76 13 of the assumptions in (1) and ways of testing not the the social and behavioural sciences (Baron & Kenny, 1986; 77 14 model in its entirety but the testable implications of the MacKinnon, 2008) primarily because the distinction between 78 15 assumptions behind each causal claim. causal parameters and their regressional surrogates was too 79 16 3. Methods of deciding, prior to taking any data, what often conflated (Pearl, 2011). The difficulties were amplified 80 17 measurements ought to be taken, whether one set of in nonlinear models, where interactions between pathways 81 18 measurements is as good as to another, and which measure- further obscure their distinction. 82 19 ments tend to bias our estimates of the target quantities. The nonparametric analysis now permits us to define the 83 20 4. Methods for devising critical statistical tests by which two target quantity in a way that reflects its actual usage in 84 21 competing theories can be distinguished. decision-making applications. For example, if our interest lies 85 22 5. Methods of deciding mathematically if the causal relation- in the fraction of cases for which mediation was sufficient for 86 23 ships of interest are estimable from nonexperimental data the response, we can pose that very fraction as our target 87 24 and, if not, what additional assumptions, measurements or question, whereas if our interest lies in the fraction of 88 25 experiments would render them estimable, responses for which mediation was necessary, we would pose 89 26 6. Methods of recognising and generating equivalent models. this fraction as our target uestion effect (Pearl, 2001, 2011). 90 27 7. Generalisation of SEM to categorical data and nonlinear In both cases, we can dispose of parametric analysis 91 28 interactions. altogether and ask under what conditions can the target 92 29 8. A formal solution to the problem of ‘external validity’ question be identified/estimated from observational or 93 30 (Campbell & Stanley, 1963), that is under what condi- experimental data. One can further show that if certain condi- 94 31 tions can results from an empirical study be transported tions of ‘no unmeasured confounders’ hold, a simple mediation 95 32 to another environment, differing from the first, how formula can be derived that captures the effects of interest. The 96 33 the results should be calibrated to account for the mediation formulas are applicable to both continuous and 97 34 differences and what measurements need be taken in each categorical variables, linear as well as nonlinear interactions, 98 35 of the two environments to license the transport (Pearl & and moreover, they can consistently be estimated from the data. 99 36 Bareinboim, 2011). I commend James Lee for illustrating so vividly the power 100 37 9. A simple, causally based solution to the so called of causal diagrams in a language familiar to personality 101 38 ‘Mediation Problem’, taking the form of estimable researchers. I am hopeful that readers will appreciate both the 102 39 formulas for direct and indirect effects that are applicable transparency of the model and the power of the approach. 103 40 104 41 105 42 Does a Directed Acyclic Graph Define Causality? 106 43 107 44 ROLF STEYER 108 45 109 46 Friedrich-Schiller-Universität, Jena, Germany 110 47 111 48 [email protected] 112 49 113 50 Abstract: It is argued that the theory of directed acyclic graphs (DAGs) does not define causality, although a DAG—just 114 51 like a structural equation model (SEM)—can be used as a causal model if appropriate assumptions are made. The causal 115 52 meaning of a DAG (and a SEM) does not come from the definition of a DAG (or the SEM). Both are just statistical models 116 53 not differing in this respect from the ANOVA model. The causal meaning comes from the theory of causality within which 117 54 we postulate certain relationships between the variables included in the DAG or SEM and the variables not included. 118 55 Neither DAGs nor SEMs address these relationships. Copyright © 2012 John Wiley & Sons, Ltd. 119 56 120 57 121 58 Reading this paper and feeling the enthusiasm for the new possibilities of causal modelling with latent 122 59 causality reminds me of the time when I learned about variables. This enthusiasm has been alive ever since and still 123 60 SEM, back in 1979. After a workshop with Karl Jöreskog, motivates me working hard every day. Guess on what? 124 61 Dag Sörbom and Bengt Muthén, I felt very excited about Right, causality! So, welcome to the club, James! 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 Discussion 13 65 2 66 3 Soon after this first experience, I began asking the models, all of them are important tools and have the 67 4 following: What is the difference between an ordinary linear potential to describe causal dependencies. However, they are 68 5 regression model and a causal or structural equation model? no theories of causality. 69 6 In special cases, they look identical: linear function of the To repair this defect, Pearl’s ‘independent background 70 7 regressor; zero correlation between regressor and error term; factors’ need an explicit place in a theory of causal 71 8 and zero expectation of the error term. Asking all experts and effects. In the real world, they all too often act as con- 72 9 reading all books and papers on the topic, I found many founders, but up to date, they do not have an adequate 73 10 answers. Let me mention three of them. First, according to representation in the theory of DAGs. Therefore, they 74 11 Wold, the relationship described in a SEM ‘is then defined spook around as unsettled ghosts poisoning the discussions 75 12 as causal if it is theoretically permissible to regard the on statistics and causality (see, e. g. Bollen & Pearl, in 76 13 variables as involved in a fictive controlled experiment’ press; Pearl, 2009, p. 104). Q1077 14 (Wold, 1954, p. 166). Second, Goldberger wrote that the Suppose we are interested in the effect of a treatment 78 15 parameters in a SEM are ‘the fundamental parameters of variable X on an outcome variable Y and we assume 79 16 the mechanism that generated the data’ (Goldberger, 1973, stochastic independence between X and all pretreatment 80 17 p. 3). Third, many other econometricians argued that the variables, then it is this assumption that allows us to give a 81 18 error term is not a residual but a disturbance, consisting of causal interpretation of the regression of Y on X and of the 82 19 all other influences on the corresponding regressand not conditional distribution of Y on X. There is no need to 83 20 included in the model. Pearl’sdefinition of a causal effect include all pretreatment variables in a DAG; they are too 84 21 (Pearl, 2009, p. 70) rests on exactly this third answer. many, anyway. A DAG and the random variables constitut- 85 22 Although each of the three answers has an element of ing it have to be embedded in a probability space that 86 23 truth, I have never been happy with them. In the ideal case, represents the random experiment to be discussed. The 87 24 the randomised experiment guarantees that the effect pretreatment variables (potential confounders) refer to the 88 25 E(Y|X =1) E(Y|X = 0) of a dichotomous treatment variable same probability space and so do omitted mediators. If we en- 89 26 X (with values 0 and 1) on the outcome variable Y is the total dow the probability space with a filtration (a nondecreasing 90 27 causal treatment effect. But how does this help in identifying family of s-algebras), a fundamental concept in the theory of Q1191 28 a causal effect in a quasi-experiment in which, by definition, stochastic processes (see, e. g. Klenke, 2008), then we have 92 29 a unit is not randomly assigned to one of the treatment the mathematical prerequisites to order all our variables so that 93 30 conditions? And how does it help in identifying direct the term ‘pretreatment variable’ has a formal representation 94 31 treatment effects? (In the meantime, we know that randomisa- (see, e. g. Steyer, 1984, 1992) not resting on a concept of 95 32 tion does not guarantee that E(Y|X =1, M = m) E(Y|X =0, causality (which would be circular; this is the problem if we 96 33 M = m)isthe(M = m)-conditional direct treatment effect, use a DAG for such an ordering). Also, our distinction between 97 34 which questions all those applications of the Baron–Kenny covariates and intermediate variables or possible confounders 98 35 approach to mediation (Baron & Kenny, 1986), that only use and possible mediators will a have a mathematical foundation 99 36 the treatment, the mediator(s) and the outcome variable in the if based on the concept of a filtration. 100 37 SEM (see, e. g., Mayer, Thömmes, Rose, Steyer, & West, Applying a DAG requires specifying a complete causal 101 38 Q9 2012). In fact, the problem is the collider problem described model for all variables involved. Only then can we decide 102 39 by Lee.) The second answer is just a metaphor that helps if which variables may be omitted (see Lee’s discussion on 103 40 we generate data in a simulation. But what does it imply in colliders) and identify the causal effect of a variable X on a 104 41 real-life studies? Finally, the third answer is contradictory. variable Y. An important implication of the stochastic theory 105 42 Pearl’s own words are as follows: ‘These disturbance terms of causal effects outlined previously (see, e.g. Steyer, Mayer, 106 43 represent independent background factors that the investigator & Fiege, in press and Steyer, Fiege, & Mayer, in press) is 107 44 chooses not to include in the analysis’ (Pearl, 2009, p. 68). that it is applicable without complete knowledge about 108 45 What is it that I do not buy? the causal relations between variables that act in the 109 46 According to Pearl, ‘each child–parent family in a DAG random experiment considered. A gross ordering such as 110 47 G represents a deterministic function xi = fi (pai ,ei ), ....’ ‘prior to treatment’, ‘in between treatment and outcome’ 111 48 Hence, together with the pai, the disturbance ei and ‘posterior to treatment’ is often sufficient. 112 49 deterministically determines xi. The problem is that the Let me add a few remarks indicating where I disagree 113 50 deterministic equation xi = fi (pai ,ei ) can be true only if with Lee. If appropriately constructed, latent variables can 114 51 the ei also ‘represent’ (whatever this term may mean) all be considered causes of its manifest measures. This point 115 52 the mediators transmitting the effects of the pai to the xi. of view is also shared by Bollen and Pearl (in press), and it Q12116 53 Otherwise, xi = fi (pai ,ei ) cannot be true. However, mediators can be proven within the theory of stochastic causality 117 54 will correlate with the pai. (Just think of a perfect causal outlined previously. (Actually, I have much more problems 118 55 chain.) Hence, ei and pai cannot be independent. with causation among latent variables, at least if there is 119 56 Because Pearl’s do(x) terms and his definition of a not a clear time sequence between them, such as in a 120 57 causal effect rest on the disturbance term, both are longitudinal study.) In contrast to Lee et al. (2012) also do 121 58 contradictory as well. This is why I do not buy the claim that not claim that SEMs are inadequately formalised. Instead, 122 59 aDAGdefines causality, although they are an important tool they treat a SEM as a special sophisticated DAG, and I can 123 60 in the analysis of causal effects. Exactly the same applies to follow them in this respect. For the reasons mentioned 124 61 SEMs and to the general linear model (GLM). As statistical previously, I do not think that the graphical framework 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 14 Discussion 65 2 66 3 ‘captures human intuitions about causality in the form of A final caveat is as follows: neither DAGs nor SEMs or any 67 4 consistent mathematical axioms’.(‘Background factors’ is other statistical model are techniques for discerning causation 68 5 not a mathematically well-definedterm.)However,if in observational data. They only help to derive logical implica- 69 6 embedded in a stochastic theory of causality, DAGs are among tions of a model and test them, to some degree, against reality 70 7 the greatest achievements in the last 50 years. They can be very (see myth # 1 in Bollen & Pearl, in press). For the rest, let me Q13 71 8 useful, as can SEM, the GLM and hierarchical linear models. congratulate the author for this great and impressive paper. 72 9 73 10 74 11 Welcome Clarity for Muddy Waters 75 12 76 13 ALEXANDER WEISS AND TIMOTHY C. BATES 77 14 78 15 Department of Psychology, University of Edinburgh 79 16 80 17 [email protected] 81 18 82 19 Abstract: In his article, Lee advocates using directed acyclic graphs to test causal theory in differential psychology. We 83 20 applaud Lee’s efforts to introduce graph theory and causal hypotheses to differential psychology. We agree that these 84 21 methods lead to better understanding of the mechanisms’ underlying behaviour. We thus join him in advocating the use 85 22 of these methods that, although require more creative effort, honestly confront and overcome the problems of assigning 86 23 causality that can plague differential psychology and public policy research. Copyright © 2012 John Wiley & Sons, Ltd. 87 24 88 25 89 26 Testing causal hypotheses against observational data is Confidence in the progress of theory 90 27 central to progress in differential psychology and the social 91 28 sciences more generally. As noted by Lee, the lack of causal One important consequence of a logical framework for 92 29 progress in the social sciences flows not from a lack of contrasting causal hypotheses is that the crisis of confidence 93 30 statistical tools but rather from which tools are used and that found its expression in the postmodern proposition that 94 31 how. Lee’s most important message is that whereas social as social constructions, all theories have equivalent value is 95 32 scientists are taught that ‘correlation does not imply set aside. Although scientists still cannot know if they have 96 33 causation’, they are not taught what correlation does imply, found the truth simply by dint of applying DAGs, they can 97 34 namely an unresolved causal structure (Shipley, 2000). Lee determine which of two competing models is closer to that 98 35 lays out the requirements for causal research, namely how truth. If a mechanism exists to objectively and iteratively 99 36 causal hypotheses must be expressed as directed acyclic select causal models that are not simply different, but which 100 37 graphs (DAGs) or equivalent structures, and how theories are more complete in an objective sense, this may be the 101 38 thus expressed can then be objectively compared. biggest impact of all the changes that Lee’s paper lays out. 102 39 Since works such as Kerlinger’s(1964)‘Foundations 103 40 of Behavioral Research’, students have been trained to Theory generation 104 41 ‘control’ variables. This method has become embedded in the 105 42 paradigm of psychological science along with the assumption If statistical tools allow us to test causal hypotheses, 106 43 that control leads to conclusions. In fact, however, it has long they also highlight the requirement for researchers to 107 44 been recognised that inappropriate controls mischaracterise generate theories. Importantly, when a model finds itself 108 45 cause and effect (e.g. Meehl, 1992). In particular, apparently containing a correlation, as with rain and mud, one must 109 46 innocuous control of a variable that is influenced by traits ‘do(mud)’ and measure the effects or lack thereof of this 110 47 under study can induce false associations between these traits treatment on the likelihood of rain. We hope that this form 111 48 of interest, which, if interpreted as real, can have harmful conse- of expression spreads widely and that readers come to expect 112 49 quences (Bingham, Heywood, & White, 1991; Figueredo, articles to be expressed in this fashion, compelling research- 113 50 Hetherington, & Sechrest, 1992). Beyond this, statistical ers to make clear the causal process they are predicting, be it 114 51 control cannot, even in principle, test causal assumptions do(school) or do(genetic polymorphism) or do(neuroticism). 115 52 (Pearl, 2000). Knowledge about just how critically limited But what if they do not? One adverse consequence of not 116 53 epidemiological models are in identifying causes is far from translating causal theory into practice is that of targeting 117 54 widespread (Smith, 2010), and hopefully, Lee’s article will outcomes rather than processes leading to outcomes. For 118 55 spread this knowledge much further. The calculus of causal instance, targeting school grades instead of effective teaching 119 56 theory, in proving the consequences of lack of control and can have perverse consequences as factors not included in 120 57 inappropriate statistical control, as well as the solutions to these causal models come into play. These factors may include 121 58 problems, places causal theorising on a firm mathematical and teachers invalidating tests as indicators of knowledge by 122 59 logical footing. There simply can no longer be any place for teaching to the test or, worse, purchasing the answers to 123 60 theories not expressed, whether in words or figures, as DAGs exams (Vasagar, 2011). Lest other fields feel smug and 124 61 making these effects explicit. secure in their methods, such errors remain common in 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 Discussion 15 65 2 66 3 areas such as medicine that are more used by now to thinking - what in Lee’s terms would be long-form labels for the emer- 67 4 causally. Variables merely associated with a disease may gent property, or even as additional indicators. Lee’s concep- 68 5 become proposed targets for intervention, sometimes to tualisation thus refocuses our attention on the need to 69 6 humorous effect (Cohen et al., 2000). Such problems should hypothesise causes for latent variables, not simply generate 70 7 be expected in the study of any system that has multiple causes labels or additional indicators for them. Just as in physics, 71 8 (see the First Law of Ecology in Hardin, 1963). the emergent properties of water are accounted for by non- 72 9 wet, nonliquid causes, so too personality domains such as 73 10 What are common factors? extraversion must be accounted for by layers of mechanisms, 74 11 from biology through typical characteristics to the objective 75 12 We will finish with a discussion of Lee’s statement biography of behaviour (McCrae, 1996), rendering a set of 76 13 regarding common factors. Lee ‘allows a factor to play the objectively specified and parameterised mechanisms generat- 77 14 role of cause or effect in graphs depicting the relations ing behaviour on the fly as these systems are run in real 78 15 among high-level emergent entities.’ The meaning ascribed environments (Lewis & Bates, 2011). 79 16 to a common factor such as extraversion is basic to psychol- Causal hypothesising and testing is, of course, no ‘royal 80 17 ogy, and we appreciated the nuanced claim that a common road’ to knowledge: while the means of testing causal 81 18 factor may ‘play the role’ of a cause. Lee is, here as else- mechanisms are established, causal hypotheses cannot be 82 19 where, taking causal reasoning seriously. Latent variable on generated automatically. As Gödel (1962) demonstrated, 83 20 structural equations modelling diagrams represent emergent steps towards completeness require creative mental effort 84 21 properties of their indicators, but, like correlations, they also that is not automatable. The power of modern differential 85 22 represent as-yet unresolved causal structures and must be psychology, then, depends on specifying theory in directed 86 23 explained by mechanisms. In psychology, explanations of acyclic graphs permitting causal inference, and we commend 87 24 constructs such as in-group favouritism are often given in Lee’s article to as broad a readership as possible. 88 25 89 26 90 27 Author’s Response 91 28 92 29 93 30 Causes and Effects of Common Factors 94 31 JAMES J. LEE 95 32 96 33 97 34 Vision Lab, Department of Psychology, Harvard University Laboratory of Biological Modelling, NIDDK, NIH Cognitive Genomics Lab, 98 35 BGI-Shenzhen 99 36 [email protected] 100 37 101 38 Abstract: The comments endorse the usefulness of the graphical framework for causal reasoning in personality 102 39 psychology. Here, I address several recurring themes: (i) details of the graphical framework not explicitly addressed 103 40 in the target article; (ii) the importance of finding a fruitful level of explanation in personality psychology; (iii) the 104 41 problem of selection bias in empirical research; (iv) a difference in outlook between nomothetic and idiographic 105 42 approaches; and (v) whether the causal links between genetic and behavioural variation are indeed empirically tractable. 106 43 Copyright © 2012 John Wiley & Sons, Ltd. 107 44 108 45 109 46 I am pleased to find a reasonably firm consensus back-door theorem. Unfortunately, the statement of the 110 47 regarding the utility of the graphical framework for causal theorem by Kievit, Waldorp, Kan and Wicherts contains Q14 111 48 reasoning in personality psychology. I divide my response several errors and ambiguities. Their hypothesis (i) states that 112 49 to the comments into five parts, each addressing a recurring all direct causes of X must be statistically controlled to 113 50 theme. At times, I express pointed disagreement but in no identify the effect of X on Y. What the back-door theorem 114 51 way should this be taken as ingratitude toward the praise actually requires, however, is that the set of statistically 115 52 garnered by my modest contribution. controlled variables blocks every path between X and Y 116 53 containing an arrow into X. A member of the blocking set 117 54 Further details of the graphical framework thus need not be a direct cause of X. Moreover, if the path 118 55 is a colliding path, then the collider—even if it is a direct 119 56 Several comments touch upon further nuances of the cause of X—must not be a member of the set. Aspendorf 120 57 graphical framework, which I now take the opportunity and I stress that statistically controlling such a variable opens 121 58 to address. its path rather than blocking it. 122 59 The back-door rule. The target article reproduced a The necessity of Kievit et al.’s hypotheses (ii) and 123 60 theorem regarding the identification of linear causal effects (iii) turns on the distinction between linear and nonlinear 124 61 that can be regarded as a corollary of what Pearl calls the models. In the target article, I focused mostly on the linear 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 16 Discussion 65 2 66 3 formulation of important concepts for simplicity. However, Foundational issues. Steyer attacks the notion of a causal 67 4 because the issue of nonlinearity is not so far in the effect of X on Y as reflecting the sensitivity of Y to the 68 5 background of several comments, I will begin expanding randomisation of X, expressing dissatisfaction with its appar- 69 6 on it here. ent inapplicability in cases where X is not (or cannot) be 70 7 Kievit et al.’s hypothesis (ii), which states that the set of experimentally controlled. This objection, however, confuses 71 8 statistically controlled variables cannot include any descen- definitions and empirical operations. Imagining the thought 72 9 dant of X, is actually only a requirement for identifying a experiments implied by each directed edge in a DAG can 73 10 total effect encompassing all directed paths from X to Y.In sharpen our justifications for including certain arcs in a 74 11 a linear system, statistically controlling at least one mediator conjectural model and deciding what kind of arcs they should 75 12 along an indirect causal path—that is at least one descendant be. But this does not imply that sensitivity to actual or 76 13 of X—is necessary to estimate any partial effect. potential human manipulation defines causation. 77 14 The expression for the total effect in a nonlinear system 78 Surely we have causation without manipulation. The 15 is enlightening. If Zd-separates all nondirected paths 79 moon causes tides, race causes discrimination, and sex 16 between X and Y, then the expected value of Y upon setting 80 causes the secretion of certain hormones and not others. 17 X equal to x is 81 1 Nature is a society of mechanisms that relentlessly sense 18 82 À the values of some variables and determine the values of 19 E Yj doðÞ x Þ¼∬ypð yj x ; zÞpzðÞdz dy 83 1 1 others; it does not wait for a human manipulator before 20 84 activating those mechanisms. (Pearl, 2009, p. 361) 21 where p() is the appropriate probability density. The form 85 22 of this expression tells us that we must average over all Steyer’s more specific point regarding indirect or condi- 86 23 possible values of Z; picking just one value may lead to a tional causal effects misses the mark for the same reason. 87 24 ‘stratum-specific’ estimate. In other words, the identified For instance, in a randomised experiment examining the 88 25 total effect is an average causal effect over the studied pop- effect of sleep deprivation on state anxiety, the average 89 26 ulation; a treatment that helps one patient may harm another. causal effect of the treatment may be identified, whereas 90 27 This observation leads to a succinct characterisation of more specific causal effects may not. For example, it may 91 28 linearity: in a linear causal system, the expected change in not be possible to identify how the treatment affected a 92 29 Y for a given magnitude of the experimental change in X does particular person (Kievit et al.; Borsboom et al.). A do Q15 93 30 not depend on ‘where we are’. That is, the expected change operation on the appropriate directed acyclic graph (DAG), 94 31 does not depend on the specific values of X, Z or any other however, mathematically defines this effect regardless of 95 32 variable. In particular, it does not depend on the specific whether the DAG’s structure permits particular ‘real-life 96 33 person to whom the manipulation is applied. studies’ to know what this effect is. In fact, much DAG 97 34 In a linear system with disturbances, it should be clear theory is devoted to precisely these concerns (Pearl). 98 35 that Kievit et al.’s hypothesis (iii), which states that the joint Steyer (along with Jackson and Spain) accuses the 99 36 probability density is almost everywhere positive, is indeed graphical framework of conflating the disturbance term in a 100 37 satisfied. Even in the nonlinear case, one should drop the causal equation with the error term in a least-squares 101 38 ‘almost’ to make (iii) a true sufficient condition because a regression. It is a geometric fact of least squares that the error 102 39 well-chosen set of measure zero with no probability density term must be uncorrelated with the predictor. Because it 103 40 can prevent the identification of certain causal quantities. cannot be true in general that the measured causes of a 104 41 There are other means besides the back-door rule for certain effect are independent of its unmeasured causes, 105 42 determining whether a given set of assumptions identifies a Steyer believes that he has undermined Pearl’s arguments 106 43 (nonlinear) causal effect. Pearl has devised a more general for the depth and essentiality of his approach. But on the 107 44 calculus for his do symbol that allows us to determine very page from which Steyer quotes, Pearl clearly allows a 108 45 whether there is a sequence of transformations eliminating semi-Markovian DAG to include correlated disturbances. If 109 46 all occurrences of do from a given statement. The this were not the case, the various theorems giving the 110 47 transformed statement, which contains only instances of circumstances under which a causal equation is a regression 111 48 see, provides an equivalent expression for the desired causal would often have a rather trivial flavour. 112 49 quantity that can be estimated from observational data. Steyer (1984) claims to offer an alternative account of 113 50 Hypothesis-free search versus hypothesis testing. causality based on probability theory. Unfortunately, I find 114 51 Kievit et al.’s concern over the number of partial correlations this account to be quite obscure. For example, Steyer’s 115 52 (conditional independencies) confuses the testing of a priori condition for the identification of a causal effect strikes me 116 53 causal models with a model-free evaluation of all possible as the very definition of a conditional expectation. Instead 117 54 partial correlations. For various reasons, I will not address of dwelling on details, I will offer some reactions based on 118 55 the latter approach. first principles. 119 56 Although inevitably sounding pedantic, I must point Pearl has convinced me that probability theory is 120 57 out that Kievit et al.’s combinatorial calculation for a five- inherently incapable of representing causal notions. One of 121 58 node graph is erroneous. 5!/(3!2!) is equal to 10, not 20. my statistics instructors once defined his subject as the 122 59 And for any given pair of variables, the number of possible use of finite data to infer the parameters of probability 123 60 partial correlations (including the zero-order correlation) is distributions; taking this notion seriously, suppose that the 124 61 eight, not six. sample size is so large that we can estimate the parameters 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 Discussion 17 65 2 66 3 of the relevant probability distribution with perfect accuracy. importance of causal notions does not diminish when we 67 4 We thus have in our hands error-free estimates of means, turn our attention from a large cross-section of a population 68 5 variances, higher moments, correlations, odds ratios, at a single time point to a small number of individuals 69 6 principal components, propensity scores, Granger-‘causality’ across many time points. Note that each directed edge in 70 7 coefficients and so on. Have we gone any way toward Cramer et al.’s (this issue) Figure 5 represents temporal order Q1771 8 understanding the causal mechanisms generating the data? rather than a cause–effect relation. To make the leap from 72 9 One could fairly reply, not yet. To say something about the these lagged correlations to cause and effect, we need to 73 10 causal process inducing the obtained distribution, we must invoke randomisation, instruments, confounding, selection 74 11 invoke assumptions about matters that are inherently nonsta- bias or other members of the conceptual family surrounding 75 12 tistical: randomisation, confounding, selection and so forth. d-separation. 76 13 I take issue with Borsboom et al.’s claim that empirical 77 Take the concept of randomisation—why is it not statistical? 14 application of graphical theories ‘has not been very success- 78 Assume that we are given a bivariate density function f(x, y) 15 ful to date’. This misconception may be based on artificially 79 and that we are told that one of the variables is randomised, 16 restricting the content of the graphical framework to narrow 80 can we tell which one it is by just examining f(x, y)? Of 17 applications such as causal search algorithms. 81 course not; therefore, following our definition, randomisa- 18 It should be re-emphasised that possessing a clear and 82 tion is a causal, not a statistical concept ....Note, however, 19 formal notion of causation does not necessarily enable us to 83 that the purpose of the causal–statistical demarcation 20 discover the causal structure of any particular system. The 84 line ...is not to exclude causal concepts from the province 21 situation is analogous to the failure of formal logic to resolve 85 of statistical analysis but, rather, to encourage investigators 22 certain philosophical disputes (Gensler, 2002). If the validity 86 to treat causal concepts distinctly, with the proper set of 23 of the premises is in doubt, then we cannot draw any firm 87 mathematical and inferential tools. Indeed, statisticians 24 conclusions. But such failures are no reason to denigrate 88 were the first to conceive of randomised experiments and 25 logic. The logic of causality is no different in this respect. 89 have used them successfully since the time of Fisher 26 Likewise, if any conclusions are warranted at all, their 90 (1926). However, both the assumptions and conclusions in 27 warrant must rest on both the requisite premises and the 91 those studies were kept implicit, in the mind of ingenious 28 appropriate governing logic. Causal conclusions are again 92 investigators; they did not make their way into the mathe- 29 no different. 93 matics. For example, one would be extremely hard pressed 30 For instance, how do we know that smoking causes 94 to find a statistics textbook, even at the graduate level, 31 death? Davey Smith cites some new evidence on this point, 95 containing a mathematical proof that randomisation indeed 32 but let us examine a more established element of the 96 produces unbiased estimates of [causal] quantities .... 33 ‘nomological net’ (Jackson & Spain). Strong evidence 97 (Pearl, 2009, p. 332) 34 against Fisher’s hypothesis that certain genotypes cause 98 35 These considerations leave me sceptical of attempts to both disease and a personality disposed to smoking comes 99 36 build a formal account of causality on purely probabilistic from studies of smoking-discordant monozygotic twins 100 37 grounds. in which the smoker tended to die first (Kaprio & 101 38 The foundational importance and distinctiveness of Koskenvuo, 1989; Carmelli & Page, 1996). Now why is this 102 39 causal notions implies that the graphical framework (or a strong evidence? Letting G stand for genotype, we have the 103 40 mathematical equivalent) is always employed, at least expected value 104 41 implicitly, whenever causal inferences are drawn. Jackson 105 ð ; j ¼ Þ¼ ð ; j ðÞ¼ Þ; 42 and Spain present instruments and propensity scores as EG death smoking G g EG death smoking see G g 106 43 alternatives to the graphical approach, but in fact, the 107 but wish to infer 44 graphical approach subsumes both of these concepts. Pearl’s 108 45 (2009) treatments of instruments and propensity scores may 109 EGðdeath; smokingj doðÞ G ¼ g Þ: 46 be the most lucid that I have seen anywhere in the literature. 110 47 Although I am more cautious than Davey Smith, I am on the 111 48 whole sympathetic toward his use of genetic variants as This substitution is legitimate because it was nature 112 49 instruments and foresee the fruitfulness of this approach in that fixed the genome to be identical for both members of a 113 50 the investigation of whether the biological correlates of a twinship. That is, because the same chain of events produced 114 51 certain personality trait are indeed causes of that trait. the genotype of each twin, the nodes in the causally prior 115 52 I share the reservations of Kievit et al., Borsboom et al., subgraph have no variation that can be transmitted to 116 53 Q16 Jackson and Spain and Davey Smith regarding cross- smoking and death; therefore, by Rule 2 of Pearl’s do 117 54 sectional studies of high-level variables that do not calculus, we can safely delete all directed edges converging 118 55 incorporate some special feature (families, genetics, natural on G. This is quite unlike matching by propensity scores, 119 56 randomisation). Longitudinal tracking of individuals should say, where individuals in the same stratum are merely 120 57 be added to this repertoire. In fact, one reason why the target observed to have the same value of the propensity score 121 58 article did not treat cyclic models is that I join Shipley (2000) (a function of the matching variables). Further assumptions 122 59 in suspecting that a cyclic model can usually be reduced to an regarding the causal processes outputting the matching 123 60 acyclic or block-acyclic model by sufficiently fine-grained variables, such as the applicability of the back-door rule, 124 61 distinctions among time points within individuals. But the must be justified before the see in the latter case can be 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 18 Discussion 65 2 66 3 replaced with do. Even if all this is already intuitively clear to quotation of the theoretical physicist David Deutsch. The 67 4 some, the rest of us can only profit from the explication and question that seems to trouble the commentators, then, is 68 5 systematisation of ad hoc intuition. whether common factors (imperfectly measured folk-psycho- 69 6 How do Borsboom et al. and Johnson explain the success logical traits) are useful high-level ‘cartographic’ features to 70 7 of genome-wide association studies (GWAS)? Given the rep- have singled out from the teeming landscape of individual 71 8 lication of GWAS results across nations and racial groups— differences (Condon, Brown-Ridell, Wilt, & Revelle). Meehl Q18 72 9 and, most importantly, within families—it has become clear (1978) admittedly regarded this task of parsing ‘continuous 73 10 that the ‘batting average’ of causal inference with this streams of observable behaviour into chunks that can be 74 11 technique is well above .500. This success rate should make reasonably well measured and organized’ as an open problem 75 12 GWAS the envy of other biomedical and behavioural rather than a fait accompli of psychological science. 76 13 scientists who must deal with observational data. We are thus Condon et al. believe that the target article provides no 77 14 entitled to ask: what special features of GWAS make causal ‘metric’ for evaluating proposed solutions to this problem. 78 15 inference, if not infallible, at least feasible? My own attempt It seems to me that no satisfactory metric of this kind has 79 16 to provide an answer is of course a post hoc explanation been proposed in any scientific discipline where the problem 80 17 rather than an a priori justification by the investigators of ‘murdering to dissect’ has arisen (Wagner, 2001; Blows, 81 18 themselves, but the timestamp on the argument is irrelevant 2007), and for now, the evaluation of ‘construct validity’ 82 19 to the basic principle that specifying the DAG containing remains one of the case-by-case, nonautomatable aspects of 83 20 the putative cause and effect, arguing for its validity and behavioural science to which Weiss and Bates refer. I will 84 21 demonstrating the identification of the desired quantity are point out, however, that the successful embedding of a 85 22 essential to the justification of any empirical study claiming common factor in a causal model has long been thought to 86 23 to advance our causal knowledge. support its validity (Cronbach & Meehl, 1955; Messick, 87 24 This is why it is misguided to dwell on ‘the difficulty of 1989). Now, it is quite plausible that the low-level causes 88 25 explicating all assumptions about which variables are of behavioural variation are arranged in a complex cyclic 89 26 measured, their causal relations and the possibility of graph (van der Maas et al., 2006). But can we reasonably 90 27 co-occurring events when applying graphical modeling’ approximate this situation with a block-acyclic graph, 91 28 (Kievit et al.), when in fact there is no nongraphical containing d-separable nodes, in which the common factor 92 29 alternative that avoids these challenges. As Pearl (2009), plays the role of a cause or effect? If so, this suggests that 93 30 pp. 173–200) shows in his tour de force treatment of we have indeed carved out a useful high-level attribute of 94 31 Simpson’s paradox, alternative frameworks do not provide the respondents. There is a suggestion of the relation between 95 32 any insight into issues such as sign reversals across levels statistical mechanics and thermodynamics, although this 96 33 of aggregation and frequently aggravate confusion. analogy should not be carried too far. 97 34 I anticipate that basic graphical notions (such as the I will add one more thought to emphasise the likely 98 35 distinction between see and do) will strike future scientists idiosyncratic nature of trait validation. By adding up 99 36 as no more distinctively ‘Pearlian’ than basic statistical randomly chosen questionnaire items and anthropometric 100 37 notions (such as the distinction between an estimate and a measurements, one can put together a wholly arbitrary and 101 38 parameter) strike us nowadays as distinctively ‘Fisherian’. trivial phenotype. In fact, many off-hand criticisms of IQ 102 39 These ideas will have become so ingrained that to attribute tests have levelled this charge of aggregating an atheoretical 103 40 them to Pearl will seem akin to attributing ‘the invention of hodgepodge. Because such a Borgesian construct will be 104 41 the wheel to Mr. So-and-So’ (Savage, 1976, p. 450). heritable if any of its summands are heritable (Johnson 105 42 et al., 2011), a sufficiently well-powered GWAS will 106 43 Common factors and levels of analysis certainly find genetic variants affecting it. The upshot is that 107 44 successful gene-trait mapping studies are not enough to 108 • Justice Antonin Scalia has the intellect to be a leader of 45 ensure that we have measured a useful trait. But what if such 109 the United States Supreme Court’s conservative wing, 46 results indicate a disproportionate clustering of causal 110 but his surly temperament has prevented him from 47 variants in particular biological pathways (Lee et al., 111 assuming this mantle. 48 2012)? Furthermore, given recent advances in the sequenc- 112 49 The graphical framework now provides tools to reason ing of ancient DNA (Rasmussen et al., 2010; Green et al., 113 50 precisely about previously difficult concepts such as 2010; Reich et al., 2010; Keller et al., 2012) and the 114 51 necessity, sufficiency and prevention that are inherent in this prediction of additive genetic values (Goddard, 2009; Yang, 115 52 statement (Pearl). Remarkably, it now seems that the Lee, Goddard, & Visscher, 2011), we may conceivably be 116 53 invocation of attributes such as intellect, conservatism able to estimate the level of g that an ancient hominin would 117 54 and surliness is the more controversial issue. Even as I have obtained if reared in a modern society. What would 118 55 maintain that factor analysis is an attempt to quantify folk- we make of a finding that a Neandertal individual had a 119 56 psychological attributes of this kind, others continue to level of g three standard units below the current mean? 120 57 question the usefulness of this enterprise (Borsboom et al.). Although this thought experiment regarding biological 121 58 It seems that at least certain high-level traits can be significance does not seem to illustrate any algorithmic 122 59 scientifically useful, either as placeholders in the course of principle of construct validation, it suggests that uses of 123 60 reductionistic research or as fundamental entities in their own common factors may not necessarily be limited to verifica- 124 61 right. This was a point that I tried to convey with my long tions of what many regard to be common sense (perhaps 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 Discussion 19 65 2 66 3 mistakenly). Followers of American politics need no scientific environments (countries differing in climate and infrastruc- 67 4 formality to believe that the statement regarding Justice Scalia ture) and nonlinearity (causal effects depending on ‘where 68 5 is probably true. Some might say that intelligence tending to we are’), perhaps the target article should have discussed 69 6 promote liberalism is also obvious; left-liberals and libertarians these matters in more detail. It seems to me, however, that 70 7 alike often claim that their views are compelled by reason. A a more fundamental issue divides us. 71 8 glib naysayer might dismiss the entire literature on construct Suppose that we could manipulate Antonin Scalia’s level 72 9 validity as the demonstration of correlations with external of g at the age of 11 so as to place him even further in the 73 10 variables that common sense already tells us to be correlated right tail of his cohort’s ability distribution. (Recalling the 74 11 with the target attribute. The kinds of biological insights that example of sprinting ability, we can be fairly confident that 75 12 might follow from genetic research, however, are certainly there is no single physical ‘thing in the head’ to be altered 76 13 no matters of common sense. to bring about this change.) We then wait until he has 77 14 reached 30 years of age before asking him to fill out a 78 15 The problem of selection bias questionnaire regarding his social and political views. Will 79 16 this counterfactual Scalia be less conservative than the actual 80 17 I agree with Aspendorf that selection bias is a taboo subject Scalia? Perhaps. But it also seems reasonable to suppose the 81 18 among behavioural scientists. It was perhaps selection bias, contrary. Scalia’s increased g may allow him to rationalise 82 19 more than any other topic, that provoked colleagues who positions that he holds for nonintellectual reasons and find 83 20 read an early draft of the target article to criticise it as the holes in the arguments of his liberal opponents. Kievit 84 21 ‘negative,’‘destructive’ and ‘pessimistic.’ et al. and Borsboom et al. express an intense interest in these 85 22 Jackson and Spain do not distinguish selection bias from kinds of idiosyncratic dynamics; they want to know why a 86 23 confounding. Figure 1 hopefully clarifies the difference. particular person is the way that he is. 87 24 Refraining from any assumptions about the graph containing I concede that linear models, which aim to approximate 88 25 X and Y, we must allow unknown confounders to affect these average causal effects (see my earlier discussion of the back- 89 26 variables and selection into the study to be affected by them door rule), are idealised simplifications that may distort the 90 27 in turn. Assuming that a specific random mechanism affects dynamics of an individual personality over the lifespan. One 91 28 X would suffice to identify any X ! Y causal effect in the argument for the primacy of an idiographic orientation is that 92 29 absence of selection bias. If selection bias is in fact present, an average causal effect in a given population seems to lack 93 30 more assumptions are necessary regarding the d-separation the invariance property one might expect from a useful law- 94 31 of all paths between X and Y passing through study like generalisation. As the composition and environment of 95 32 appearance. Bareinboim and Pearl () study this issue in the population changes, perhaps under the influence of the very 96 33 detail. One sufficient assumption is that whether a participant causal system under consideration, the average causal effect 97 34 appears in the study is also determined by a random mecha- will change and conceivably even switch sign. 98 35 nism. A random sample of individuals who are currently But there is a compelling argument for the other 99 36 accessible will satisfy this assumption in some cases. side. Ronald Fisher was well aware that the same allelic 100 37 However, if death, disability or the like has removed certain substitution may bring about different phenotypic effects in 101 38 individuals from the pool of potential participants, then even different individuals. This might happen, for example, 102 39 random sampling from the remainder may not be enough. because of differences between two people at other loci 103 40 This difficulty admittedly complicates studies of ageing. affecting the trait (Johnson). Nevertheless, Fisher thought 104 41 Figure 1 suggests a succinct formulation of confounding that the best linear predictions of genotypic values were more 105 42 and selection bias: confounding is any contribution to the fundamental than actual genotypic values—so much so that 106 43 association between putative cause (X) and effect (Y) that he called the former true genetic values and conceived of 107 44 can be removed by randomisation of X, whereas selection the discrepancies as substantively unimportant errors (Fisher, 108 45 bias is any contribution that can be removed by randomisa- 1918, 1999). In other words, Fisher was already retreating 109 46 tion of appearance in the study. from the ideal of deterministic (‘mechanistic’) prediction 110 47 I join Aspendorf in calling for empirical reports to discuss mentioned by Condon. It is not clear that anyone has fully 111 48 whether selection bias might unduly affect the results. We understood Fisher’s reasoning on these matters, but one 112 49 seem to be in full agreement that the graphical framework’s important motivation for his view seems to have been the 113 50 highlighting of selection bias should not be construed as fact that the number of possible genotypes greatly exceeds 114 51 a negative contribution; any and all insights into the the number of allele frequencies on which they depend 115 52 roadblocks on the way to causal knowledge are welcome. I (Fisher, 1941). For L causal loci, there are 3L multilocus 116 53 will paraphrase John F. Kennedy: ‘We do not do science genotypes. If L is equal to 23—one trait-affecting locus per 117 54 because it is easy; we do it because it is hard.’ chromosome—the number of possible genotypes already 118 55 exceeds the current size of the human population by more 119 56 Nomothetic and idiographic orientations than 10-fold. It is now apparent that traits such as g and 120 57 schizophrenia are affected by thousands of loci, which means 121 58 Kievit et al. and Borsboom et al. take me to task for failing that the number of possible genotypes dwarfs the number of 122 59 to distinguish between within-person causal effects and protons in the observable universe. These calculations 123 60 across-person correlations. Although the graphical frame- harbour some surprising consequences. For instance, a 124 61 work does in fact encompass transportability across genotype that is relatively probable, in the sense that its 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 20 Discussion 65 2 66 3 constituent alleles are common in the population, will often There seems to be little point in rehashing the target 67 4 fail to have a single exemplar. article’s arguments in the face of such innuendos. Instead, I 68 5 Given the enormous difficulty facing any attempt to will reiterate my deepening conviction that there is indeed a 69 6 elucidate the complete nonlinear genotype–phenotype special connection between genetics and the notion of cau- 70 7 mapping, the nomothetic bias inherent in the theoretical sality. Long before Darwin, biologists had already 71 8 importance that Fisher attached to the average effect of an marvelled at the exquisite adaptation of organisms to 72 9 allelic substitution poses some obvious advantages in their natural environments. To capture what we mean by 73 10 practicality and economy of thought. Moreover, whether adaptation a little more precisely, we can conceive of an 74 11 the average effects suffer from a lack of invariance is not organism’s actual mean phenotype as a point in a high- 75 12 an all-or-nothing matter; both the relative magnitude of the dimensional space and the optimal phenotype given the 76 13 additive genetic variance and the transportability of genetic organism’s environment as another point in this same space 77 14 findings across populations provide checks on the degree to (Fisher, 1999). In this conception, adaptation is a high 78 15 which the average effects tend to be ‘slowly varying correlation between the coordinates of these two points. 79 16 functions’ of the causal background. Thus, in the context of Now, recall the graphical taxonomy of correlations, which 80 17 genetic research at least, a nomothetic orientation has a states that a noncoincidental correlation between X 81 18 sound rationale backed by an impressive and mounting (phenotype) and Y (environment) must be attributable to 82 19 record of empirical success. 83 I. X causing Y, 20 Kievit et al. and Borsboom et al. contemplate longitudi- 84 II. Y causing X, 21 nal studies where the putative causes, unlike genotypes, 85 III. X and Y being effects of a common cause or 22 show variation within individuals across time. It is not 86 IV. X and Y being causes of a common effect that has been 23 clear to me that this approach avoids any problems of 87 statistically controlled. 24 combinatorial explosion or high dimensionality. Even if 88 25 we have enough replications over time to establish that a To explain biological adaptation, pre-Darwinians often 89 26 certain person consistently avoids joining stampedes out invoked explanation (3), ascribing the role of common cause 90 27 of allegedly burning theatres, the question remains as to to a benevolent Creator. After Darwin and Mendel, many 91 28 why some people flee and others freeze. By raising these biologists favoured explanation (2), invoking hypothetical 92 29 issues, however, I do not mean to imply that the mere mechanisms by which environmental circumstances might 93 30 presence of difficulties should deter this ambitious and mould the causes of phenotypic variation. Weismann 94 31 worthwhile research programme. In recent years, we (1893) gave reasons for rejecting Lamarckianism and other 95 32 have perhaps neglected Allport’s (1937) vision of an all- explanations within this class that remain cogent today. 96 33 encompassing personality psychology, unduly emphasising Explanation (1), in which organisms seek out or create 97 34 the nomothetic over the idiographic. We should not lose environments promoting their own fitness, obviously cannot 98 35 contact with either approach. suffice because such niche-seeking capacities are themselves 99 36 complex adaptations. It was the genius of Darwin to 100 37 Causal inference in gene-trait association studies realise the power of explanation (4): phenotypes and 101 38 environments cohere in such an uncanny way because nature 102 39 I regrettably do not understand Johnson’s argument. Does is a statistician who has allowed only a subset of the logically 103 40 she claim that most GWAS results from studies of unrelated possible combinations to persist over time. 104 41 individuals are false positives? Does she deny that family Although phenotypes are what nature selects, it cannot 105 42 studies whose causal assumptions invoke only Mendel’s be phenotypes alone that preserve the record of natural 106 43 laws are immune to confounding? Her reference to gene selection. Phenotypes typically lack the property that 107 44 expression is puzzling because detailed studies of gene variations in them are replicated with high fidelity across 108 45 expression have been used to follow up mapping studies, an indefinite number of generations. DNA, however, does 109 46 tracing the intermediate mechanisms between genotype and have this property—hence the memorable phrase ‘the 110 47 phenotype (Pomerantz et al., 2009; Musunuru et al., 2010; immortal replicator’ (Dawkins, 1976). If DNA is further- 111 48 Visser, Kayser, & Palstra, 2012). I believe that Johnson more causally efficacious, such that the possession of one 112 49 unintentionally reveals the disciplinary value in supplement- variant rather than another has phenotypic consequences 113 50 ing verbal arguments with graphical ones. Naturally, I that are reasonably robust, then we have the potential for 114 51 disagree that the transparency of the graphical framework natural selection to bring about a lasting correlation 115 52 ‘lies completely in the hands of the researcher’. The ease between environmental demands and the causes of adapta- 116 53 with which depicted DAGs stimulate the proclivity of tion to those very same demands. 117 54 scientists to evoke alternative causal scenarios is one of the When statistically controlling fitness, nature does not 118 55 graphical framework’s attractive features. actually use the average effect of any allele. If an allele 119 56 With the phrase ‘ultimate causality’, Johnson seems to has a positive average excess in fitness, for any reason 120 57 mock the target article’s emphasis on genetics. She believes whatsoever, it will tend to displace its alternatives. 121 58 that the fallacy of pointing to genetics—of all things—as a Nevertheless, it seems to be the case that nature correctly 122 59 clean system for the isolation of cause and effect is so obvious picks out alleles for their effects often enough; the results are 123 60 that she sees no need to accompany it with any detailed evident in the living world all around us. Davey Smith and 124 61 argument or even a bare mention of specific genetic phenomena. I are confident. Copyright © 2012 John Wiley & Sons, Ltd. 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 1 Discussion 21 65 2 66 3 REFERENCES exposure. Journal of the National Cancer Institute. 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Q30 30 94 31 95 32 96 33 97 34 98 35 99 36 100 37 101 38 102 39 103 40 104 41 105 42 106 43 107 44 108 45 109 46 110 47 111 48 112 49 113 50 114 51 115 52 116 53 117 54 118 55 119 56 120 57 121 58 122 59 123 60 124 61 125 62 126 63 Copyright © 2012 John Wiley & Sons, Ltd. Eur. J. Pers. (2012) 127 64 DOI: 10.1002/per 128 Author Query Form

Journal: European Journal of Personality Article: per_1865

Dear Author,

During the copyediting of your paper, the following queries arose. Please respond to these by annotating your proofs with the necessary changes/additions. • If you intend to annotate your proof electronically, please refer to the E-annotation guidelines. • If you intend to annotate your proof by means of hard-copy mark-up, please refer to the proof mark-up symbols guidelines. If manually writing corrections on your proof and returning it by fax, do not write too close to the edge of the paper. Please re- member that illegible mark-ups may delay publication. Whether you opt for hard-copy or electronic annotation of your proofs, we recommend that you provide additional clarification of answers to queries by entering your answers on the query sheet, in addition to the text mark-up.

Query No. Query Remark

Q1 AUTHOR: For ‘Lee (2012)’, do you mean ‘Lee, DeCandia, Ripke, and Yang (2012)’? Please check. If not, please provide complete reference details for ‘Lee (2012)’. Q2 AUTHOR: ’Unlike the examples made of height, hair morphology and Parkinson’s’.Do you mean ’Unlike the examples made of height, hair morphology and Parkinson’s disease’? Please check. Q3 AUTHOR: The reference citation ‘Davey Smith, Lawlor, Harbord, Timpson, Ebrahim, 2008’ has been changed to ‘Davey Smith et al., 2008’ because ‘Day, I.’ is included in the reference list. Please check this change and confirm that it is correct. Q4 AUTHOR: ‘Supplementary Table 4’ is cited in the text but is not provided. Please check. Q5 AUTHOR: Superscript number ’6’ has been deleted because no footnote is given. Please check. Q6 AUTHOR: “Almund et al., 2011” is cited in text but not given in the reference list. Please provide details in the list or delete the citation from the text. Q7 AUTHOR: “Rubin, 1980; 1991” is cited in text but not given in the reference list. Please provide details in the list or delete the citation from the text. Q8 AUTHOR: “Jackson et al., 2012” is cited in text but not given in the reference list. Please provide details in the list or delete the citation from the text. Q9 AUTHOR: The citation “Mayer, Thoemmes, Rose, Steyer, 2012” (original) has been changed to “Mayer, Thömmes, Rose, Steyer and West, 2012”. Please check if appropriate. Q10 AUTHOR: The citation “Bollen & Pearl, 2012” (original) has been changed to “Bollen & Pearl, in press”. Please check if appropriate. Q11 AUTHOR: Please check used symbol if correct. Q12 AUTHOR: The citation “Bollen and Pearl (2012)” (original) has been changed to “Bollen and Pearl (in press)”. Please check if appropriate. Q13 AUTHOR: The citation “Bollen & Pearl, 2012” (original) has been changed to “Bollen & Pearl, in press”. Please check if appropriate. Q14 AUTHOR: “Kievit, Waldorp, Kan and Wicherts” is cited in text but not given in the reference list. Please provide details in the list or delete the citation from the text. Query No. Query Remark

Q15 AUTHOR: “Borsboom et al” is cited in text but not given in the reference list. Please provide details in the list or delete the citation from the text. Q16 AUTHOR: “Jackson and Spain” is cited in text but not given in the reference list. Please provide details in the list or delete the citation from the text. Q17 AUTHOR: “Cramer et al.” is cited in text but not given in the reference list. Please provide details in the list or delete the citation from the text. Q18 AUTHOR: “Condon, Brown-Ridell, Wilt, & Revelle” is cited in text but not given in the reference list. Please provide details in the list or delete the citation from the text. Q19 Reference “Davey Smith (2012)” has not cited in the text. Please indicate where it should be cited; or delete from the reference list. Q20 AUTHOR: If a reference has more than 8 authors, retain the six author names followed by ellipsis and not “et al” then the last author. Please check. Q21 Reference “Jackson et al. (in press)” has not cited in the text. Please indicate where it should be cited; or delete from the reference list. Q22 AUTHOR: If a reference has more than 8 authors, retain the six author names followed by ellipsis and not “et al” then the last author. Please check. Q23 AUTHOR: If this reference has now been published in print, please add relevant volume/ issue/page and year information. Q24 AUTHOR: If a reference has more than 8 authors, retain the six author names followed by ellipsis and not “et al” then the last author. Please check. Q25 AUTHOR: If a reference has more than 8 authors, retain the six author names followed by ellipsis and not “et al” then the last author. Please check. Q26 AUTHOR: If a reference has more than 8 authors, retain the six author names followed by ellipsis and not “et al” then the last author. Please check. Q27 AUTHOR: If this reference has now been published in print, please add relevant volume/ issue/page and year information. Q28 AUTHOR: Please provide city location of publisher for this reference. Q29 AUTHOR: If a reference has more than 8 authors, retain the six author names followed by ellipsis and not “et al” then the last author. Please check. Q30 AUTHOR: If a reference has more than 8 authors, retain the six author names followed by ellipsis and not “et al” then the last author. Please check.

USING e-ANNOTATION TOOLS FOR ELECTRONIC PROOF CORRECTION

Required software to e-Annotate PDFs: Adobe Acrobat Professional or Adobe Reader (version 8.0 or above). (Note that this document uses screenshots from Adobe Reader X) The latest version of Acrobat Reader can be downloaded for free at: http://get.adobe.com/reader/

Once you have Acrobat Reader open on your computer, click on the Comment tab at the right of the toolbar:

This will open up a panel down the right side of the document. The majority of tools you will use for annotating your proof will be in the Annotations section, pictured opposite. We’ve picked out some of these tools below:

1. Replace (Ins) Tool – for replacing text. 2. Strikethrough (Del) Tool – for deleting text.

Strikes a line through text and opens up a text Strikes a red line through text that is to be

box where replacement text can be entered. deleted.

How to use it How to use it  Highlight a word or sentence.  Highlight a word or sentence.  Click on the Replace (Ins) icon in the Annotations  Click on the Strikethrough (Del) icon in the section. Annotations section.  Type the replacement text into the blue box that appears.

3. Add note to text Tool – for highlighting a section 4. Add sticky note Tool – for making notes at to be changed to bold or italic. specific points in the text.

Highlights text in yellow and opens up a text Marks a point in the proof where a comment box where comments can be entered. needs to be highlighted.

How to use it How to use it

 Highlight the relevant section of text.  Click on the Add sticky note icon in the

 Click on the Add note to text icon in the Annotations section.

Annotations section.  Click at the point in the proof where the comment

 Type instruction on what should be changed should be inserted. regarding the text into the yellow box that  Type the comment into the yellow box that appears. appears.

USING e-ANNOTATION TOOLS FOR ELECTRONIC PROOF CORRECTION

5. Attach File Tool – for inserting large amounts of 6. Add stamp Tool – for approving a proof if no

text or replacement figures. corrections are required.

Inserts an icon linking to the attached file in the Inserts a selected stamp onto an appropriate

appropriate pace in the text. place in the proof.

How to use it How to use it  Click on the Attach File icon in the Annotations  Click on the Add stamp icon in the Annotations section. section.  Click on the proof to where you’d like the attached  Select the stamp you want to use. (The Approved file to be linked. stamp is usually available directly in the menu that appears).  Select the file to be attached from your computer or network.  Click on the proof where you’d like the stamp to

 Select the colour and type of icon that will appear appear. (Where a proof is to be approved as it is,

in the proof. Click OK. this would normally be on the first page).

7. Drawing Markups Tools – for drawing shapes, lines and freeform

annotations on proofs and commenting on these marks.

Allows shapes, lines and freeform annotations to be drawn on proofs and for comment to be made on these marks..

How to use it

 Click on one of the shapes in the Drawing

Markups section.

 Click on the proof at the relevant point and draw the selected shape with the cursor.

 To add a comment to the drawn shape,

move the cursor over the shape until an

arrowhead appears.

 Double click on the shape and type any

text in the red box that appears.

For further information on how to annotate proofs, click on the Help menu to reveal a list of further options: