New and Emerging Models of Human Intelligence Andrew R

Overview New and emerging models of human intelligence Andrew R. A. Conway1 and Kristof Kovacs2,3

In the last decade, new models of human intelligence have altered the theoretical landscape in psychometrics and cognitive science. In the current article, we provide an overview of key distinguishing features of these new models. Compared to 20th century models of intelligence, the new models proposed in the 21st century are unique for three primary reasons; (1) new models interpret the general factor, or g,asanemergentpropertyreﬂectingthepatternofpositivecorrelationsobserved among test scores, not as a causal latent variable, and therefore challenge the notion of general ability, (2) new models bridge correlational and experimental psychology and account for inter-individual differences in behavior in terms of intra-individual psychological processes, and (3) new models make novel predictions about the neural correlates of intelligent behavior. © 2015 Wiley Periodicals, Inc.

How to cite this article: WIREs Cogn Sci 2015. doi: 10.1002/wcs.1356

INTRODUCTION afreshperspectiveandnewapproachtothescienceof intelligence. ntelligence is one of the most extensively investi- The article also does not provide a formal gated constructs in the history of cognitive science. I defnition of intelligence. As mentioned, there is no Despite this research effort, or perhaps because of it, consensus defnition of the term. Thus, in order there is still no single consensus defnition, model, or to be objective here, we could only provide a list theory of human intelligence. The purpose of the cur- of acceptable defnitions, rather than the defnition. rent article is to provide an overview of new models More importantly, most previous defnitions (apart of intelligence. The feld of intelligence is currently in from the one, ‘Intelligence is what IQ tests measure’,1) a stage of signifcant progress, so our goal here is to revolve around the interpretation of the general factor convey to a broad audience what is novel and exciting of intelligence as something that is refected by IQ about these so-called new models. tests. That is, these defnitions implicitly adhere to the Given the focus on what is new, the current idea that there is something out there that we can call article does not address old controversies or political intelligence, and this single construct is measured by a arguments about intelligence research. In our opin- variety of different ability tests. In this article, we argue ion, the feld has fnally moved beyond all that. A that this interpretation is incorrect: intelligence, best new generation of intelligence researchers, equipped defned, is a set of different cognitive abilities rather with more advanced statistical methods and a more than an overarching, general mechanism involved in sophisticated understanding of the brain, are asking all cognitive activity. much more compelling questions about cognitive abil- Of course, the debate on general ability versus ities. As we embark upon the second century of intel- multiple abilities has been around for over a century ligence research, there is opportunity, and reason, for now, so what is new, or different, about ‘new models’ of intelligence? In our view, a lot, but let us start with ∗Correspondence to: [email protected] a glimpse of just three recent developments in the feld 1Department of Psychology, Princeton University, Princeton, NJ, USA of intelligence research. We will elaborate upon each 2Department of Psychology, Eszterházy Károly College, Hungary of these topics later. 3Department of Psychological Methods, University of Amsterdam, Amsterdam, Netherlands • The general factor of intelligence, or g, which Confict of interest: The authors have declared no conficts of interest is reliably observed when the all-positive for this article. covariance matrix of mental test scores is

factor analyzed, is interpreted as an emergent of intelligence. A theory is a set of ideas intended to rather than a latent property. That is, instead explain something or some type of phenomenon and of interpreting g as a causal general ability, is based on general principles independent of the thing, implicitly linked to a unitary psychological trait, or the phenomenon, being explained. Strong theories new models interpret g as an emergent property make empirical predictions and are therefore falsif- and individual scores on g as an index of the able. In contrast, a model is an implementation of collective performance on a battery of tests. In the theory. In order to implement a theory, a particu- less technical terms, according to new models of lar modeling framework must be adopted, and certain intelligence, g does not have a causal infuence assumptions may be necessary for the model to oper- on test scores, which means that the concept ate in a manner consistent with the theory. of ‘general ability’ is not a necessary feature It is also important here at the outset to clarify of a theory of intelligence. To be clear, new the distinction between two broad categories of mod- models of intelligence do not deny the existence els in cognitive science: psychometric and cognitive. of g, it clearly exists, and is predictive of many Psychometric models have dominated the landscape important life outcomes.2 of intelligence research and will be described in more • New models of intelligence can formally connect detail below. In short, psychometric models attempt psychometrics and cognitive science in a com- to capture the structure of intelligence but often times putational manner. In psychometrics, the pur- fail to convey much information about function. In pose of a ‘model’ is to explain the pattern of contrast, cognitive models of intellectual behavior, correlations among test scores, i.e., the covari- such as reasoning and working memory, attempt ance structure, in terms of a latent variable to capture the cognitive processes involved in com- model and to explain responses to test items plex cognition but often fail to explain individual in terms of item response models. In cogni- differences in performance. tive science, the goal of a ‘model’ is to provide To appreciate the divide between psychomet- acomputationalaccountofthecognitivepro- ric models of intelligence and computational models cesses involved in the performance of some cog- of cognition, let us take a look at two contem- nitive task. It has been argued that computational porary and highly infuential models: the Cattell- models have greater scientifc potential in cogni- Horn-Carroll (CHC) model of intelligence3–5 and the tive science than theoretical frameworks because embedded-process model of working memory.6–8 The they make more specifc, quantifable predic- CHC model is presented in Figure 1 and the working tions about the processes being modeled. New memory process model is presented in Figure 2. models of intelligence are attempting to connect The CHC model provides an excellent ft to these different modeling approaches. The goal a broad range of individual differences data and is is to ft psychometric models with parameters therefore considered one of the best, if not the best, from cognitive models and thereby account for latent variable models of intelligence in the psycho- inter-individual differences in behavior in terms metric literature. According to the hierarchical model, of intra-individual psychological processes, and there is a general factor at the apex, which has a do so in formal mathematical fashion, such that causal infuence on several ‘broad stratum’ factors, proposed models can be subject to novel predic- and these factors in turn have a causal infuence on tions, objectively falsifed, and updated. ‘narrow stratum’ factors, and these factors in turn • New models of intelligence make novel predic- have a causal infuence on test scores. As mentioned, tions about the neural bases of intelligence and the CHC provides a comprehensive account of covari- these predictions are being met with a staggering ance structures, but it does not translate well into a amount of new data from neuroscience. Theo- cognitive process model. For instance, Carrol4 does ries of intelligence have always been informed not specify what g represents in terms of a cognitive by our scientifc understanding of the brain but process, nor does he explain the causal mechanism now, with the rise of neuroimaging methods, neu- relating g to other factors. To be fair, that is not the ral data from large samples of healthy subjects primary goal of a latent variable model. are being combined with behavioral data, allow- In contrast, consider the working memory model ing for much more accurate predictions about the in Figure 2. It provides a detailed account of the neural bases of intelligent behavior. cognitive processes involved in perception, attention, and memory, and each component of the model It is important here at the outset to clarify the dis- is supported by decades of cognitive experimental tinction between a theory of intelligence and a model psychological research. For example, the focus of

FIGURE 1 The Cattell-Horn-Carrol (CHC) latent variable model of intelligence.

FIGURE 2 The embedded-process model of working memory.6 attention is| limited to a small number of mem- there are many other models of working memory, ory representations, and information maintained in with similar features, but it is fair to say that the this state is more readily accessible than informa- embedded-process model is among the most infu- tion represented in the short-term store, and this ential models of working memory in cognitive sci- information is more readily accessible than infor- ence. Yet, looking at the model, one is left guessing mation represented in the long-term memory.6 As as to which of the components gives rise to varia- another example, note that novel stimuli, unlike habit- tion in task performance across individuals. Again, to uated stimuli, can capture attention and gain imme- be fair, that is not the primary goal of this type of diate access into the focus of attention. To be clear, model.

The point of this ‘model comparison’ exercise is that incorporate both a general factor and lower order to demonstrate that these two models have different group factors provide the best ft to data. This helps to primary goals. The primary goal of latent variable explain why this historical line of research culminated models is to explain covariance structures and the in the CHC model. Looking back, it is interesting to primary goal of cognitive models is to explain the notice that despite substantive differences among early processes involved in complex cognitive behavior, theorists, they each attributed an important role of from a nomothetic perspective. As a result, one reasoning, learning, problem solving, and comprehen- adheres to the correlational discipline of psychology sion in human intelligence. and the other adheres to the experimental discipline. In the 1970s and 1980s, this conception of intel- To be fair, some researchers have attempted to bridge ligence was criticized as too narrow, and as a result, these two disciplines, especially in the realm of work- theories and models emerged that differed substan- ing memory and its relation to fuid intelligence (for tially from prior work. For example, the triarchic the- example, Ref 8, 9); indeed, this work lays the foun- ory of intelligence challenged the status quo defnition dation for one of the theoretical frameworks, Process of intelligence and proposed that there are other psy- Overlap Theory, which we will discuss in more detail chological processes and behaviors that can be ben- below. efcial in school, work, and society in general, and In sum, new models of intelligence are attempt- should therefore be considered expressions of intelli- ing to provide a more unifed perspective. The goal gence. The triarchic theory included analytic intelli- is to both (a) account for individual differences in gence but added creativity and practical intelligence.12 behavior, on par with the CHC model, and (b) provide Moreover, this approach conveyed that there are dif- a cognitive process account of behavior in terms of ferent cognitive processes underlying these different intra-individual psychological processes, on par with forms, or components, of intelligence. the working memory model. In the 1980s, an even broader view of intelligence was proposed, called multiple intelligence theory. According to the multiple intelligence theory, HISTORICAL PERSPECTIVE there are at least eight independent abilities that The frst, and perhaps the most well known, theory of should be conceived as forms of intelligence, including intelligence is general intelligence theory.10 Spearman musical ability, kinesthetic ability, and interpersonal initially argued that the positive pattern of correlations ability, among others.13 so often observed among test scores, which we refer Sternberg and Gardner challenged the status quo to here as the positive manifold, was due to a single approach to intelligence, especially in psychometrics, general ability factor (some kind of energy or power) and their ideas garnered a great deal of popular atten- that has a causal infuence on the performance of all tion. However, despite some initial success linking tests. This was represented by a latent variable model, information-processing models to theories of intel- consisting of a general factor, now famously known as ligence (for a review, see Ref 12), these theoretical Spearman’s g, and the causal paths from the general frameworks ultimately failed to generate sustainable factor to all tests. programs of research, especially when compared to Following Spearman, several alternative theo- the theoretical frameworks that preceded them. ries and models of intelligence were proposed in the Indeed, by the end of the 20th century, the most frst half of the 20th century. Factor analysis and widely accepted theoretical framework in the feld of latent variable models were used to test compet- intelligence was the CHC model, which is much more ing theories. For example, after Spearman’s initial consistent with original theories of intelligence pro- work, it became immediately clear that a single factor posed by Spearman and Thurstone than it is with the model could not account for the patterns of conver- theories of Sternberg or Gardner. Again, according to gence and divergence within the positive manifold and the CHC theory, the structure of intelligence is hierar- so alternative models proposing various ‘group fac- chical, with general intelligence, or g, at the apex, and tors’ emerged. Group factors typically represent more multiple group factors, akin to Thurstone’s Primary domain-specifcconstructs,suchasverbalabilityand Abilities, at the level below g. Among these group fac- visual–spatial skills. Perhaps the most infuential of tors are fuid intelligence and crystallized intelligence, these models was Thurstone’s Primary Mental Abili- adistinctionfrst proposed by Cattell3 and Horn.5 ties model, according to which there are several group While crystallized intelligence refers to the skills and factors but – initially – no general factor.11 This type knowledge one acquires in the enculturation process, of latent variable model has also been rejected because broadly speaking, fuid intelligence is defned as ‘an group factors are typically correlated and so models expression of the level of complexity of relationships

©2015WileyPeriodicals,Inc. WIREs Cognitive Science New and emerging models which an individual can perceive and act upon when on is mostly due to Bartholomew et al.20,21 The most he does not have recourse to answers to such com- important part of their work is a mathematical demon- plex issues already stored in memory’ (Ref 14 p 99) stration showing that there is no statistical means of The fuid/crystallized distinction has been infuential distinguishing between g-models and the sampling because it explains individual differences data and it model: even though they are conceptually very differ- has been supported, broadly speaking, by experimen- ent, they can equally account for the positive manifold tal research. For example, cognitive aging research and hierarchical structure in intelligence. That is, demonstrates that fuid intelligence declines with age Bartholomew et al.20 provide a mathematical proof but crystallized intelligence does not.15 Also, neu- illustrating that both general factor models and sam- roimaging research suggests distinct neural correlates pling models can provide an adequate ft of the covari- underlying performance of tests of fuid intelligence ance structures typically observed when a large battery versus crystallized intelligence.16 Finally, tests of fuid of tests is administered to a large sample of subjects. intelligence are strongly correlated with measures of This is a pivotal turning point for the feld working memory capacity, whereas the correlations because it implies that comparing the ft of different between tests of crystallized intelligence and working types of latent variable models no longer provides any memory capacity are weak.17 These, and other fnd- theoretical leverage whatsoever when evaluating com- ings, helped to blur the line between correlational and peting theories of intelligence. The larger implication experimental psychology. here is that the feld must move beyond psychometrics and take a converging operations approach, con- sidering evidence from other felds, such as cognitive NEW MODELS OF INTELLIGENCE science, developmental psychology, and neuroscience. The last decade has seen the birth of novel theoreti- The second theoretical account of the posi- cal approaches to human intelligence. In this section, tive manifold to discuss is the mutualism model, we survey a few important consequences of three of a developmental account of the positive manifold, these: the (reformulated) sampling model, the mutu- inspired by mathematical models in ecology. Mutu- alism model, and the process overlap theory. Albeit alism assumes that positive reciprocal interactions offering different accounts of the positive manifold, a take place between cognitive processes during devel- common aspect of these theories is that they all point opment. According to this model, at the beginning of out that general intelligence, a single common cause of development, individual differences in cognitive abili- the positive correlations between mental tests, is surely ties are uncorrelated. The positive manifold, and thus a suffcient, but defnitely not a necessary, explanation. the structure of individual differences in intelligence, is That is, even though they acknowledge the existence the result of mutually benefcial interactions between of psychometric g,theydoubttheexistenceofpsycho- modules or processes. In adults, tests unidimension- logical g: a cognitive process or mechanism that could ally tap specifc cognitive capabilities, but they are still be equated with the general factor. Yet, as we shall correlated because of their interaction during develop- see, this approach has substantial consequences on the ment. Just like sampling, this model is also capable of conceptualization of psychometric g, too. providing a mathematical explanation of the positive The frst ‘new’ model, the ‘sampling model’ or manifold without assuming the causal action of a sin- ‘bonds theory’, is not entirely novel; in fact, it was gle general factor.22 frst established in 1916 by Godfrey Thomson, a The third novel explanation of the positive man- contemporary of Spearman. Thomson demonstrated ifold is process overlap theory, a novel sampling that the positive manifold can emerge without a account, based upon cognitive process models, specif- general factor if there is an almost infnite number of ically models of working memory.23 In particular, psychological components, some of which are tapped the theory draws substantially on the fnding that by a large number of tests: ‘The mind, in carrying out the positive manifold is not confned to covariance any activity such as a mental test, has two levels at matrices of the intelligence literature: it is also com- which it can operate. The elements of activity at the monly observed in working memory tasks. The theory lower level are entirely specifc, but those at the higher assumes that any item or task requires a number of level are such that they may come into play in different domain-specifcaswellasdomain-generalcognitive activities. Any activity is a sample of these elements’.18 processes and their corresponding neural mechanisms. In the 100 years since its formulation, there Domain-general processes involved in executive atten- have been statistical elaborations and extensions of tion, and mainly tapping the dorsolateral prefrontal the sampling model (e.g., Ref 19), but its modern cortex, are central to working memory task perfor- version and the statistical reformulation it is based mance. That is, they are activated by a large number

(a)δ1 δ2 δ3 (b) ζ1 variables are socioeconomic status (SES) and general health, each of which tap the common variance between measures, but do not explain it – according X X X to sampling, mutualism, and process overlap theory, 1 2 3 η1 g is no different. Moreover, g can even be treated as

λ1 λ2 λ3 a weighted sum-score: if the unique variance of the γ γ γ 1 2 3 formative latent variable, noted with ! in Figure 3, is ξ removed, then g, interpreted as general intelligence, is 1 X X X 1 2 3 indeed simply determined by what IQ tests measure.25 The difference in the direction of causality between formative and refective models has drastic 26 27 FIGURE 3 Illustration of a reﬂective latent variable (a) and a implications. , In refective models, the latent vari- formative latent variable (b). able is a common cause of the indicators, whereas in formative models, it is their common consequence. | of test items, alongside with domain-specifcprocesses Because in refective models, measures are indicators tapped by specifc types of tests only. Such an overlap of the latent construct, they are interchangeable. For of executive processes explains the positive manifold instance, tests of vocabulary and general knowledge as well as the hierarchical structure of cognitive both purportedly measure crystallized intelligence; if abilities. one of the measures is replaced by the other in a model, Even though these theoretical accounts are very the theoretical meaning of the construct is supposed to different, a common characteristic is that they all chal- be unaltered. A formative latent variable, on the other lenge the idea that the across-domain correlations hand, is determined by its indicators, which cannot be between diverse mental tests are caused by an underly- interchanged without a corresponding change in the ing factor; instead, they propose that the positive man- conceptual interpretation of the construct. ifold is an emergent property. This idea has a number Besides purely formative and refective models, of important consequences for the modeling of human there are hybrid models, which are in part refective, intelligence. In order to understand these implications, in part formative (e.g., Ref 28). These models have one has to briefyfamiliarizewiththeconceptofrefec- latent variables that are causing, as well as the ones tive and formative models, illustrated in Figure 3. that are, the result of covariance. Process Overlap The model on the left is a refective model, which Theory provides exactly such a hybrid model.23 In is the standard approach in psychology. This model the model, group factors on the lower levels of the requires a stance of entity realism with respect to the hierarchy refect real cognitive abilities; hence, they modeled construct.24 Simply, in order for refective are indeed refected by individual measures, and they measurement to make sense, one must assume that have a causal effect on the measures’ covariance. On there is something out there, represented by the con- the highest level of the hierarchy, g emerges as a for- struct, and the measures are (imperfect) indicators of mative construct, which is caused by the covariance this something. In the case of g, it is assumed that g between the group factors. That is, the general fac- causes the measures as well as the covariance among tor does not explain the correlations between group the measures. According to the theory of general intel- factors – according to Process Overlap Theory, it is ligence, g causes the measures because, ceteris paribus, explained by the overlap between processes tapped by a person’s score on the measure, i.e., the IQ test, is tests that measure the individual group factors. determined by his/her score on the latent variable i.e., The issue of formative measures will not be fur- g. Consequently, someone having a higher position on ther dealt with here. The take-home message is that the g factor will have a higher score on the IQ test than new models of intelligence that explain the positive someone with a lower position on g,andtherefore manifold without postulating a causal general factor variance in the latent variable determines variance have overwhelming consequences on how a general in the measure. Finally, the measures’ covariance is factor can be interpreted to be in accordance with caused by the latent variable, because any two IQ these models. The analysis of such consequences is tests covary to the extent to which they covary with g. only beginning to unfold, and future research on the In formative models, the chain of causation is modeling of intelligence will probably involve a thor- the opposite. The latent variable emerges because of ough elaboration on how a formative general fac- the indicators and not the other way around,a hence tor can be conceptualized. It is predictable, however, g is the result, rather than the cause of the correla- that a general factor so interpreted will be more a tions between group factors. Similar formative latent tool for predicting real-life outcomes than a concept

©2015WileyPeriodicals,Inc. WIREs Cognitive Science New and emerging models appropriate for theory testing – the latter will proba- So it seems that the feld of intelligence is bly be restricted to group factors, which do fttoa moving full steam ahead, equipped with new theo- realist ontology. retical frameworks and more advanced and statisti- cally powerful research methods. However, there is one thing that we, as intelligence researches, must improve – the teaching of intelligence. The current lack of formal course instruction on the topic of intelli- FUTURE DIRECTIONS gence, especially at American Universities, is alarming. Given these new models, where is intelligence research The majority of students who earn a college degree in headed? Our prediction is that future research will psychology today are likely to know very little about be highly interdisciplinary. For example, more work the science of intelligence testing. This is a serious is needed to link psychometric models of intelligence problem, especially given the societal impact of stan- and computational models of working memory. On dardized tests and assessment of academic achieve- the topic of the neural correlates of intelligence, psy- ment. For decades now, these topics have generated chometric issues with respect to neural measurement serious contentious debates, and sadly the science of are just beginning to be explored in the realm of testing is rarely part of the conversation, in large part neuroimaging. Research teams will require a work- because the science is not well understood. As these ing knowledge of measurement theory, neuroscience, exciting new research programs develop, we must also promote the teaching of the science of intelligence, to and imaging methods. Finally, more work is needed inform future generations of parents, educators, and in developmental psychology and this work too must policy makers and to inspire the next generation of be able to bridge psychometrics, cognitive science, intelligence researchers. and neuroscience. Fortunately, large datasets are being acquired in all of these felds; for example, large sample neuroimaging studies are much more common NOTE now than just 5 years ago. Also, there seems to be a a greater appreciation now for implementing longitudi- This fact has motivated a few authors to not even nal designs to explore change within individuals over call formative constructs latent variables. We will keep time, especially in early childhood and in later stages the term, however, emphasizing the fact that both of life. This is all good news for the future of the feld. formative and refective constructs are unobservable.

ACKNOWLEDGMENT The second author’s research was funded by a Marie Curie Intra-European Fellowship of the European Commission.

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FURTHER READING McFarland DJ. A single g factor is not necessary to simulate positive correlations between cognitive tests. JClinExp Neuropsychol 2012, 34:378–384. doi:10.1080/13803395.2011.645018.