A Single G Factor Is Not Necessary to Simulate Positive Correlations Between Cognitive Tests

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A Single G Factor Is Not Necessary to Simulate Positive Correlations Between Cognitive Tests Journal of Clinical and Experimental Neuropsychology ISSN: 1380-3395 (Print) 1744-411X (Online) Journal homepage: http://www.tandfonline.com/loi/ncen20 A single g factor is not necessary to simulate positive correlations between cognitive tests Dennis J. McFarland To cite this article: Dennis J. McFarland (2012) A single g factor is not necessary to simulate positive correlations between cognitive tests, Journal of Clinical and Experimental Neuropsychology, 34:4, 378-384, DOI: 10.1080/13803395.2011.645018 To link to this article: http://dx.doi.org/10.1080/13803395.2011.645018 Published online: 20 Jan 2012. Submit your article to this journal Article views: 218 View related articles Citing articles: 2 View citing articles Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=ncen20 Download by: [Tufts University] Date: 28 September 2016, At: 08:05 JOURNAL OF CLINICAL AND EXPERIMENTAL NEUROPSYCHOLOGY 2012, 34 (4), 378–384 A single g factor is not necessary to simulate positive correlations between cognitive tests Dennis J. McFarland Laboratory of Neural Injury and Repair, Wadsworth Center, New York State Department of Health, Albany, NY, USA In the area of abilities testing, one issue of continued dissent is whether abilities are best conceptualized as man- ifestations of a single underlying general factor or as reflecting the combination of multiple traits that may be dissociable. The fact that diverse cognitive tests tend to be positively correlated has been taken as evidence for a single general ability or “g” factor. In the present study, simulations of test performance were run to evaluate the hypothesis that multiple independent abilities that affect test performance in a consistent manner will produce a positive manifold. Correlation matrices were simulated from models using either one or eight independent factors. The extent to which these factors operated in a consistent manner across tests (i.e., that a factor that facilitates performance on one test tends to facilitate performance on other tests) was manipulated by varying the mean value of the randomly selected weights. The tendency of both a single factor and eight independent factors to produce positive correlations increased as the randomly selected weights operated in a more consistent fashion. Thus the presence of a positive manifold in the correlations between diverse cognitive tests does not provide differential support for either single factor or multiple factor models of general abilities. Keywords: Abilities; Simulation; Positive manifold. Currently one of the principal arguments for the cognitive abilities may be antithetical to the mod- construct of general intelligence, or g, is the fact ular approach taken by most neuropsychologists that a matrix of correlations between diverse cog- (Anderson, 2005). There have been attempts at inte- nitive tests can be described as a positive mani- gration. For example, it has been suggested that the fold (Carroll, 1993; Molenaar, Dolan, Wicherts, & construct of psychometric intelligence is associated van der Maas, 2010; Murphy, Dzieweczynski, & with the frontal lobes (Duncan, 2005). However this Zhang, 2009; Spearman, 1904). That is, correla- view contrasts with the description of frontal lobe tions between tests of abilities tend to be positive. function as fractionated (Stuss & Levine, 2002). This positive manifold is generally thought to result Thus, the notion of a single general factor is at odds from the operation of a common factor that influ- with the view of specific dissociable abilities that is ences performance on all tests of mental abilities. common in neuropsychology. Alternative viewpoints hold that intelligence is best There have been recent attempts to explain the described as multiple independent abilities (e.g., positive manifold without recourse to g. Van der Gardner, 1983; Guilford, 1972). However, in a sur- Maas et al. (2006) suggest that the positive manifold vey of opinions, Reeve and Charles (2008) found could result from multiple independent cognitive that there seems to be a general consensus among abilities that become correlated through a process experts that g is a valid construct. of mutualism. Mutualism is described as a process The construct of a general factor accounting of positive beneficial interactions between cogni- for a large portion of the variance in tests of tive factors during development. Van der Maas I thank Loretta S. Malta for her helpful discussions and comments on this manuscript. Address correspondence to Dennis J. McFarland, Wadsworth Center, New York State Dept. of Health, P. O. Box 509, Empire State Plaza, Albany, New York 12201-0509, USA (E-mail: [email protected]). © 2012 Psychology Press, an imprint of the Taylor & Francis Group, an Informa business http://www.psypress.com/jcen http://dx.doi.org/10.1080/13803395.2011.645018 SIMULATION OF A POSITIVE MANIFOLD 379 et al. (2006) demonstrate how this might occur could be obtained from a set of uncorrelated abili- by means of simulated test scores. Bartholomew, ties with weights that were continuous rather than Deary, and Lawn (2009) discuss a bonds model binary. derived from a proposal originally suggested by The bonds model is a specific case of a more Thompson (1920) as a competing explanation for general condition in which individual differences Spearman’s (1904) observations. The bonds model affect performance in a relatively consistent man- posits multiple factors that are sampled by any ner across cognitive tasks. Given that a factor has given test score. Bartholomew (2007) showed that a relatively consistent effect across a set of tests, the Spearman (1904) and Thompson (1920) models its mean weight across tests will differ from zero. are statistically indistinguishable. In contrast, if the values of the weights associated A feature of the bonds model is that each of the with a specific ability in W had a mean of zero and independent factors (bonds) contribute to all test some standard deviation σ , then larger values of a scores in the same way; that is, because a bond has a would be expected to decrease performance on a weight of either 0 or 1, if a bond affects test scores, it given test as often as they increased performance. will always do so in a positive manner. Specifically, In this case, abilities would not operate in a consis- Bartholomew (2007) expressed this bonds model as tent manner across tests (i.e., across tests, a given ability would decrease performance as often as it t = Wa (1) improved performance). In practice, it can be dif- ficult to test this hypothesis without knowing the where t is a vector of test scores, W is a matrix of true extent to which individual differences affect coefficients that describe whether a given bond has performance. Simulation studies can fill this knowl- been sampled by a given test, and a is a vector of edge gap, because the effects of a factor or factors random values that describe individual differences on test performance can be systematically manip- in these bonds. (The notation has been changed ulated by varying the mean value of the factor but the model is identical to that discussed by weights. Bartholomew, 2007.) Thus, if sampled by test i, Sternberg (1979) describes two major approaches larger values of ai, the variable describing individ- that have emerged in the study of mental abili- ual differences, always produce larger values of ti, ties. The differential approach has primarily studied the variable representing test scores. If the proba- relationships between patterns of test scores within bility of a bond being included on the ith test is p, individuals, principally by means of factor analysis. then the mean value of the weights in W is equal The information-processing approach has primar- to p and thus varies between 0 and 1. As a result, if ily varied attributes of cognitive tasks, focusing a bond affects a test score, it is always in a positive on task attributes rather than subject attributes. manner, and thus the bonds model holds that indi- Simulations of cognitive performance have been vidual differences operate in a consistent manner employed by the information-processing approach. across tasks—that is, a bond will not have a negative Simulation has not been a favored method of the effect on performance. differential approach. However, simulation is a use- While the bonds model represents a case where ful form of modeling that has shown great utility in a positive manifold can be produced without the modeling complex and otherwise intractable prob- need to postulate a general factor, it is a highly lems in physics (Rohrlich, 1990). It well might also specific case since it assumes weighting on any prove useful in the biological and social sciences, given task of either 0 or 1. The notion that a spe- including differential psychology. cific ability has equivalent effects on all tasks that Hence, the present study used simulations to it influences is unlikely to be the case in prac- examine the general conditions whereby a positive tice. This assumption is not made in research on manifold could result from multiple uncorrelated models of abilities, which generally estimate the latent abilities. The hypothesis is that a positive weighing of each factor separately and find that manifold results when these multiple abilities oper- the resulting estimates are not equal as would ate in a relatively consistent manner across diverse be predicted by the bonds model (e.g., Tulsky & tasks. For example, we would expect an ability such Price, 2003). Furthermore, it is entirely possible as freedom from distraction to facilitate perfor- that in some cases a given ability might actually be mance on most cognitive tests. While it might be associated with poorer performance. Thus, a more more important for some cognitive tasks than oth- general model that allows for a continuum of fac- ers, in general, freedom from distraction should tor weights on different tests would have greater not have detrimental affects on test performance.
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