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Combining Nonlinear Biometric and Psychometric Models of Cognitive Abilities Behav Genet DOI 10.1007/s10519-009-9288-6 ORIGINAL RESEARCH Combining Nonlinear Biometric and Psychometric Models of Cognitive Abilities Elliot M. Tucker-Drob Æ K. Paige Harden Æ Eric Turkheimer Received: 2 December 2008 / Accepted: 8 July 2009 Ó Springer Science+Business Media, LLC 2009 Abstract It is well-established that genetic factors account of human cognitive abilities on two fronts. First, using for large proportions of individual differences in multiple siblings and other relatives, early behavior geneticists sought cognitive abilities. It is also well-established that individual to decompose between-person variation in cognitive ability differences in performance on many different cognitive ability estimates into proportions attributable to genetic influences measures are strongly correlated. Recent empirical investi- and proportions attributable to environmental influences. gations, however, have suggested two interesting qualifica- Pearson (1903) asked teachers to rate their students as tions to these well-established findings: Genetic variance in either ‘‘Quick Intelligent,’’ ‘‘Intelligent,’’ ‘‘Slow Intelligent,’’ cognitive abilities is higher in richer home environments ‘‘Slow,’’ ‘‘Slow Dull,’’ ‘‘Very Dull,’’ or ‘‘Inaccurate-Erratic.’’ (gene-by-environment interaction), and common variance in He found that siblings correlated on these ratings at approx- different cognitive abilities is lower at higher levels of overall imately 0.5, the same value obtained for sibling correlations ability (nonlinear factor structure). Although they have been on physical characteristics (e.g., head size and height), which investigated independently, these two phenomena may he reasoned were in large part genetic. This led him to the interact, because richer environments are routinely associated conclusion that, like physical characteristics, ‘‘mental’’ with higher ability levels. Using simulation we demonstrate characteristics are largely inherited from one’s parents. how un-modeled nonlinear factor structure can obscure Second, early psychometricians sought to decompose interpretation of gene-by-environment interaction. We then between-person variation in performance on multiple reanalyze data from the National Collaborative Perinatal cognitive tests into proportions attributable to common and Project, previously used by Turkheimer et al. (2003; Psychol unique influences. Spearman (1904) found positive corre- Science), with a two-step method to model both phenomena. lations among school children’s scores on examinations of Classics, French, English, Mathematics, and Music, levels Keywords Intelligence Á Differentiation Á of performance on pitch discrimination, weight discrimi- Gene-by-environment interaction Á Nonlinear nation, and visual discrimination tasks, teacher ratings of factor analysis cleverness, and peer ratings of common sense. He posited that these positive correlations resulted from a common influence, which he termed general intelligence (‘‘g’’). Introduction Variation that he could not attribute to g, he attributed to specific factors (‘‘s’’) and error of measurement. Over the course of the early twentieth century researchers Owing in large part to the development and refinement of made significant progress toward the scientific understanding behavior-genetic and psychometric theories, data, and meth- ods over the past century, two major phenemona are now well- Edited by Stacey Cherny. established. First, performance on many different sorts of cognitive tests can be attributed to a smaller number of dif- & E. M. Tucker-Drob ( ) Á K. P. Harden Á E. Turkheimer ferent abilities (e.g., spatial visualization, speed of processing, Department of Psychology, University of Virginia, P.O. Box 400400, Charlottesville, VA 22904-4400, USA and long term memory, to name a few), and these abilities are e-mail: [email protected] strongly related to one another, such that a single common 123 Behav Genet Fig. 1 A latent variable model Twin 1DZ = .5 / MZ = 1.0 Twin 2 often used to examine multivariate cognitive ability data obtained from monozygotic 1 1 1 (MZ) and dizygotic (DZ) twins 1 1 reared together. Observed variables (e.g., the different cognitive tests, Y[m], E1 A1 C A2 E2 Y[n],…,Y[x]) are represented as squares, latent variables (e.g., Biometric Portion general cognitive ability, and its ea c ca e genetic and environmental influences) are represented as g circles, variances and g 1 SES 2 covariance relationships are ss represented as two-headed arrows, and regression Psychometric Portion m n [x] m n [x] relationships are represented as one-headed arrows. SES Y[m] Y[n] Y[x] represents socioeconomic Y[m]1 Y[n]1 … Y[x]1 2 2 … 2 status, a family-level covariate m n [x] m n [x] MZ m1,m2 / DZ m1,m2 MZ [x]1,[x]2/ DZ [x]1,[x]2 MZ n1,n2/ DZ n1,n2 factor can be presumed to influence them all (Carroll 1993). Additive linear relations among variables is a central Second, approximately half of the variation in the single assumption of the standard structural equation modeling common factor (or a representative composite measure) can approach. This assumption requires that the relations be attributed to genetic factors (Bouchard and McGue 2003). between any two variables do not vary in magnitude Such behavior genetic and psychometric results can be according to the levels of those variables or any other simultaneously represented using a structural equation variables. Recently, however, researchers have begun to modeling framework. Figure 1 depicts a popular version of construct and employ statistical methodologies that are such a representation, which is based on data from mono- capable of explicitly testing non-additive, nonlinear, zygotic and dizygotic twins reared together. This model can structural equation models (e.g., Eaves and Erkanli 2003; be subcategorized into a psychometric portion at the sub- Muthe´n and Asparouhov 2003; Neale 1998; Purcell 2002; ordinate level and a biometric portion at the superordinate Klein and Moosbrugger 2000). level. The psychometric portion of the model relies on the These new nonlinear methodologies are increasingly relations among multiple variables to infer a common being applied by behavior-genetic researchers to address phenotypic trait, whereas the biometric portion of the model questions of gene-by-environment interaction. Based on relies on differences in the degrees of similarity between such methods, Turkheimer et al. (2003) and Harden et al. relatives of varying degrees of genetic relatedness in order (2007) have reported results which suggest that the genetic to decompose variation in the trait into genetic, shared and environmental contributions to children’s and adoles- environmental, and nonshared environmental components. cents’ general cognitive ability differ according to socio- Although they occupy separate regions of the model, economic status (a gene-by-environment interaction), such these psychometric and biometric levels of analysis are not that genetic influences are higher and environmental influ- independent. Rather, inference at the superordinate, bio- ences are lower at higher levels of socioeconomic status metric, level of analysis is dependent on the assumptions of (SES).1 These results are consistent with theories (e.g., the subordinate, psychometric, level. One well-known Bronfenbrenner and Ceci 1994; Turkheimer and Gottesman example of this dependency is when perfect measurement is 1991) which suggest that genetic propensities can be more incorrectly assumed, such that measurement error at the fully cultivated, expressed, and actuated in more enriched psychometric level is confounded with nonshared environ- ement (‘‘E’’) at the biometric level. The focus of the current 1 Although SES is generally considered an index of environmental article is on a less well-recognized example of this depen- quality, it may also partially reflect genetic factors as a result of the dency. We are specifically interested in the consequences gene-environment correlation that occurs when children are reared by their biological parents. While this possibility may have substantive for biometric analyses when a nonlinear factor structure implications, it does not appear to affect the empirical finding that holds but is not modeled. heritability is higher at higher levels of SES (Loehlin et al. 2009). 123 Behav Genet and supportive environments. Bronfenbrenner and Ceci As we suggested earlier, these findings from behavior- (1994; p. 572) have suggested that such mechanisms may genetic and psychometric analyses of nonlinearity may not include ‘‘enduring forms of interaction in the immediate be independent. For illustrative purposes, consider the most environment…found in parent–child and child–child activ- basic behavior-genetic model: a comparison of the test ities, group or solitary play, reading, learning new skills, scores of monozygotic (MZ) twins reared apart. The higher problem solving, performing complex tasks, and acquiring the correlation between the twins’ scores, the higher the new knowledge and know-how.’’ estimated heritability. Let us assume that the true herita- Nonlinear methodologies have also recently been applied bility of general cognitive ability is constant across SES for psychometric scrutiny of the conventional linear factor levels. Now, if abilities are less related to one another with model. There are at least two reasons to expect the factor increasing general ability level, and if ability levels structure of cognitive abilities to depart from linearity. The increase with
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