Testing structural equation models for twin data using LISREL

Simple genetic models can be fitted to twin data using software packages such as LISREL (Jöreskog and Sörbom, 1986a). After discussion of data preparation and routine checks on possible violation of assumptions of the twin method, we illustrate univariate, bivariate, and multivariate genetic models which can be tested in cross-sectional twin data using LISREL. These include models for cohort or cohabitation effects, genotype x sex interaction, and certain types of genotype x environment interaction and genotype-environment correlation.This research was supported in part by NIH Grants GM30250, AG04954, HD19802, and HD18426 and by ADAMHA Grants AA06781 and MH40828. This paper is modified from a presentation at a workshop on twin data analysis held at the Catholic University of Leuven, supported by NATO Grant 86/0823 and grants from the Belgian National Research Eund, the State University of Gent, and the Catholic University of Leuven.     

Latent variable growth within behavior genetic models

The purpose of this paper is to introduce one kind of latent-variable structural-equation model for multivariate longitudinal data which includes behavioral genetic components. A generic structural-equation model termedRAM (McArdle, J. J. and McDonald, R. P. (1984).Br. J. Math. Stat. Psychol.,37:239–251.) is used to define the univariate twin design, including both covariances and means. This model is extended to multivariate form using a latent-variable growth-curve model recently presented by W. Meredith and J. Tisak [(1984). Tuckerizing curves. Psychometric Society Annual Meetings]. The model presented herein further permits hypothesis testing of various biometric models of the sources of these individual differences in latent growth. Aspects of this model are illustrated using the LISREL algorithm [Jöreskog, K. G. and Sörbom, D. (1979).Advances in Factor Analysis and Structural Equation Models, Abt Books, Cambridge, Mass.] and longitudinal twin data on early childhood abilities [Wilson, R. S. (1983).Child Dev. 54:298–316].This research was funded by National Institute on Aging Grant AG04704.     

Using the Mplus Computer Program to Estimate Models for Continuous and Categorical Data from Twins

Historically, the focus of behavior genetic research was to obtain estimates of the sources of familial resemblance for a single phenotype. Current research strategies have moved beyond heritability estimates to the search for physiological and behavioral mechanisms by which genetic risk is translated into individual differences in behavior and disease liability. Such research questions often require multivariate designs and complex analytic models, including the analysis of continuous and categorical dependent variables within the same model. Recent advances in computer software for categorical data analysis have increased the tools available for researchers in behavior genetics. This paper describes how to use the Mplus software program (Muthén and Muthén, 1998, 2002) for the analysis of data obtained from twins. Example analyses include two- and five-group twin models for univariate and bivariate continuous and categorical variables. Data on alcoholism and age at first drink drawn from the Virginia Adult Twin Study of Psychiatric and Substance Use Disorders are used to illustrate how Mplus can be used to analyze multiple-category variables, recode and transform variables, select subgroups for analysis, handle subjects with incomplete data, include constraints to ensure non-negative loadings, include model covariates, model sex differences, and test alternative hypotheses about mediation of genetic risk by measured variables.     

Mixed-Effects Variance Components Models for Biometric Family Analyses

Recent substantive research on biometric analyses of twin and family data has used both a biometric path analysis model (PAM) and a biometric variance components model (VCM). Methodological research on these same topics have suggested benefits of using linear structural equation model algorithms (SEMA) as well as mixed effect multilevel algorithms (MEMA). To better understand the potential similarities and differences among these approaches we first highlight the algebraic equivalence between the standard biometric PAM and the corresponding biometric VCM models for family data. Second, we demonstrate how several SEMA programs based on either the PAM or VCM approach produce equivalent estimates for all phenotypic and biometric parameters. Third, we show how the biometric VCM approach (but not the PAM approach) can be easily programmed using current MEMA programs (e.g., SAS PROC MIXED). We then expand the scope of these different approaches to include measured covariates, observed variable interactions and multiple relatives within each family. MEMA software is compared to SEMA software for programming complex models, including the flexibility of data input, treatment of missing data, inclusion of covariates, and ease of accommodating varying numbers of observations (per family or individual).     

Phenotypic and behavioral genetic covariation between elemental cognitive components and scholastic measures

The study subjected nine elementary cognitive task variables from the Cognitive Assessment Tasks (CAT) and three scholastic measures from the Metropolitan Achievement Test (MAT) to phenotypic and behavioral genetic structural equation modeling based on data for 277 pairs of same sex monozygotic (MZ) and dizygotic (DZ) twins from the Western Reserve Twin Project. Phenotypic and behavioral genetic covariation between certain elemental cognitive components and scholastic performance was examined to determine (a) whether these elemental cognitive components contribute substantially to the variance of scholastic performance; (b) whether such contributions vary across different domains of school knowledge or from specific domains to a general aptitude; (c) the behavioral genetic composition of the elemental cognitive components and the scholastic variables; and (d) how the association between the cognitive components and scholastic performance is genetically and environmentally mediated. The results of the study showed that as much as 30% of the phenotypic variance of scholastic performance was accounted for by the CAT general factor, which was presumably related to mental speed. A mainly genetic covariation was found between the mental speed component and scholastic performance, although each of the two variables was strongly influenced by both heritability and common family environment. The magnitude and etiology of the covariation were largely invariant whether mental speed was related to a common scholastic aptitude or to individual achievement measures covering different knowledge domains. Taken in conjunction with previous findings that mental speed has a substantial genetic correlation with psychometric g, and psychometric g has a mostly genetic covariation with scholastic achievement, the findings of the present study seems to point to a more global picture; namely, there is a causal sequence that starts from mental speed as the explanatory factor for both psychometric g and scholastic performance, and the etiology of the causal link is chiefly genetic.     

Bi- and multivariate analyses of diallel crosses: A tool for the genetic dissection of neurobehavioral phenotypes

The genetic-correlational approach provides a very powerful tool for the analysis of causal relationships between phenotypes. It appears to be particularly appropriate for investigating the functional organization of behavior and/or of causal relationships between brain and behavior. A method for the bivariate analysis of diallel crosses that permits the estimation of correlations due to environmental effects, additive-genetic effects, and/or dominance deviations is described, together with a worked-out example stemming from a five times replicated 4×4 diallel cross between inbred mouse strains. The phenotypes chosen to illustrate the analysis were locomotor activity and rearing frequency in an open field. Large, positive additive-genetic and dominance correlations between these two phenotypes were obtained. This finding was replicated in another, independently executed, diallel cross.     

Multivariate multipoint linkage analysis of quantitative trait loci

Resolution of the genetic components of complex disorders may require simultaneous analysis of the contribution of individual quantitative trait loci (QTLs) to multiple variables. A likelihood approach is used to illustrate how the complexities of multivariate data may be resolved with multipoint linkage analysis. Sibling pair data were simulated from a model in which two QTLs and trait-specific polygenic effects explained all the sibling resemblance within and between five variables. Multipoint linkage analysis was used to obtain individual pair probabilities of having zero, one, or two alleles identical by descent, and these probabilities were applied in a weighted maximum-likelihood fit function. The results were compared with those obtained using conventional linear structural equation modeling to estimate the contribution of latent genetic factors to the genetic covariance in the multiple measures. Both analyses were conducted using the Mx package. Relatively poor agreement was found between genetic factors defined in purely statistical terms by varimax rotation of the first two factors of the genetic covariance matrix and the structure obtained by fitting a model jointly to the phenotypic and the multipoint linkage data.     

The Mixed or Multilevel Model for Behavior Genetic Analysis

We propose the mixed model or multilevel model as a general alternative approach to existing behavior genetic analysis—an alternative to correlation analysis, the DeFries-Fulker analysis, and structural equation modeling. The mixed or multilevel model handles readily families of behavioral genetic data, which include paired sibling data (e.g., pairs of MZ and DZ twins) and clustered sibling data (e.g., a family of more than two biological siblings) as special cases. Not only can a family of behavioral genetic data have more than two siblings, it can also contain multiple types of siblings (e.g., a pair of MZ twins, a pair of DZ twins, a full sibling, and a half sibling). In contrast to the traditional approaches, the mixed or multilevel model is insensitive to the order of the siblings in a sibling cluster. We apply our approach to a large, nationally representative behavior genetic sample collected recently by the Add Health Study. We demonstrate the approach through several applications using both clustered and family complex behavioral genetic data: conventional variance decomposition analysis, analysis of interactions between genetic and environmental influences, and analysis of the possible genetic basis for friendship selection. We compare results from the mixed or multilevel model, Pearson's correlation analysis, and the structural equation model.     

Development and validation of the chinese rehearsal scale for preadolescent chinese children

Roger ( 1997 ) defined rehearsal as “the tendency to rehearse or ruminate on emotionally upsetting events” (p. 71). The Rehearsal Scale for Children–Chinese (RSC‐C) was developed from the original 14‐item Rehearsal Scale of the Emotion Control Questionnaire (Roger & Nesshoever, 1987 ) after translation and modification for Hong Kong Chinese preadolescents (aged 6–12 years). Confirmatory factor analysis using structural equation modeling revealed that with 1 item deleted from the original scale, the RSC‐C possessed good internal validity and satisfactory test‐retest reliability within a 1‐year period. The new 13‐item RSC‐C also showed good external validity and internal reliability (α=.76). Convergent and discriminant validity was evidenced against the Emotional Problem and the Prosocial Behavior Subscales of the Strengths and Difficulties Questionnaire (Goodman, 1997 ), respectively. No gender differences in rehearsal scores were found. It was concluded that the 13‐item RSC‐C could be useful for measuring rehearsal in Chinese preadolescents. © 2010 Wiley Periodicals, Inc. J Clin Psychol 66: 1–10, 2010.