Using Multimodel Inference/Model Averaging to Model Causes of Covariation Between Variables in Twins

Abstract

Objective: To explore and apply multimodel inference to test the relative contributions of latent genetic, environmental and direct causal factors to the covariation between two variables with data from the classical twin design by estimating model-averaged parameters.

Methods: Behavior genetics is concerned with understanding the causes of variation in phenotypes and the causes of covariation between two or more phenotypes. Two variables may correlate as a result of genetic, shared environmental or unique environmental factors contributing to variation in both variables. Two variables may also correlate because one or both directly cause variation in the other. Furthermore, covariation may result from any combination of these sources, leading to 25 different identified structural equation models. OpenMx was used to fit all these models to account for covariation between two variables collected in twins. Multimodel inference and model averaging were used to summarize the key sources of covariation, and estimate the magnitude of these causes of covariance. Extensions of these models to test heterogeneity by sex are discussed.

Results: We illustrate the application of multimodel inference by fitting a comprehensive set of bivariate models to twin data from the Virginia Twin Study of Psychiatric and Substance Use Disorders. Analyses of body mass index and tobacco consumption data show sufficient power to reject distinct models, and to estimate the contribution of each of the five potential sources of covariation, irrespective of selecting the best fitting model. Discrimination between models on sample size, type of variable (continuous versus binary or ordinal measures) and the effect size of sources of variance and covariance.

Conclusions: We introduce multimodel inference and model averaging approaches to the behavior genetics community, in the context of testing models for the causes of covariation between traits in term of genetic, environmental and causal explanations.

Keywords: ACE model; Bivariate; Covariance; Multimodel inference; Twins.

Figure 1:

Alternative representations of bivariate twin models: triple Cholesky (top) and correlated factors model (bottom)

Figure 2:

Sources of covariation, identifiable with data from the classical twin design, representing 5 of the 25 identified bivariate submodels

Figure 3:

Models with any two (top) or any three (bottom) sources of covariation between two variables

Figure 4:

Model-averaged parameter estimates from fitting bivariate models to data of females (4a), males (4b), jointly with full sex limitation (4c) and with quantitative sex differences only (4d) for continuous, ordinal and binary measures of BMI & ITOB (need to add error bars)

Figure 4:

Model-averaged parameter estimates from fitting bivariate models to data of females (4a), males (4b), jointly with full sex limitation (4c) and with quantitative sex differences only (4d) for continuous, ordinal and binary measures of BMI & ITOB (need to add error bars)