Including measured genotypes in statistical models to study the interplay of multiple factors affecting complex traits.

The etiology of complex traits may perhaps best be conceptualized by an interplay of multiple factors that mediate the influence of the genes on the eventual outcome. The possibilities of studying aspects of this interplay using existing methods are generally limited. We therefore propose a model with observed and latent variables that does not impose restrictions on the number of variables or the direction of their causal relations and provides a general approach for fitting structural equation models to empirical data. The model is very flexible and (1) allows for genetic effects on the means, variances, and relations between variables, (2) can control for stratification effects on all these components, (3) can be fitted in nuclear families of any size, (4) is estimated using an interpretable parameterization, and (5) can incorporate di- and multi-allelic loci, marker haplotypes, multiple loci simultaneously, and parental genotypes. We indicate how the model can be estimated with the Mx software (Neale et al., 1999) and have written a program to enable geneticists who are not acquainted with Mx to fit their own submodels in a simple and efficient way. A simulation study showed that the model yielded correct Type I errors, unbiased parameter estimates, and satisfactory power to discriminate between alternative models. An example is also given that illustrates how the model could be applied to real data.