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Offspring: Human Fertility Behavior in Biodemographic Perspective
bly higher than the DZ twin correlations. Also, for females the within-MZ twin-pair correlation for fertility is more than twice as large as the corresponding correlation for DZ twins. This pattern is suggestive of the possibility of nonlinear genetic influences such as dominance or epistasis. Detailed analysis of these effects, however, is beyond the scope of this chapter.
The starting point for most biometrical analyses using behavioral genetics designs is the ACE model, in which A refers to a latent genetic influence, C to a latent common (or shared) environmental influence, and E to a combination of measurement error and nonshared environmental influence. The relative importance of these influences is usually expressed in terms of heritability, h2, which is equal to the proportion of total phenotypic variance attributable to (additive) genetic variance, and the coefficient of shared environmental influences, c2, which is equal to the proportion of the total variance related to differences in shared-environmental conditions, such as parental background, and socialization. Estimates for heritability and shared environmental influence are conditional on a specific behavioral genetics model and are typically obtained by either structural equations modeling (SEM) or a regression method called DeFries-Fulker (or DF) analysis (DeFries and Fulker, 1985). SEM approaches use maximum likelihood as the fitting criterion and require both a structural model explaining the relationship between the constructs of the model and a measurement model explaining the relationship between the constructs and the variables used to measure the constructs. Mx (Neale et al., 1999) is a statistical software package that implements SEM methodology specifically to estimate behavioral genetics models.
Once the basic ACE model is fit to a particular dependent variable (often called the “phenotype” in the literature), additional adjustments can be made in the models to help understand the processes that generated the data. For example, fitting dominance models instead of additive models is possible (e.g., an ADE model). Dropping parts of the model with statistically meaningless parameter values results in fitting AE or CE models.
In the context of this chapter, the most interesting and valuable extension of the basic ACE model is the bivariate or multivariate model, in which overlapping sources of variance are evaluated. We estimate this model in Mx using the Cholesky decomposition model shown in Figure 3-1 for females and Figure 3-2 for males.5,6 Because completed education is
To save space, we have only represented the model for one member of the kin pair; the other twin’s model is identical, and the two are linked with bidirectional paths between the A and C components.
In a related application (Rodgers et al., 2003), we fit similar bivariate behavioral genetics models to evaluate whether there was overlapping variance between the number of children and age at first pregnancy attempt.