Path analysis under generalized marital resemblance: Evaluation of the assumptions underlying the mixed homogamy model by the Monte Carlo method

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Abstract
Path analysis of nuclear family data has been widely applied to resolve genetic and environmental sources of familial resemblance. Here we report the results of a systematic evaluation of the effects of departures from five modeling assumptions often made when analyzing nuclear family data; i) the observed environmental index is unaffected by the genotype, ii) the basis of marital resemblance is correctly specified in the model, iii) there are no intergenerational differences in either the genetic or cultural heritability, iv) there is no genetic dominance, and v) there is no genotype by family environment interaction. “Deterministic simulations” identified various situations where model misspecification could lead to substantial bias in the estimation of the heritabilities. For these situations, “stochastic simulations” were performed to determine whether the “goodness-of-fit” test used in path analysis would correctly reject the misspecified model. In samples of 500 nuclear families, each comprising two parents and two children, the goodness-of-fit test was found to be sensitive to misspecifications of the source of marital resemblance and the existence of intergenerational differences in heritabilities, although reduced power would make the test less sensitive in smaller samples. The test was largely insensitive to misspecifications of possible genetic effects on the environmental index, and to the existence of multiplicative interaction between the genotype and familial environment. When genetic effects on the index are ignored, the genetic heritability (h2) is understimated, the cultural heritability (c2) is overestimated, but h2 + c2 remains unchanged. Neglecting the interaction was found to result in an overestimate of h2.