DF-like analyses of binary, ordered, and censored variables using probit and tobit approaches

Binary and censored variables can lead to erroneous inferences about heritability in family studies if the dichotomous or censored nature of the dependent variable is not properly accounted for. The bivariate probit and tobit models proposed in this paper provide a unified approach to family studies with binary, ordered, and censored variables. Each model in this paper is derived from a similar latent-variable structure which can contain covariates that affect the expected value of the dependent variable, as well as genetic and shared environmental influences that lead to an association among related individuals. We apply the models to the fertility outcome and fertility motivations of Danish twins born 1953-1964 and find relevant genetic influences on the number of children as well as the desired timing of the first child.