Nonlinear path models with continuous or dichotomous variables

Methodology and tools exist, and are commonly used in practice, for analyzing and estimating the coefficients in recursive path models, based on linear relationships with continuous endogenous variables. However, the methods that are traditionally implemented are limited by requirements for linear models, as well as assumptions of independent and normally distributed error terms.;In this dissertation, methodology is presented that extends the traditional path model method of the "Calculus of Coefficients" (COC). An analog of the COC is developed, called the "Calculus of Effects" (COE), that is applicable to recursive path models involving nonlinear relationships among the endogenous variables. This COE methodology results in a partitioning of the total effect into sums of the direct effect and all indirect effects through intermediate variables in the causal chain, as is also true in the more classical COC.;Techniques for estimation and testing of direct and indirect effects are developed. Estimates of effects are based on maximum likelihood estimation and may, under certain model specifications, require Monte Carlo estimation of some effects. Testing of effects is based on asymptotic independence of parameter estimates for nonlinear recursive path models, which is developed and shown herein.;The COE is also presented as applied to models strictly containing endogenous variables that are dichotomous, which is an example of a dependent error structure and, thus, an extension of COC to models without requiring an assumption of independent error terms. Special cases of models containing both continuous and dichotomous variables are analyzed and discussed. Applications of the COE, parameter estimation and testing of direct and indirect effects to fields of maternal and child health and Alzheimer's disease are included.