INCORPORATING CAUSAL STRUCTURE AND EXOGENOUS INFORMATION WITH PROBABILISTIC MODELS: WITH SPECIAL REFERENCE TO CHOICE, GRAVITY, MIGRATION, AND MARKOV CHAINS.

Several methods of analyzing the parameters of the Semi-Markov model and incorporating exogeneous information about its states are presented. Regression analysis of parameter estimates and doubly stochastic processes are discussed. Theoretical models for the structure of transition matrices, based on Luce's theory of choice behavior, are derived. Gravity models of varying specificity, useful in the study of migration, are special cases. Maximum likelihood procedures for estimating parameters, with fully operational numerical methods for solution of the likelihood equations, are given. Thus the integration of probabilistic models with theoretical and empirical analysis of causal structure, called for in the previous article, is carried out. [ABSTRACT FROM AUTHOR]