Univariate and Multivariate Log-Linear and Logistic Models
Delineates the inappropriateness of certain methods of analysis and summarizes existing maximum-likelihood methods and models for dealing with qualitative data. The log-linear model is extended and related to a general logistic model for the analysis of jointly dependent qualitative variables. The analysis of covariance methods common in regression analysis are extended to the case of jointly dependent qualitative variables, and analogies are provided for structural and reduced form equations for continuously measurable endogenous variables. The conditional probability of a qualitative variable may be interpreted as an analog of the structural equation in a system of simultaneous equations. A computer program is developed for the analysis of jointly dependent qualitative data, the probabilities of which depend on exogenous variables that may vary continuously or categorically. These procedures are used to analyze three bodies of empirical data and to compare the results obtained by other methods.