ESTIMATION OF PARAMETERS FOR THE LOGISTIC REGRESSION MODEL WITH PARTIALLY INCOMPLETE OBSERVATIONS (EM ALGORITHM, DISCRIMINANT FUNCTION)

摘要

The logistic regression model, which is widely used in econometrics, biostatistics, engineering, and social sciences, is a distribution model that expresses the log odds of an event with.;qualitative characteristics as a linear function of covariate values, x(,1), x(,2), ..., x(,p).;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;In this paper, Walker and Duncan's method of estimating the parameters of the logistic regression model for the dichotomous case is extended to the polychotomous case. It is shown that Walker and Duncan's method is equivalent to the maximum likelihood method for the logistic regression model in both the dichotomous and polychotomous cases.;Frequently, one or more independent variables (covariates) for some observations are missing. Various methods of accounting for missing data in the dichotomous logistic regression model are explored. In this paper, several methods of estimating multiple regression parameters are adapted to the problem of estimating parameters for the logistic regression model in the presence of missing values. Additionally, the iterative mean substitution method and a quasi-EM algorithm are also developed for the problem of missing values in continuous independent variables. To obtain the quasi-EM algorithm for the logistic regression model, the EM algorithm for the logistic form of Fisher's discriminant function is developed under the multivariate normal theory. This algorithm is then adapted to the logistic regression model. These methods are illustrated by example and are compared empirically to other missing-value methods: complete case, mean substitution, and regression. In general, the iterative mean substitution method and the quasi-EM algorithm perform well.