Associazione ed efficienza nei modelli logit-multivariati

Abstract

The goal of this work is to investigate the role that the association, among categorical variables, plays in estimating of the so-called marginal parameters of a Multivariate Logit Models. By comparing, in terms of asymptotic efficiency, the maximum likelihood estimators of the vector of the marginal parameters to the one obtained under the wrong hypothesis of stochastic independence (misspecification), we provide the general conditions of equality among asymptotic variance matrices of the two alternative estimators. Furthermore, by analyzing the particular case of bivariate binary variables with constraints of homogeneity (between, within and complete) on the marginal probabilities, we show that there are situations in which the gain of efficiency of the maximum likelihood estimator with respect to that of misspecification grows when the association among variables increases too.