Estimating Parameters of Logit Model on Multivariate Binary Response Using Mle and Gee

Abstract

In this paper, we discuss binary multivariate response modeling based on extreme value distribution. Independent variables used in these models are some attributes of the alternative (labeled Zijt) and some attributes of the decision maker (labeled Xi). We assumed that n the decision maker observed with T response. Yit is tnd response variables from decision maker i and value Yit is binary. Response of decision maker i can be expressed as Yi = (Yi1,...,YiT). In each of the decision maker, we have data (Yi, Xi, Zi). Models are derived by the assumption that maximum random utility which the decision maker i choose one of the alternatives having greatest utility. Methods of parameter estimation are Maximum Likelihood Estimator (MLE) method and Generalized Estimating Equation (GEE). First discussion in this study is the estimation by MLE with independent assumption among response and then the MLE estimation using joint distribution by Bahadur’s representation. By MLE and GEE, estimating equations are obtained and solved by numerical (like’s Newthon-Rahpson method) in the condition that not all of the parameters of individual attributes can be estimated (identified). Based on testing simulation data with R.2.5.0, we recommend (a) in low correlation, GEE is better than MLE (b) in moderate correlation, MLE is most efficient but not stable (c) in high or moderate correlation, MLE and GEE should be used (d) correlation estimators cannot explain the real correlation because of its bias.