The Hierarchical Logistic Regression Model for Multilevel Analysis

Abstract

A hierarchical logistic regression model is proposed for studying data with group structure and a binary response variable. The group structure is defined by the presence of micro observations embedded within contexts (macro observations), and the specification is at both of these levels. At the first (micro) level, the usual logistic regression model is defined for each context. The same regressors are used in each context, but the micro regression coefficients are free to vary over contexts. At the second level, the micro coefficients are treated as functions of macro regressors. An empirical Bayes estimation procedure is proposed for estimating the micro and macro coefficients. Explicit formulas are provided that are computationally feasible for large-scale data analyses; these include an algorithm for finding the maximum likelihood estimates of the covariance components representing within— and between—macro-equation error variability. The methodology is applied to World Fertility Survey data, with individuals viewed as micro observations and countries as macro observations.