Logistic Regression Models for Analysis of Multistage Survey Data

are extensively used in analyzing sample survey data to study the relationship between a binary response and a group of independent variables. Due to cost and efficiency considerations, stratified multistage samples are the norm. However, these samples, while efficient for estimation of the descriptive population quantities, pose challenges for model-based statistical inference. This sampling scheme often introduces multilevel correlation among the observations that can have implications for model parameter estimates. For multistage clustered samples, the dependence among observations often comes from several levels. Thus, drawing appropriate inferences from survey data may require complicated modeling techniques and very often, the computation required for this is very time consuming. This paper is focused on model-based analysis for binary data with a structure similar to that of the National Health Interview Survey. It proposes a logistic regression model which fits the between-cluster variation with random effects. The model also takes into account the correlation among small groups of observations within each cluster. An algorithm is proposed that makes the computation feasible for the mixed logistic regression model on large survey data. Generalized estimating equations (Liang and Zeger, 1986) are used in the estimation procedure to accommodate the correlation among the observations within small groups, avoiding problems associated with the use of random effects to model correlations among large numbers of small groups. An adjustment is applied to eliminate the bias in estimation of fixed effects that exists in some procedures for random effects logistic regression noted by Rodriguez and Goldman, 1995.