Analysis of Categorical Data Under Logistic Regression Model

This chapter considers analysis of categorical data under logistic regression models when the data are generated from complex surveys. Section 6.2 addresses binary logistic regression model due to Roberts et al. (Biometrika 74:1–12, 1987), and finds the pseudo ML estimators of the population parameter along with its asymptotic covariance matrix. The goodness-of-fit statistics $$X_P^2$$ and $$G^2$$ , and a Wald statistic have been considered and their asymptotic distributions derived. The modifications of these statistics using Rao-Scott corrections and F ratio have been examined. All the above problems have been considered in the light of nested models. We also considered problem of choosing appropriate cell-sample-sizes for running logistic regression program in a standard computer package. Following Morel (Surv Methodol 15:203–223, 1989) polytomous logistic regression has been considered in Sect. 6.5. Finally, using empirical logits the model has been converted into general linear model which uses generalized least square procedures for estimation. The model has been extended to accommodate cluster effects and procedures for testing of hypotheses under the extended model investigated.