Some Classical Models in Categorical Data Analysis

Abstract

This chapter makes a brief review of classical models of categorical data and their analysis. After a glimpse of general theory of fitting of statistical models and testing of parameters using goodness-of-fit tests, Wald’s maximum likelihood statistic, Rao’s statistic, likelihood ratio statistic, we return to the main distributions of categorical variables—multinomial distribution, Poisson distribution, and multinomial-Poisson distribution and examine the associated test procedures. Subsequently, log-linear models and logistic regression models, both binomial and multinomial, are looked into and their roles in offering model parameters emphasized. Lastly, some modifications of classical test procedures for analysis of data from complex surveys under logistic regression model have been introduced.