Analysis of categorical data for complex surveys

This paper reviews methods for handling complex sampling schemes when analysing categorical survey data. It is generally assumed that the complex sampling scheme does not affect the specification of the parameters of interest, only the methodology for making inference about these parameters. The organisation of the paper is loosely chronological. Contingency table data is emphasized first before moving on to the analysis of unit-level data. Weighted least squares methods, introduced in the mid 1970s along with methods for two-way tables, receive early attention. They are followed by more general methods based on maximum likelihood, particularly pseudo maximum likelihood estimation. Point estimation methods typically involve the use of survey weights in some way. Variance estimation methods are described in broad terms. There is a particular emphasis on methods of testing. The main modelling methods considered are log-linear models, logit models, generalized linear models and latent variable models. There is no coverage of multilevel models.