The analysis of hierarchical and unbalanced complex survey data using multilevel models

Abstract

Multilevel analysis allows characteristics of different groups to be included in models of individual behaviour. Most analyses of social sciences data entail the analysis of data with built-in hierarchies, usually obtained as a consequence of complex sampling methods. The formulation of such models and estimation procedures may be seen as an effort to develop a new family of analytical tools that correspond to the classical experimental designs. The purpose of this dissertation is to investigate the efficient analysis of level-3 models, which includes the estimation of the unknown parameters and statistical inference. Use is made of the Expected Maximization algorithm and the Iterative Generalized Least Squares algorithm. As most data sets from the social sciences are quite large, the feasibility of analysing large data sets efficiently is investigated. Attention is given to the problem of developing a computer program that is easy to use as a standard statistical package. Theoretical results required for the estimation of the unknown parameters are extended to a general level-3 model, allowing for complex variance structures on all levels of the hierarchy. Since it often happens that there may be more than one response variable of interest, for example in a personality test with a number of items, the analysis of models with two or more continuous response variables is also considered. Survey data in the social sciences are usually of a categorical nature. It is shown how data with a categorical response variable can be analysed within the general framework developed. The theory is extended to accommodate the simultaneous analysis of more than one categorical response variable. Suggestions for further research are given, including guidelines for the handling of non-linear multilevel models. Most of the theory derived in this study is illustrated with examples based on real data and has been implemented in FORTRAN programs.