Haberman S. Analysis of Qualitative Data: New Developments

London: Academic Press, Inc., 1979. — 256 p. — ISBN 0123125022, 9780123125026In this book a variety of models for qualitative data are explored; these go beyond the hierarchical log-linear models and logit models of Volume 1. Chapter 6 discusses multinomial response models appropriate for the complete
factorial tables considered in Volume 1. These models are generalizations of the hierarchical log-linear models of Chapters 2-4 and of the logit models of Chapter 5. As in the case of logit models, the models of Chapter 6 can be used to exploit ordered categories and can be used with continuous predicting variables. Chapter 7 examines log-linear models for incomplete factorial tables. The chapter emphasizes for incomplete two-way tables quasi-independence models which have been the subject of much early work on log-linear models. Hierarchical log-linear models for incomplete multi-way tables and multinomial response models for incomplete tables are also studied. Both iterative proportional fitting and Newton-Raphson algorithms are developed. In Chapter 8 models are considered for contingency tables in which several variables have the same categories. Symmetry models, quasi-symmetry models, marginal-homogeneity models, and distance models are introduced and related to quasi-independence models and to parametrizations developed for hierarchical log-linear models. Again, both iterative proportional fitting and the Newton-Raphson algorithm are used for numerical work. In Chapter 9 adjustment of data is studied through numerical methods developed in earlier chapters for use with log-linear models. The methods of Deming and Stephan for adjustment of marginal totals are related to the iterative proportional fitting algorithm for hierarchical log-linear models. Alternative methods of adjustment of data are also studied. In contrast with most earlier treatments of adjustment of data, emphasis is given to estimation of standard deviations of estimates.