The Analysis of Residuals in Cross-Classified Tables

In regression analysis and analysis of variance, examination of residuals forms an important part of good statistical practice (see Draper and Smith [1966]). More general uses of residuals have also been explored by Cox and Snell [1968]. In this paper, methods of residual analysis developed for loglinear models for cross-classified tables by Haberman [1972b] are used to examine models for quantal response and for complete and incomplete r X c contingency tables. Section 2 contains a brief summary of results of Haberman [1972b] which are used in this paper. A more complete summary is provided in the appendix. In section 3, residual analysis is used in the hypothesis of row and column independence in a complete r X c table. In section 4, methods are developed appropriate for analysis of quasi-independence models in incomplete r X c tables, and in section 5, methods for use in logit analysis are considered.