Rao, J. N. K. Analysis of categorical data from sample surveys. (English) Zbl 0616.62078 New perspectives in theoretical and applied statistics, Sel. Pap. 3rd Int. Meet. Stat., Bilbao/Spain 1986, 45-60 (1987). [For the entire collection see Zbl 0608.00013.] A review of some recent work on methods for analyzing categorical data arising from sample surveys is provided. The topics covered include: (a) The impact of survey design on standard \(\chi^ 2\) tests (or likelihood ratio tests \(G^ 2)\) for a multiway table, under log-linear models. (b) Simple corrections to \(\chi^ 2\) or \(G^ 2\) taking account of the survey design but requiring the knowledge of only the design effects for the cells and/or the marginals. (c) Improved corrections to \(\chi^ 2\) (or \(G^ 2)\) or alternative tests requiring the knowledge of full estimated covariance matrix of cell estimates. (d) Standard errors of parameter estimates and of ”smoothed” cell estimates, and residual analysis taking the design into account. (e) Small sample properties of test statistics for the special case of a simple goodness-of-fit test. (f) Simple corrections to \(\chi^ 2\) (or \(G^ 2)\) under a logistic regression (logit) model involving a binary response variable, in terms of deffs of response proportions for each factor combination. (g) Standard errors of parameter estimates and of ”smoothed” estimates of response proportions, under a logit model. MSC: 62H17 Contingency tables 62-07 Data analysis (statistics) (MSC2010) 62D05 Sampling theory, sample surveys Keywords:chi square test; Satterthwaite approximation; Wald statistic; review paper; methods for analyzing categorical data; sample surveys; survey design; likelihood ratio tests; log-linear models; Small sample properties; goodness-of-fit test; logistic regression; logit Citations:Zbl 0608.00013 PDFBibTeX XML