Discrete variable analysis for individuals grouped into families

Abstract

When categorical data arise from individuals grouped into families, because of the within-family dependence the conventional methods of inference, which are based on multinomial sampling, will generally be inappropriate, for example in testing simple or complex hypotheses about the unknown cell probabilities. Inequalities for the appropriate chi-squared statistics are derived under very weak assumptions about the nature of the within-family dependence. Cohen (1976) introduced the problem in a demographic context for families of size two, and his results are extended here. The approach used here has something in common with that of Wedderburn (1974) in that one wants to analyze the data without actually having to write down the exact form of the likelihood function. Here only the first-and second-order properties of the distribution are used.