MARGINAL REGRESSION-MODELS FOR CLUSTERED ORDINAL MEASUREMENTS

This article constructs statistical models for clustered ordinal measu rements. We specify two regression models: one for the marginal means and one for the marginal pairwise global odds ratios. Of particular in terest are problems in which the odds ratio regression is a focus. Sim ple assumptions about higher-order conditional moments give a quadrati c exponential likelihood function with second-order estimating equatio ns (GEE2) as score equations. But computational difficulty can arise f or large clusters when both the mean response and the association betw een measures is of interest. First, we present GEE1 as an alternative estimation strategy. Second, we extend to repeated ordinal measurement s the method developed by Carey et al. for binary observations that is based on alternating logistic regressions (ALR) for the marginal mean parameters and the pairwise log-odds ratio parameters. We study the e fficiency-of GEE1 and ALR relative to full maximum likelihood. We demo nstrate the utility of our regression methods for ordinal data by appl ying the methods to a surgical follow-up study.