Generalized log-linear models with random effects, with application to smoothing contingency tables

摘要: We define a class of generalized log-linear models with random effects. For vector Poisson or multinomial means m and matrices constants C A, the model has form log Aμ = Xβ + Zu, where β are fixed effects u The contains most standard currently used for categorical data analysis. suggest some new that special cases this useful applications such as smoothing large contingency tables modeling heterogeneity in odds ratios. present examples its use applications. In many cases, maximum likelihood fitting can be handled existing methods software. outline extensions other cases. also summarize several challenges future research, general deriving properties estimates tables.