Residual-based specification of the random-effects distribution for cluster data

We propose a method for specifying the distribution of random effects included in a model for cluster data. The class of models we consider includes mixed models and frailty models whose random effects and explanatory variables are constant within clusters. The method is based on cluster residuals obtained by assuming that the random effects are equal between clusters. We exhibit an asymptotic relationship between the cluster residuals and variations of the random effects as the number of observations increases and the variance of the random effects decreases. The asymptotic relationship is used to specify the random-effects distribution. The method is applied to a frailty model and a model used to describe the spread of plant diseases.