ABSTRACT
Inferential methods based on individual estimates and linearization of the model, discussed in Chapters 5 and 6, respectively, are appropriate under the fully parametric model specification given in section 4.3.1. The assumption that the random effects b i in a parametric model for the βi arise from a specific parametric family of distributions, the normal, is fundamental to these techniques. Estimates of the βi obtained using empirical Bayes methods may be quite nonrobust to nonnormality. If the distribution of the random parameters has heavier tails than the normal, or is skewed or multimodal, the ‘shrinkage’ toward the mean is likely to be misleading. The utility of graphical model-building strategies based on empirical Bayes estimates may thus be compromised. Moreover, as discussed in section 4.3.3, identification of misspecified systematic components of the model may be difficult under a restrictive parametric distributional assumption.
