Random effects models with non-parametric priors.

We discuss the performance of non-parametric maximum likelihood (NPML) estimators for the distribution of a univariate random effect in the analysis of longitudinal data. For continuous data, we analyse generated and real data sets, and compare the NPML method to those that assume a Gaussian random effects distribution and to ordinary least squares. For binary outcomes we use generated data to study the moderate and large-sample performance of the NPML compared with a method based on a Gaussian random effect distribution in logistic regression. We find that estimated fixed effects are compatible for all approaches, but that appropriate standard errors for the NPML require adjusting the likelihood-based standard errors. We conclude that the non-parametric approach provides an attractive alternative to Gaussian-based methods, though additional evaluations are necessary before it can be recommended for general use.