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.