NPML estimation of the mixing distribution in general statistical models with unobserved random effects

Abstract

General maximum likelihood computational methods have recently been described for longitudinal analysis and related problems using generalized linear models. These developments extend the standard methods of generalized linear modelling to deal with overdispersion and variance component structures caused by the presence of unobserved random effects in the models. The value of these methods is that they are not restricted by particular statistical model assumptions about the distribution of the random effects, which if incorrect might invalidate the conclusions. Despite this generality these methods are fully efficient, in the sense that the model is fitted by (nonparametric) maximum likelihood, rather than by approximate or inefficient methods. The computational implementation of the methods is straightforward in GLM packages like GLIM4 and S+.

An important feature of these computational methods is that they are applicable to a much broader class of models than the GLMs described above, and provide new general computational solutions to fitting a very wide range of models using latent variables.