Likelihood for random - effect models

For inferences from random-effect models Lee and Nelder (1996) proposed to use hierarchical likelihood (h-likelihood). It allows inference from models that may include both fixed and random parameters. Because of the presence of unobserved random variables h-likelihood is not a likelihood in the Fisherian sense. The Fisher likelihood framework has advantages such as generality of application, statistical and computational efficiency. We introduce an extended likelihood framework and discuss why it is a proper extension, maintaining the advantages of the original likelihood framework. The new framework allows likelihood inferences to be drawn for a much wider class of models. MSC: 62F10 62F15 62F30