ML Inference in the Presence of Incidental Parameters

This chapter presents methodology to protect the maximum likelihood (ML) estimators of specified parameters from undesirable consequences that might arise from the estimation of other parameters. The mixed-effects analysis includes a demonstration of the integrated likelihood. The approach taken in the chapter is to use a modified form of the likelihood function for inference about ψ. It is desired to obtain a form of likelihood that is a function of ψ alone, and which encapsulates the information about ψ that is present in the (standard) likelihood L(θ). The focus in the chapter is on conditional likelihood, due to its theoretical underpinning and its wide use in mixed-effects modelling where it is more commonly known as restricted maximum likelihood (REML). The chapter presents the paired t-test in the context of modelling paired normally distributed data, and shows that it is an application of conditional inference. Controlled Vocabulary Terms conditional likelihood; incidental parameters; maximum likelihood estimator; REML