ML Inference in the Presence of Incidental Parameters
Russell Brian Millar · 2011
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