The modified profile likelihood function

Abstract In Chapter 8 it was shown that, in some cases, inference about a parameter of interest ψ may be based on a marginal or conditional likelihood function. Those methods are only available however when the model has a particular structure. Furthermore, even when a marginal or conditional likelihood function exists, calculation of the likelihood function is often difficult.In this chapter, we consider the modified profile likelihood, a pseudo-likelihood function that is available for general models. The modified profile likelihood may be derived as an approximation to either a marginal or conditional likelihood when either of those likelihoods exists. Furthermore, the calculation of the modified profile likelihood function does not require the existence of a marginal or conditional likelihood and, hence, it has been adopted for general use.