Monte Carlo modified profile likelihood for panel data models
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The main focus of the analysts who deal with panel data is usually not on the clustering variables, and hence the group-specific parameters are treated as nuisance. If a fixed effects formulation is preferred and the total number of clusters is large relative to the single-stratum sizes, classical frequentist techniques relying on the profile likelihood are often misleading. The use of alternative tools, such as modifications to the profile likelihood or integrated likelihoods, for making accurate inference on a parameter of interest can be complicated by the presence of nonstandard modelling and/or sampling assumptions. We show here how to employ Monte Carlo simulation in order to approximate the modified profile likelihood in some of these unconventional frameworks. The proposed solution is widely applicable and retains the usual properties of the modified profile likelihood. The effectiveness of the approach is examined, in particular, for missing data models and survival models with unspecified censoring distribution, via simulation studies and one application to an HIV clinical trial.
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