Approximate marginal inference in models with stratum nuisance parameters, with applications to fishery data

Tobin, Jared (2010) Approximate marginal inference in models with stratum nuisance parameters, with applications to fishery data. Masters thesis, Memorial University of Newfoundland.

[English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (9MB)

Abstract

The profile likelihood is commonly used in cases where the maximum likelihood estimator for a shape or dispersion parameter depends on knowledge of the mean. We demonstrate that, in stratified models with many mean parameters, the maximum profile likelihood estimator for a common shape parameter can be severely biased or even inconsistent when the sample size per stratum is low. We note a 'marginal' likelihood function that eliminates these problematic mean parameters, but is usually intractable or even impossible to calculate in practice. We discuss approximations to this marginal likelihood - notably the modified profile likelihood of Barndorff-Nielsen [5], the adjusted profile likelihood of Cox & Reid [16], and quasi-likelihood variants - and demonstrate that estimators based on these functions have better bias properties than those based on the full likelihood. We apply these estimators to a stratified negative binomial model and achieve accurate estimates for the negative binomial dispersion parameter κ in a simulation experiment. Finally, we provide an application of our methods to fishery data.

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