Estimating the negative binomial dispersion parameter with highly stratified surveys

We investigate several estimators of the negative binomial (NB) dispersion parameter for highly stratified count data for which the statistical model has a separate mean parameter for each stratum. If the number of samples per stratum is small then the model is highly parameterized and the maximum likelihood estimator (MLE) of the NB dispersion parameter can be biased and inefficient. Some of the estimators we investigate include adjustments for the number of mean parameters to reduce bias. We extend other estimators that were developed for the iid case, to reduce bias when there are many mean parameters. We demonstrate using simulations that an adjusted double extended quasi-likelihood estimator we proposed gives much improved estimates compared to the MLE. Adjusted extended quasi-likelihood and adjusted maximum likelihood estimators also give much-improved results. We illustrate the various estimators with stratified random bottom trawl survey data for cod (Gadus morhua) off the south coast of Newfoundland, Canada.