Estimating relative efficiency from paired-count data with over-dispersion, with application to fishery survey calibration studies

In many of the multi-species trawl surveys conducted by Fisheries and Oceans Canada, the survey vessel "Wilfred Templeman" (WT) may be replaced by the vessel "Alfred Needier" (AN). We examined paired-trawl experiments involving these two vessels to examine for differences in catchability. In particular, we examine for differences in catchability of the Witch flounder species. -- The relative efficiency of the AN compared to the WT is defined as the ratio of the means from both trawl catches. Four models are investigated in this thesis, Conditional Poisson (i.e. Binomial), Mixed Binomial, Negative Binomial and Conditional Negative Binomial. When catch data are Poisson distributed, the approach is clear and well-developed. However, over-dispersion creates problems, and over-dispersion is common in many types of data including fisheries data. -- We dealt with the over-dispersion problem using the Negative Binomial distribution to model the paired-counts instead of the Poisson distribution. We develop Conditional Negative Binomial (Conditional NB) and Concentrated Negative Binomial (Concentrated NB) models for estimating relative efficiency. We compared estimates with those from the more commonly used approaches involving standard logistic regression and also a mixed binomial regression model. We found that the Conditional NB and mixed binomial models performed better. -- Our results suggest that there were no significant differences in the relative catchability of the two vessels, based on the Mixed Binomial and Conditional NB models.