Heteroscedastic and Homoscedastic GLMM and GLM: Application to Effort Estimation in the Gulf of Mexico Shrimp Fishery, 1984 through 2001

摘要

This article presents an overview of the homoscedastic and heteroscedastic Generalized Linear Mixed Model (GLMM) and General Linear Model (GLM). Mathematical relations are defined which map categorical variables onto continuous covariates. It is shown that these relations can be used for different purposes including the addition of pairwise interactions and higher order terms (such as nested terms) to the models. The impacts of these relations on 1984 through 2001 shrimp efforts data in the Gulf of Mexico (GOM), year by year or all years together are compared in the paper. These data sets are also checked for possible heteroscedasticity using Breusch-Pagan and the White’s test. It was observed that these data sets show some degree of the heteroscedasticity. The method of weighted least square (WLS) was applied to these data sets and shrimp efforts were estimated before and after the corrections for the heteroscedasticity were made. In addition, it was shown that both the GLMM and the GLM represent these data sets in a satisfactory manner. Efforts generated via a GLMM and a GLM for both homoscedastic and heteroscedastic models showed that although each data set was heteroscedastic, the severity of the heteroscedasticity was compromised when the data sets 1984 through 2001 were compared.