An empirical study on estimators for linear regression analyses in fisheries and ecology

Linear regression analysis is often used in fisheries and ecological studies. Parameters in a linear model are estimated by fitting the model to observed fisheries data with assumptions made concerning model error structure. The commonly used estimation method in fisheries and ecology is ordinary least squares (LS) which is based on the Gauss-Markov assumption on the model error. Data observed in fisheries studies are often contaminated by various errors. Outliers frequently arise when fitting models to the data. The model error structure is difficult to define with confidence in fisheries and ecological studies. It is thus necessary to evaluate the robustness of an estimator to assumptions on the model error structure. In this study, we evaluate five estimators, least squares (LS), geometric means (GM), least median of squares (LMS), LMS-based reweighted least squares (RLS), and LMS-based reweighted geometric means (RGM), in fitting linear models with assumptions of different model error structures. We show that the selection of a suitable estimator for a regression analysis depends upon the error structures of the dependent and independent variables. However, overall the LMS-based RGM method tends to be more robust than other estimators to the assumed error structures. We suggest a three-step procedure in analyzing fisheries and ecological data using linear regression analysis: identify outliers by a LMS analysis, evaluate the identified outliers based on background information about the study, and then apply the LMS-based GM where appropriate. The method used in step 3 can be changed if the error structures of observed data are known. (C) 2000 Elsevier Science B.V. All rights reserved.