Robust Regression Approach to Analyzing Fisheries Data

Abstract

Fisheries data often contain inaccuracies due to various errors, if such errors meet the Gauss–Markov conditions and the normality assumption, strong theoretical justification can be made for traditional least-squares (LS) estimates. However, these assumptions are not always met. Rather, it is more common that errors do not follow the Gauss–Markov and normality assumptions. Outliers may arise due to heterogenous variabilities. This results in a biased regression analysis. The sensitivity of the LS regression analysis to atypical values in the dependent and/or independent variables makes it difficult to identify outliers in a residual analysis. A robust regression method, least median squares (LMS), is insensitive to atypical values in the dependent and/or independent variables in a regression analysis. Thus, outliers that have significantly different variances from the rest of the data can be identified in a residual analysis. Using simulated and field data, we explore the application of LMS in the analysis of fisheries data. A two-step procedure is suggested in analyzing fisheries data.