Robust regression approach to estimating fish mortality rates with a cohort-based model

Natural mortality rate (M) and fishing catchability coefficient (q) were estimated by using the Paloheimo pairwise linear regression model with simulated and real catch-effort data. The four estimation methods used were least squares (LS), least absolute value (LAV), least median of squares (LMS), and LMS-based reweighted least squares (RLS). When catch or effort data or both contained homogeneous error variances, mean squared errors (MSE) of LS and RLS were significantly smaller than those of LAV and LMS. However, there was no significant difference in MSE between LS and RLS. When catch-effort data contained variances inconsistent among years. MSEs of the robust methods were much smaller than those of LS. Reweighted least squares substantially reduced the variances in the LS-estimated q and M. and it had the smallest MSE among the four estimation methods. We suggest using the following procedures in estimating q and M based on the Paloheimo pairwise regression model: (1) applying LMS to the model to identify outliers in the data; and (2) weighting the defined outliers by a factor of 0 and normal data points by a factor of 1 and applying LS to the model to estimate q and M and their associated variances.