Use of robust regression methods to detect outliers and estimate parameters for Length-Weight relationships in fishes

The most commonly used regression method to analyse Length and Weight data of fishes is Ordinary Least Squares (OLS). The OLS method, however, relies on assumptions that data is normally distributed and free from outliers maybe due to measurement or recording errors. Outliers are often encountered in Length-Weight data and can lead to spurious parameter estimates and potentially erroneous analyses. Robust Regression (RR) is a statistical method that can identify and account for (down-weight) outliers. Using Length-Weight data from 2 species of fishes, we demonstrate the application of RR models and their superior performance over OLS both in identifying outliers, accounting for them and estimating equation parameters. A recently developed RR method called Multiple Options (MO) performed especially well, generating a useful plot for inspection of outlier data. The results of this study suggest that the entire problem of outliers in analysing Length-Weight data can be circumvented by using RR methods. We recommend future studies of Length-Weight relationships in fishes use RR methods to estimate model parameters rather than the OLS method.