A robust regression analysis of recruitment in fisheries

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Abstract
Variations in environmental variables and (or) errors in measuring stock and recruitment often result in large and heterogeneous variations in fitting fish stock–recruitment (SR) data to a regression model. This makes the commonly used least squares (LS) method inappropriate in estimating the SR relationship. Hence, we propose the following procedure: (i) identify possible outliers in fitting data to a given SR model using the least median of the squared orthogonal distance that is not sensitive to atypical values and requires no assumption on distribution of errors and (ii) apply the LS method to the SR data with defined outliers being down weighted. We showed by simulation that the SR parameters of the Ricker model could be estimated with smaller estimation errors and biases using the proposed procedures than with the traditional LS approach. Examination of four sets of published field data leads us to suggest fitting fish SR data to suitable models using the proposed estimation method and interpreting the results with the assistance of knowledge on the relevant environmental variables and measurement errors. However, our interpretation should be viewed as a working hypothesis requiring special studies to clarify the causal links between environmental variables and recruitment.

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