Using cross validation model selection to determine the shape of nonparametric selectivity curves in fisheries stock assessment models

We used hold-out cross validation model selection to determine the most appropriate form of the selectivity curve, using a nonparametric approach to represent selectivity. The cross-validation method is based on setting aside a portion of the catch-at-age (or catch-at-length) data to use as a test data set. The remaining catch-at-age data, along with other data (e.g. relative indices of abundance) are used to estimate the parameters of the stock assessment model, including the selectivity parameters. These parameter estimates are then used to predict the catch at age for the test data set. The selectivity model that produces the closest predictions to the test data set is chosen as the selectivity model to use in the assessment. The selectivity model we use is nonparametric, based on estimating an individual selectivity parameter for each age and then applying smoothness penalties to constrain how much the selectivity can change from age to age. The smoothness penalties we consider are the first, second, and third differences, a length-based penalty, and a monotonic penalty. The penalties are applied on the logarithm of selectivity to avoid scale-related problems and improve stability. The method was applied to the assessment of bigeye tuna in the eastern Pacific Ocean. We found that the estimated management quantities were relatively robust within the set of smoothness penalties that gave low cross-validations scores. We also found that poor choices for the smoothness penalties could give very different results. Poor choices include both under-smoothing (e.g. no penalties) and over-smoothing (penalties that are too large). The most influential factor was the inclusion of a monotonic penalty.