A stepwise-selected spline approximation to time-varying parameters, with application to occupancy modelling
Thorson, JT and Zhou, S and Punt, AE and Smith, ADM, A stepwise-selected spline approximation to time-varying parameters, with application to occupancy modelling, Methods in Ecology and Evolution, 4, (2) pp. 123-132. ISSN 2041-210X (2013) [Refereed Article]
Many population dynamics models and common software packages, including for capture–mark–recapture, occupancy and catch-at-age models, are estimable using parameters that are either constant for all years or vary annually.
We develop a spline approximation to time-varying parameters, which includes the constant or annually varying case as two extremes, where the Akaike Information Criterion is used to select an appropriate degree of smoothness, ranging from change in every year to no change at all. Simulation modelling is used to evaluate the performance of this method relative to constant, annually varying, or random-effect parameter estimates when applied to an occupancy model that simultaneously estimates abundance and detectability in multiple sampling strata. We also demonstrate this method by approximating time-varying abundance using 25 years of detection/non-detection data for 42 Chondrichthyes species off northern Australia.
Simulation modelling indicates that the stepwise-spline approximation results in lower estimation errors for the proportion of abundance in each stratum, regardless of sample sizes, the underlying form for time-varying abundance and the inclusion of unmodelled process errors.
Applied to the Chondrichthyes data from northern Australia, the spline approximation identifies temporal variability in abundance for 34 of 42 species, and an annually varying model is never selected.
We recommend this stepwise-spline approximation in cases where a decision is necessary between constant or annually varying forms for an estimated parameter. Possible applications include occupancy, capture–mark–recapture, catch-at-age and index standardization models.
Akaike Information Criterion, annually varying parameter, Chondrichthys, datapoor, detectability, detection/non-detection data, hierarchical model, presence/absence, stepwise model selection, temporal variability