Modeling Seabird Bycatch in the U.S. Atlantic Pelagic Longline Fishery: A Simulation Study on Random Year Effect Versus Fixed Year Effect

Year is usually modeled as a fixed factor in catch rate standardization or catch/bycatch assessments because the annual variation is of interest. However, question rises when estimation results are sensitive to whether modeling year as a random or fixed factor. With the observer data from the National Marine Fisheries Service Pelagic Observer Program (POP) for the period of 1992-2010, we estimated seabird bycatch using both random-year-effect and fixed-year-effect delta models. We found that annual estimates from the fixed-year-effect models differed substantially for certain years with those from the random-year-effect models and seemed more sensitive to the observer data. We conducted a simulation study to compare the performances of random-year-effect and fixed-year-effect delta models using the observer data.  Four scenarios were constructed, including both true positive catch data and true binary data with year effect; true positive catch data with and true binary data without year effect; true positive catch data without and true binary data with year effect; and both true positive catch data and true binary data without year effect. Four delta models were evaluated under each of the four scenarios, including the delta model with two random-year-effect sub-models for postive catch data and binary data; the delta model with a random-year-effect sub-model for positive catch data and a fixed-year-effect sub-model for binary data; the delta model with a fixed-year-effect sub-model for positive catch data and a random-year-effect sub-model for binary data; and the delta model with two fixed-year-effect sub-models for postive catch data and binary data. We found that the random-year-effect sub-model for positive catch data performed better than the fixed-year-effect sub-model regardless of whether true data had year effect; the random-year-effect sub-model for binary data performed equivalently with the fixed-year-effect sub-model when true data had year effect and better when true data had no year effect; the delta model with two random-year-effect sub-models in overall showed superiority over the other three delta models under the four scenarios. We suggest conduct a simulation study as ours in seabird bycatch assessment, especially in cases where estimates from the random-year-effect and the fixed-year-effect models show great discrepancy.