Comparison of model building and selection strategies

One challenge an analyst often encounters when dealing with complex mark–recapture models is how to limit the number of a priori models. While all possible combinations of model structures on the different parameters (e.g., ϕ, p) can be considered, such a strategy often results in a burdensome number of models, leading to the use of ad hoc strategies to reduce the number of models constructed. For the Cormack–Jolly–Seber data type, one example of an ad hoc strategy is to hold a general ϕ model structure constant while investigating model structures on p, and then to hold the resulting best structure on p constant and investigate structures on ϕ. Many comparable strategies exist. The effect of following ad hoc strategies on parameter estimates as well as for variable selection and whether model averaging can ameliorate any problems are unknown. By means of a simulation study, we have investigated this informational gap by comparing the all-combinations model building strategy with two ad hoc strategies and with truth, as well as considering the results of model averaging. We found that model selection strategy had little effect on parameter estimator bias and precision and that model averaging did improve bias and precision slightly. In terms of variable selection (i.e., cumulative Akaike’s information criterion weights), model sets based on ad hoc strategies did not perform as well as those based on all combinations, as less important variables often had higher weights with the former than with the all possible combinations strategy. Increased sample size resulted in increased variable weights, with an infinite sample size resulting in all variable weights equaling 1 for variables with any predictive influence. Thus, the distinction between statistical importance (dependent on sample size) and biological importance must be recognized when utilizing cumulative weights. We recommend that all-combinations model strategy and model averaging be used. However, if an ad hoc strategy is relied upon to reduce the computational demand, parameter estimates will generally be comparable to the all-combinations strategy, but variable weights will not correspond to the all-combinations strategy.