Evaluation of some random effects methodology applicable to bird ringing data

Existing models for ring recovery and recapture data analysis treat temporal variations in annual survival probability (S) as fixed e ects. Often there is no explainable structure to the temporal variation in S-1,..., S-k; random e ects can then be a useful model: S-i = E( S) + epsilon(i). Here, the temporal variation in survival probability is treated as random with average value E(epsilon(2)) sigma(2). This random e ects model can now be fit in program MARK. Resultant inferences include point and interval estimation for process variation, sigma(2), estimation of E(S) and var((E) over cap (S)) where the latter includes a component for sigma(2) as well as the traditional component for (v) over bar ar( (S) over cap\(S) over cap). Furthermore, the random e ects model leads to shrinkage estimates, (S) over tilde (i), as improved (in mean square error) estimators of S-i compared to the MLE, (S) over cap (i), from the unrestricted time-e ects model. Appropriate confidence intervals based on the (S) over tilde (i) are also provided. In addition, AIC has been generalized to random e ects models. This paper presents results of a Monte Carlo evaluation of inference performance under the simple random e ects model. Examined by simulation, under the simple one group Cormack-Jolly-Seber (CJS) model, are issues such as bias of (sigma) over cap (2), confidence interval coverage on sigma(2), coverage and mean square error comparisons for inference about S-i based on shrinkage versus maximum likelihood estimators, and performance of AIC model selection over three models: S-i =S (no e ects), S-i = E(S) + epsilon(i) (random e ects), and S-1,...,S-k (fixed e ects). For the cases simulated, the random e ects methods performed well and were uniformly better than fixed e ects MLE for the S-i.