Evaluation of the Kullback‐Leibler Discrepancy for Model Selection in Open Population Capture‐Recapture Models

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Abstract
The objective of this paper is to introduce the logical basis of AIC‐based model selection to persons analyzing capture‐recapture data and to explore the key theorettical aspect of AIC based model selection, for open‐model capture‐recapture, needed for AIC to perform well in this context. Almost all previous work on AIC assumes a Gaussian model; that assumption does not hold for capture‐recapture models. Assuming the Cormack‐Jolly‐Seber model as the true model, we used numerical methods to evaluate the expectation of the log‐likelihood relative to Akaike's target predictive log‐likelihood. The use of this particular target criterion was motivated by the idea of using the Kullback‐Leibler discrepancy for model selection, for which Akaike found the bias of the sample log‐likelihood was asymptoticallyK, whereK= the number of estimated (by MLE) parameters. In some sense, then, AIC is a bias‐adjusted log‐likelihood. For a set of 81 plausible cases, we evaluated this bias almost exactly. The ratio of this bias to the first order theory (bias ofK) and to second order theory (K+ a sample size adjustment) is essentially 1 for these 81 cases. Thus, AIC should be a suitable basis for model selection in open model capture‐recapture.