Discussion comments on: the use of auxiliary variables in capture-recapture modelling. An overview

The incorporation of auxiliary variables into capturerecapture models provides the biologist the opportunity to explore many biological hypotheses, and thus provides a powerful technique for extending the analysis of encounter history data. However, cause-and-eþ ect relationships cannot be gained without experimental manipulation of the system. That is, even though an auxiliary variable in a capturerecapture model may provide a good predictor of survival, unless the auxiliary variable is part of a manipulative investigation, the relationship is only correlative and lacks the stronger frame of inference provided by experimental manipulation. Opportunities to incorporate covariates into designed, manipulative experiments should not be declined. The Achilles’ heel of using auxiliary variables in capturerecapture modelling is assessing goodness-of-® t. With the procedures presented by Burnham & Anderson (1998), quasi-likelihood approaches are used for model selection and for adjustments to the variance of the estimates to correct for over-dispersion of the capturerecapture data. An estimate of the over-dispersion parameter, c, is necessary to make these adjustments. However, no general, robust, procedures are currently available for estimating c. Although much of the goodness-of® t literature concerns testing the hypothesis of lack of ® t, I instead view the problem as estimation of c. Logistic regression also su þ ers from the detriment of no generally robust methodology to estimate c. The goodness-of® t procedure derived from likelihood theory suggests the deviance of the model is chi-square distributed with degrees of freedom equal to sample size of the data minus the number of estimated parameters