Quasi-likelihood Estimation of Marked Fish Recapture

Abstract

In models of the fraction of fish recaptured in field experiments on gear efficiency the binomial error distribution is usually assumed. However, variance in excess of that defined by the error distribution (overdispersion) is typical in fish capture because of heterogeneity among and within groups of individuals and incomplete model specification. Quasi-likelihood offers a parsimonious solution to the typical problem of incomplete definition of an error distribution with discrete responses. An example is given from the recapture of marked fish following rotenone treatment in lake enclosures, in which a generalized linear-logistic model includes an extra-binomial variance as a function of the mean. Estimated standard errors of fitted parameters were two to three times lower in a linear-logistic maximum likelihood model than in the quasi-likelihood model because extra-binomial variation (overdispersion) was ignored in the former model. In a cross-validation trial, 95% confidence intervals included 85% of independent observations with the quasi-likelihood model compared with 69% with the maximum likelihood model.