Statistical Modelling of Fish Stocks

Major sources of information for the estimation of the size of the sh stocks and the rate of their exploitation are samples from which the agecomposition of catches may be determined. However, the age-composition in the catches often varies as a result of several factors. Strati cation of the sampling is desirable because it leads to better estimates of the agecomposition and the corresponding variances and covariances. The analysis is impeded by the fact that the response is ordered categorical. The paper introduces an easily applicable method to analyse such data. The method combines continuation-ratio logits and the theory for generalised linear 72 Appendix A. Using Continuation ratio Logits... mixed models. Continuation-ratio logits are designed for ordered multinomial response and have the feature that the associated likelihood splits into separate terms for each category level. Thus, the continuation-ratio logits may be modelled as if they were associated binomial distributions which were independent of each other. Thus, generalised linear mixed models can be applied separately to each level of the logits. The method is illustrated by the analysis of age-composition data collected from the Danish sandeel shery in the North Sea in 1993. The signi cance of possible sources of variations is evaluated and formulae for estimating the proportions of each age group, and their variance-covariance matrix, are derived.