A model for categorical length data from groundfish surveys

An extension of the multinomial model of counts is presented to account for overdispersion and different correlation structure. Such models are needed in biological applications such as the analysis of length measurements from surveys of heterogeneous populations used for assessments of marine resources. One of the goals of such a survey is to estimate the length distribution of each species within a particular area. Using data on Atlantic cod (Gadus morhua) in Icelandic waters, it is demonstrated that the assumptions used in practice for categorical length data are seriously violated. The length data on cod exhibit variances that are larger than those of the standard multinomial model and correlation coefficients that are greater than those of the Dirichlet-multinomial model. To alleviate these problems, a hierarchical model based on the multinomial distribution and the logistically transformed multivariate Gaussian distribution is proposed. It is illustrated that this model captures the complex covariance structure of the data. The parameters in the models are estimated using a Bayesian estimation procedure based on Markov chain Monte Carlo.