A linear mixed model with temporal covariance structures in modelling catch per unit effort of Baltic herring

Mikkonen, S., Rahikainen, M., Virtanen, J., Lehtonen, R., Kuikka, S., and Ahvonen, A. 2008. A linear mixed model with temporal covariance structures in modelling catch per unit effort of Baltic herring. – ICES Journal of Marine Science, 65: 1645–1654. Changes in the structure and attributes of a fleet over time will break down the proportionality of catch per unit effort (cpue) and stock biomass. Moreover, logbook data from commercial fisheries are hierarchical and autocorrelated. Such features not only complicate the analysis of cpue data but also seriously limit the application of a generalized linear model approach, which nevertheless is applied commonly. We demonstrate a linear mixed model application for a large hierarchical dataset containing autocorrelated observations. In the analysis, the key idea is to explore the properties of the error term of the model. We modified the residual covariance matrix, allowing the introduction of assumed fisher behaviour, influencing the catch rate. Fisher behaviour consists of accumulated knowledge and learning processes from their earlier area- and time-specific catch rates. Also, we investigated the effects of vessel-specific parameters by introducing random intercepts and slopes in the model. A model with the autoregressive moving average residual covariance matrix structure was superior over the block-diagonal and autoregressive (AR1) structure for the data, having a time-dependent correlation among trawl hauls. The results address the benefits of statistically advanced methods in obtaining precise and unbiased estimates from cpue data, to be used further in stock assessment. Fisheries agencies are encouraged to monitor the relevant vessel and gear attributes, including engine power and gear size, and the deployment practices of the gear.