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ICES Journal of Marine Science: Journal du Conseil Advance Access originally published online on August 28, 2008
ICES Journal of Marine Science: Journal du Conseil 2008 65(9):1645-1654; doi:10.1093/icesjms/fsn135
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© 2008 International Council for the Exploration of the Sea. Published by Oxford Journals. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

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

S. Mikkonen1, M. Rahikainen2, J. Virtanen3, R. Lehtonen4, S. Kuikka5 and A. Ahvonen3

1 Department of Physics, University of Kuopio, PO Box 1627, FIN-70211 Kuopio, Finland
2 Department of Economics and Management, University of Helsinki, PO Box 27, FIN-00014 Helsinki, Finland
3 Finnish Game and Fisheries Research Institute, PO Box 6, FIN-00721 Helsinki, Finland
4 Department of Mathematics and Statistics, University of Helsinki, PO Box 68, FIN-00014 Helsinki, Finland
5 Department of Biological and Environmental Sciences, University of Helsinki, PO Box 56, FIN-00014 Helsinki, Finland

Correspondence to S. Mikkonen: tel: +358 17 162319; fax: +358 17 16 2585; e-mail: santtu.mikkonen{at}uku.fi.

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.

Keywords: Baltic herring, catch per unit effort, hierarchical model, hyperdepletion, linear mixed model, longitudinal data

Received 20 August 2007; accepted 12 June 2008; advance access publication 28 August 2008.


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