Linear mixed-effects models for weight–length relationships

Length and weight data are often analyzed in fisheries science to derive a parametric weight–length relationship for estimating biomass and to develop indices of condition for comparing the ‘wellness’ of different populations of fish. However, analysis of such data often ignores the inherent spatial and temporal grouping of the observations, and hence, the data hierarchy. This paper proposes the use of linear mixed-effects models as an effective means of analyzing and comparing weight–length relationships and indices of condition when there are many groups. The use of simple linear regression (where grouping is ignored), ANCOVA (where group effects are incorporated as fixed-effects), and linear mixed-effects models (where group effects are random-effects) are compared using data for Atlantic sea scallops (Placopecten magellanicus). The group means of residuals is proposed as a measure of relative weight or index of population condition. Linear mixed-effects models should be used to analyze grouped data because the variability among groups is ignored in simple linear regression and ANCOVA. Also, it is important that explanatory variables be incorporated in analyses of grouped data because their influence may mask the true differences among groups.