Abstract
Having recognized that variation around the population-level "Golden Mean" of labile traits contains biologically meaningful information, behavioural ecologists have focused increasingly on exploring the causes and consequences of individual variation in behaviour. These are exciting new directions for the field, assisted in no small part by the adoption of mixed-effects modelling techniques that enable the partitioning of among- and within-individual behavioural variation. It has become commonplace to extract predictions of individual random effects from such models for use in subsequent analyses (for example, between a personality trait and other individual traits such as cognition, physiology, or fitness-related measures). However, these predictions are made with large amounts of error that is not carried forward, rendering further tests susceptible to spurious P values from these individual-level point estimates. We briefly summarize the problems with such statistical methods that are used regularly by behavioural ecologists, and highlight the robust solutions that exist within the mixed model framework, providing tutorials to aid in their implementation.
Highlights
Avoiding the misuse of best linear unbiased predictors (BLUPs) in behavioural ecologyIt has become common practice to extract predictions of individual random effects from fitted mixed models and to use these in subsequent analyses, such as correlation tests or linear regression models (Table 1)
Having recognized that variation around the population-level “Golden Mean” of labile traits contains biologically meaningful information, behavioural ecologists have focused increasingly on exploring the causes and consequences of individual variation in behaviour
We briefly summarize the problems with such statistical methods that are used regularly by behavioural ecologists, and highlight the robust solutions that exist within the mixed model framework, providing tutorials to aid in their implementation
Summary
It has become common practice to extract predictions of individual random effects from fitted mixed models and to use these in subsequent analyses, such as correlation tests or linear regression models (Table 1) Problems arise from this approach because individual point estimates from random effects in mixed models (sometimes known as conditional modes, or best linear unbiased predictors, BLUPs) are predicted with large amounts of error. Their use in secondary analyses can lead to highly anticonservative tests of biological hypotheses, because the error inherent in their prediction is excluded from these further tests (Hadfield et al 2010). Examples in the behavioural literature of questions regarding individual variation in behaviour (“personality”) and behavioural plasticity, using best linear unbiased predictors (BLUPs) in secondary analyses rather than multivariate models
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