Should I use fixed effects or random effects when I have fewer than five levels of a grouping factor in a mixed-effects model?

Abstract

As linear mixed-effects models (LMMs) have become a widespread tool in ecology, the need to guide the use of such tools is increasingly important. One common guideline is that one needs at least five levels of the grouping variable associated with a random effect. Having so few levels makes the estimation of the variance of random effects terms (such as ecological sites, individuals, or populations) difficult, but it need not muddy one’s ability to estimate fixed effects terms—which are often of primary interest in ecology. Here, I simulate datasets and fit simple models to show that having few random effects levels does not strongly influence the parameter estimates or uncertainty around those estimates for fixed effects terms—at least in the case presented here. Instead, the coverage probability of fixed effects estimates is sample size dependent. LMMs including low-level random effects terms may come at the expense of increased singular fits, but this did not appear to influence coverage probability or RMSE, except in low sample size (N = 30) scenarios. Thus, it may be acceptable to use fewer than five levels of random effects if one is not interested in making inferences about the random effects terms (i.e. when they are ‘nuisance’ parameters used to group non-independent data), but further work is needed to explore alternative scenarios. Given the widespread accessibility of LMMs in ecology and evolution, future simulation studies and further assessments of these statistical methods are necessary to understand the consequences both of violating and of routinely following simple guidelines.

Keywords

• Statistics
• Hierarchical modelling
• Block-design
• Experimental design
• Varying effects
• Quantitative