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bioRxiv · 10.1101/2021.05.03.442487

Fixed or random? On the reliability of mixed-effect models for a small number of levels in grouping variables

Oberpriller, J.·de Souza Leite, M.·Pichler, M.
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Abstract

O_LIBiological data are often intrinsically hierarchical. Due to their ability to account for such dependencies, mixed-effects models have become a common analysis technique in ecology and evolution. While many questions around their theoretical foundations and practical applications are solved, one fundamental question is still highly debated: When facing a low number of levels should we model a grouping (blocking, clustering) variable as a random or fixed effect? In such situation, the variance of the random effect is imprecise, but whether this affects the statistical properties of the population effect is unclear. C_LIO_LIHere, we analyzed the consequences of including a grouping variable as fixed or random effect in the correctly specified and other possible miss-specified models (too simple or too complex models) for data with small number of levels (2 - 8). For all these options, we calculated type I error rates and power. Moreover, we show how these statistical properties change with the study design. C_LIO_LIWe found that the model choice does not influence the statistical properties of the population effect when the effect is the same at all levels However, if an ecological effect differs among levels, using a random slope and intercept model, and switching to a fixed-effect model only in case of a singular fit, avoids overconfidence in the results. Additionally, power and type I error are strongly influenced by the number of and difference between levels. C_LIO_LIWe conclude that inferring the correct random effect structure is of high importance to get correct statistical properties. When in doubt, we recommend starting with the simpler model and using model diagnostics to identify missing components. When having identified the correct structure, we encourage to start with a mixed-effects model independent of the number of levels and switch to a fixed-effect model only in case of a singular fit. With these recommendations, we allow for more informative choices about study design and data analysis and thus make ecological inference with mixed-effects models more robust for small number of levels. C_LI

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Oberpriller, J., de Souza Leite, M., Pichler, M.. 2021-05-04. Fixed or random? On the reliability of mixed-effect models for a small number of levels in grouping variables. https://doi.org/10.1101/2021.05.03.442487

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