field | Part 1 | Part2 |
---|---|---|
1 | A | B |
2 | A | B |
3 | A | B |
4 | B | A |
5 | B | A |
6 | B | A |
7 | B | A |
8 | A | B |
9 | A | B |
10 | B | A |
Required number of levels for a random effects
When we analyse a mixed models, the question often arises whether a covariate should be used as a random effect or as a fixed effects. Let’s assume a simple design. Two types of fertilizer are tested on a number of fields (fertiliser
as a fixed effect and field
as a random effect.
While this makes conceptually sense, we might run into computational problems. Instead of estimating each individual field effect, we want to estimate the variability due to field effect. This is the variance of the random effect, rather than the estimates for the individual random effect levels. But how precise is the estimate of this random effect variance? The sample variance
This equation makes it straightforward to calculate the distribution of the
Even when with a large number of levels (
A thousand random effect levels is not always feasible. So what will happen if we use a more realistic number of random effect levels, e.g.
How low can we go? The figure below depicts the density of
Recommendations
We see that the number of random effect levels has a strong impact on the uncertainty of the estimate variance. The figure below displays the 97.5% quantile of
- get
levels when an accurate estimate of the random effect variance is crucial. E.g. when a single number will be use for power calculations. - get
levels when a reasonable estimate of the random effect variance is sufficient. E.g. power calculations with sensitivity analysis of the random effect variance. - get
levels for an experimental study - in case
you should validate the model very cautious before using the output - in case
it is safer to use the variable as a fixed effect.
Session info
These R packages were used to create this post.
─ Session info ───────────────────────────────────────────────────────────────
setting value
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language nl_BE:nl
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date 2023-09-02
pandoc 3.1.1 @ /usr/lib/rstudio/resources/app/bin/quarto/bin/tools/ (via rmarkdown)
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