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I'm implementing a multilevel logistic regression model in R to predict a binary courtroom decision with 8 categorical and 7 numerical predictors. I believe a multilevel model to be appropriate because each observation (defendant) is nested within judges. There are a few questions I have that I can't seem to find discrete answers to.

  1. There are 18 different judges, so the number of level-2 groups is 18. I have read in multiple scholarly sources that 30 or 50 groups are needed for unbiased fixed-effect parameters and Type 1 error rates. McNeish and Stapleton (2016) suggest these three fixes: (a) RPL variance component, (b) Kenward-Roger adjustment, and (c) bootstrapping. Is J=18 acceptable? How can I use R to determine if the small number of groups produces biased estimates? If 18 is too few level-2 groups, how do I address this in the model? What R packages or commands can I use to fix this?
  2. The judges themselves are nested within two neighboring counties in the same state in the US. I believe I have four options: (a) I could do two separate models for each county, (b) make the multilevel model have three levels, (c) add COUNTY as a level-1 predictor, or (d) ignore COUNTY altogether. There are 2403 observations in County A (6 judges in County A) and 1137 observations in County B (12 judges in County B). How do I know which option is best?

I have background in statistics, but a lot of the more complicated stuff goes over my head. I am quite familiar with R, but I would sincerely appreciate commands and their explanation so I understand what's going on. I am very grateful for your help.

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    $\begingroup$ I should add that I've been using the glmer() function in the lme4 package. $\endgroup$ Jun 23, 2023 at 15:17

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Regarding both questions, Gomes (2022) investigated this age-old issue, and suggested that variables could be used as grouping factors even if they have less than five levels, as long as the interest is not in the random effects but rather in the fixed effects.

Based on the above reference, as well as Brauer and Curtin (2018) and other references cited in these papers, it seems that 18 levels is often acceptable. Two levels, on the contrary, would be more contentious. Therefore, the option of including COUNTY as a fixed effect seems very reasonable to me.

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