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.
- 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?
- 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.