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questions about firthlogit

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Hello, my dependent variable is binary and I am running models using the firthlogit command. My total sample size is over 3,000, but there are only 28 people in the "1" category. I have a few questions:

1. I have compared different models using AIC and BIC (using the firthfit command), and my "best" model has 10 variables, most of which are categorical (note: if you include each dummy variable in the count, then there are 33 variables in total). This model consists of variables that are either statistically significant or are not statistically significant but removing them would lead to a worse value of BIC or AIC. My question is: does this model have too many variables? If so, how should I proceed in removing variables?

2. I noticed that when using this command, there are quite a few variables that are statistically significant, even with small numbers of people in some of the groups. Does this make sense?

3. There are a number of R^2 values that come after firthfit. Is there one that is generally considered to be the best one to use?

Many thanks in advance for any advice!
Caroline


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