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I am creating a binary logistic regression model with the inputs as a single categorical variable with 100 levels. My goal is to find which level of the categorical variable is most likely to result in the output variable being in class 1 versus class 0.

My original thought process was to hypothesis test each coefficient individually, and perform 99 tests, one for each dummy variable. To maintain my level of confidence I believe this will require me to perform some kind of multiple test correction e.g. Bonferroni correction. With so many levels in this categorical variable, this requires very large coefficients to meet statistical significance. In this scenario, most of my predictors are statistically insignificant.

Alternatively, would it be more valid to consider the categorical variable to be one variable, even though it has 99 dummy variables representing it? Under this scenario, I would test for significance in the overall model, and if this is the case, then I could compare individual coefficients without any test correction. Which is more valid?

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If your sample size is very large you can test the group with 99 degrees of freedom thus obtaining a kind of "perfect" multiplicity adjustment. If this test is not significant it is dangerous to proceed.

But your problem really calls for shrinkage using either penalized maximum likelihood estimation or random effects. Otherwise the categories that are apparently most different from one another will have the differences grossly exaggerated.

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If it makes sense with your data, you can collapse the variable into fewer levels. This would also make it easier to interpret the results.

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