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I have run a multinomial logistic regression with one dependent variable (category) and 28 independent variables.

In order to compare each category with each category, I run the test 10 times, use the same dependent variable, but each time set one category as the baseline.

So, will this be considered as multiple times of running? Do I need to use Bonferroni correction to adjust p-value? The reviewer asked me to do so but I doubt if it is necessary.

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If you do multiple comparisons (as you seem to do), then there is a multiple comparison problem. If you then want to use p-values or confidence intervals, and want to interpret them (more or less) as usual, then some correction is needed. The Bonferroni correction is very easy to apply, but more problem specific ones can be a lot more efficient.

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  • $\begingroup$ What specific one I can use? The Bonferroni one is way too conservative for the study (which I think is unnecessary). I already used multinomial logistic regression which already adjusted the p-value inflation. It is just I changed the comparison level in the dependent variable for 10 times that I feel is different from traditionally multiple comparisons (it is not I use binomial logistic regression for 10 times with different IV or DV). $\endgroup$ – zyy Jul 10 '17 at 9:32
  • $\begingroup$ I mean, I changed the reference level in the dependent variable. $\endgroup$ – zyy Jul 10 '17 at 9:42
  • $\begingroup$ How many comparisons are you looking at? Just because you do all your comparisons within a single model, does not automatically resolve the multiple comparisons issue, so it is not clear how your multinomial logistic regression has already adjusted for this issue. If you have already done something there, then that may address the reviewer's concerns, if not I share the concerns. Some software will offer you easy access to some options such as resampling based p-values (or based on the joint distribution of test statistics with estimated covariance matrix). $\endgroup$ – Björn Jul 10 '17 at 10:26
  • $\begingroup$ I need to compare the 10 categories with each other. $\endgroup$ – zyy Jul 10 '17 at 11:48

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