# Logistic regression: Ranking of Betas (Categorical variable)

I am running a logistic regression in Stata and would like to rank a categorical predictor variable (which is translated into four binary variables). Stata gives out three of them and compares them with the fourth which is defined as the standard.

The confidence intervals overlap each other so that I can't easily rank them using the intervals.

Does anyone has an idea how to check if they are significantly different from each other (not only from 0) so that I may rank them?

I heard of two possible ways:

• work with margins (Stata command: margins, dydx): However, there are so many variations of this specific command that I am not sure if it works and if yes, which one would work.

• work with standardized coefficients: The Stata command listcoef is supposed to calculate the Beta values for standardized data. Also here I am not sure which - if any - of the different columns of that output count and how to interpret other values which might change within this output.

• I think you're confusing the p-value, which is a statistic, & not something you can set, with the confidence level, the probability that your upper & lower bounds cover the true value of the coefficient, & which you can set. To get Wald confidence intervals simply multiply the standard error of the coefficient by the appropriate quantile of the Normal distribution & add/subtract from the point estimate. For profile-likelihood confidence intervals using STATA, see stata-journal.com/article.html?article=st0132. – Scortchi - Reinstate Monica Nov 16 '15 at 9:36
• As mentioned in the previous comment, there seems to be confusion in your mind regarding what the p-values mean. Maybe adding more detail to your question might help clarify what you are actually asking. – Arun Jose Nov 16 '15 at 9:44
• Thank you for your comments. You are right, I might be confused. My understanding of the p-value is that it reflects the chance of the values to lie within the confidence intervals. So my conclusion was, that having that in mind and I allow more deviation of the interval, my p-value will increase and my intervals will approach each other. Where is my mistake? Thanks a lot! – Lukas Nov 16 '15 at 10:32
• – Tim Nov 16 '15 at 11:08
• Your understanding is wrong: see e.g. What is the meaning of p values and t values in statistical tests?, Meaning of p-values in regression, Intepreting p-value of a regression coefficient, & What, precisely, is a confidence interval?. Briefly the p-values reported by software after a regression are for the (typically Wald) tests of the null hypotheses that each coefficient is equal to nought. – Scortchi - Reinstate Monica Nov 16 '15 at 11:16