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I'm running a GLM with a tweedie, log-link function. That said, I have a categorical variable that transformed to dummy variables leaving off one of those variables when I modeled.

Now that I'm done modeling and constructing a coefficient table with the 95% confidence intervals, how would I get the standard error and confidence intervals for the base level that was left out of the model?

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The "base" level (often called the 'reference level') should not have been left out of the model. It is represented by the intercept. The other levels are typically specified in your output, but those coefficients are not actually the values for those levels, instead they are the differences between the values for the indicated level and the base level. So you should have the information you need, just form a confidence interval for the intercept.

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  • $\begingroup$ I think I misspoke when saying it was left out of the model. What I meant is I left that variable out naturally as I always leave one variable out of my choices of dummy variables. Understand the other variables are actually values relative to the reference level. The intercept’s standard error is unusually large for the variable I’m trying to compute, but not in relation to the mean of the total model. $\endgroup$ – Jordan Aug 26 '19 at 23:29
  • $\begingroup$ @Jordan, when you leave out one variable as you create dummy variables, you in essence make that variable the reference level. Its value is encoded by the intercept. So use that value & its associated standard error to make confidence intervals. $\endgroup$ – gung - Reinstate Monica Aug 27 '19 at 1:28

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