# An idea for multinomial logit model

I am running a multinomial logistic regression. I have a sample size of 500.

I regressed the four categories/segments (A, B, C, D) on several independent variables including the intercept, setting A as the reference category, thus using the normal procedure. I understand that I have to interpret the estimated results for each segment B, C, and D in relation to the reference segment A. However, the respective interpretation is somehow hard, not intuitive, and partly confusing. It also makes it more difficult to understand the specifics of a group relative to the whole sample. However, that is what I would like to discuss.

Here I got an idea about analyzing the multinomial logit model differently and would like to know your opinions: I keep my four segments and add a fifths segment. This 5th segment (segment E) is the sum of all four segments. Thus, I duplicate the entire sample. I run a multinominal regression analysis on the (new) sample (N=1000 including the original A, B, C, and D categories as well as the extra category E) setting the category E as the reference group. In this case, I can interpret the obtained results for each of the segments A, B, C, D relative to the whole sample (category E). While this is very convenient/intuitive from an interpretation point of view I wonder whether there is anything wrong with that procedure from a methodological/econometrics point of view.

Let me stress again. Each observation in my model would occur twice, once in either group A, B, C or D and once in E. E is the aggregate of A, B, C and D. In the multinomial logistic regression I would use this aggregate as the reference category.

Not all software will offer that to you, but if your software lets you specify your own log-likelihoods, you can always specify this yourself by having free parameters $\beta_1, \beta_2, \beta_3$ and specifying $\beta_4=-(\beta_1 + \beta_2 + \beta_3)$.