# What to do in a multinomial logistic regression when all levels of DV are of interest?

I am running a multinomial logistic regression. The outcome variable is categorical with seven levels. The predictor is binary.

Very briefly, the experiment is such that I am asking whether a stimulus belonging to level A or B of the predictor makes a person's response more likely to belong to any of the seven levels of the dependent variable.

However, I am interested in the effect of the predictor on the likelihood of choose each of the sevev levels of the DV. This is troublesome because I know that one level of the dependent variable has to be treated as a reference case.

What should I do? Is there a way to still discern the effect of the predictor on the likelihood of choosing the reference category? Is it common practice to run and report the analysis with different levels being treated as the reference?

• "Effect of the predictor" relative to what? Isn't that the basic statistical lesson to be drawn from the mathematical need for a reference case: that without it, the meaning of "effect" is indeterminate? Nevertheless, if you have only a single categorical regressor, why not just use effects coding for it? – whuber Jun 13 '17 at 21:48
• If I were to use effects coding instead of dummy coding for the predictor, would that give me a result for each level of the dependent variable? – Dave Jun 13 '17 at 22:01
• That indeed is the point of effects coding: the coefficients are interpreted as individual effects relative to an average. You can also code each level of the predictor with a binary indicator and simply leave out the constant term (which is the sum of all the binary indicators). – whuber Jun 13 '17 at 22:03
• A single binary predictor isn't much to work with. I would start with a 2-way table as a much more straightforward approach. In this discussion-in-comments I think the role of your variables is getting confused. To be clear, Dave, your dependent/response variable is categorical with 7 unordered possibilities? And your only independent predictor variable is binary? – Gregor Thomas Jun 13 '17 at 22:08
• In the first place, why do you want to estimate this model? Having a binary predictor to predict 7 events sounds "over killed" - A simple cross-tabulation would do the job. – Umka Jun 13 '17 at 22:14