Yes, you can. A dummy variable is no different, mathematically, from any other fixed effect you might choose to include. Presumably, if some of the categories all have the same impact on the response, it would make sense to zero them out and push their effect into the intercept term.

That said, using Wald statistics to cull variables is risky. You may get the right set of variables, but this isn't necessarily the case.

When you say "random slope", are you talking about the coefficient of the categorical variable? If so, I would do some model checking. Look at the estimated random effects and see if they are trying to cover small but real differences in your categories.

To clarify that last point: suppose I have 4 categories: A,B,C and D. I decide to omit the dummies associated with C and D. The intercept in the model now corresponds to the case where categories C or D occur. It's like I'm recoding to A, B and Other. But let's suppose that C and D really are real, but just fairly small.

Now fit the random effects model. You will get random intercepts for individuals coded "Other" ... but if you plot these against the true categories (C and D), you might find that the C effects are large and the D effects are small (say), or vice versa. When you add random effects, you are giving a bunch of extra parameters to your model, which it could use to cover up for defects of the model itself.

## Best Answer

It's just a generalization of the situation with a single multi-category predictor.

The intercept is the estimate when

allsuch predictors are at their reference levels. The regression coefficients for other levels of those predictors are just the associateddifferencesfrom what is estimated at the corresponding reference level.