# Interpreting categorical variable if reference class includes several levels

I have a dataset with several categorical variables. I have been running some regressions and used dummy coding for these categorical variables. The problem is that some specifications lead to perfect collinearity between a few vars when including all (but one) levels of a categorical variable of interest. Thus I need to omit two levels instead of one.

For instance, suppose variable $$x_1$$ is categorical and has four levels. Including the first three levels as dummies leads to perfect collinearity between the third level and variable $$x_2$$. Thus, the third level of $$x_1$$ is dropped for modeling purposes. Then variable $$x_1$$ has two instead of one reference levels.

This leads to statistically significant results, but I am not sure it is correct to do this at all. If so, is there any proper way to interpret the results?

• Welcome. You may not have a problem at all. What do these variables represent? Do you have any output to share? May 24 '21 at 23:50