# How can I perform all pairwise comparisons of categorical levels in a linear regression with other control variables? [duplicate]

I want to perform a linear regression with some categorical predictor $$z$$ and some other continuous and categorical control variables. I use one-hot dummy encoding for $$z$$, with e.g. $$z_a$$ as the base level and dummies for levels $$z_b, z_c,$$ and $$z_d$$. However, with this regression I can only compare and test the difference between levels $$z_b, z_c,$$ and $$z_d$$ with level $$z_a$$, but not with each other.

To compare $$z_b$$ and $$z_c$$ I could use a new dummy encoding with $$z_b$$ as base level and perform a new regression. For all pair-wise comparisons I could choose each level of $$z$$ as the base level once. Is there an easier way to do this (in Python or R)?

From what I understand, with Tukey's test I can compare all means, but cannot correct for any other variables.