Get p-value for group mean difference without refitting linear model with a new reference level

Question

When we have a linear model with a factor variable X (with levels A, B, and C)

y ~ factor(X) + Var2 + Var3 
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Answer 1

You could use the library car, and use the function linearHypothesis with the parameter vcov.

Set this as the variance-covariance matrix of your model.

The function takes formulas or a matrix to describe the system of equations that you would like to test.