What is ref in fixest's feols used for fixed-effect estimation?

When you estimate a model with a categorical predictors entered as a series of dummy variables or, equivalent, a fixed effects models, you must always omit one of the dummies to avoid perfect collinearity. The dummy you omit is the “reference category”.

The choice of reference category is arbitrary, it does not change the predictions of the model, but it does affect how you interpret the coefficients of the remaining dummy variables. This is well-known, and in most regression intro textbooks.

In fixest, you can use the ref argument of the i() function to determine which category will be omitted. Below, you will see that the drat coefficient stays exactly the same, but that the other coefficients change because the reference category changes:

library(fixest)
library(modelsummary)

mod1 <- lm(mpg ~ drat + factor(cyl) * hp, data = mtcars)
mod2 <- feols(mpg ~ drat + hp * i(cyl), data = mtcars)
#> The variable 'hp:cyl::8' has been removed because of collinearity (see $collin.var).
mod3 <- feols(mpg ~ drat + hp * i(cyl, ref = 8), data = mtcars)
models <- list(mod1, mod2, mod3)

modelsummary(models, fmt = 6)