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

Question

I am going through an R example of using interaction terms in a fixed effect model. The example can be found here.

The example uses the fixest package and uses the syntax var::fe(ref). I don't understand what ref is and what it does here. How do I select the value for ref?

I have come across this explanation on Google: "You can interact a numeric variable with a "factor-like" variable by using i(factor_var, continuous_var, ref), where continuous_var will be interacted with each value of factor_var and the argument ref is a value of factor_var taken as a reference (optional)." - I do not understand the role of this "reference" here.

Any insight will be highly appreciated.

score 2 · Accepted Answer · answered Sep 10 '22 at 02:25

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)

	Model 1	Model 2	Model 3
(Intercept)	26.771696	26.771696	13.796313
	(8.719507)	(8.719507)	(5.057123)
drat	1.939525	1.939525	1.939525
	(1.646230)	(1.646230)	(1.646230)
factor(cyl)6	-12.041741
	(7.883606)
factor(cyl)8	-12.975383
	(6.689497)
hp	-0.096854	-0.023706	-0.023706
	(0.047378)	(0.018221)	(0.018221)
factor(cyl)6 × hp	0.080976
	(0.071010)
factor(cyl)8 × hp	0.073149
	(0.052855)
cyl = 6		-12.041741	0.933642
		(7.883606)	(7.341465)
cyl = 8		-12.975383
		(6.689497)
hp × cyl = 4		-0.073149	-0.073149
		(0.052855)	(0.052855)
hp × cyl = 6		0.007828	0.007828
		(0.053174)	(0.053174)
cyl = 4			12.975383
			(6.689497)
Num.Obs.	32	32	32
R2	0.799	0.799	0.799
R2 Adj.	0.751	0.751	0.751
AIC	169.4	169.4	169.4
BIC	181.1	181.1	181.1
Log.Lik.	-76.677
F	16.601
RMSE	2.66	2.66	2.66
Std.Errors		IID	IID

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

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