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rconfidence-intervalmarginal-effectsfixestr-marginaleffects
RobertoAS
RobertoAS

Reputation: 89

How marginaleffects::predictions calculates confidence intervals in R?

I am using package marginaleffects in R to get confidence intervals for my predictions of a marginal effect. However, I did some calculations by hand and some of the confidence intervals I am getting with marginaleffects::predictions seem too large. Am I missing something on how these confidence intervals are calculated or is there something weird going on?

I have the following regression model: Y = b_1 endogenous + b_2 endogenous^2 + b_3 controls + error

Because I have endogenous variables, I employ instrument. In terms of code, I use package fixest to estimate the model below:

model <- feols(outcome ~ control1 + control2 + control3 + control4 |
                    fixed_effect1 + fixed_effect2 |
                    endogenous + I(endogenous^2) ~ instrument + I(instrument^2) ,
                  data = dataset,  se = "cluster", cluster = "cluster_id")
Variable Estimate Std. Error
fit_endogenous -0.041626570 0.156600333
fit_I(endogenous^2) 0.037313536 0.264656733
control1 0.003302789 0.001053634
control2 -0.004176099 0.003436881
control3 0.000320232 0.000164557
control4 -0.000000270 0.000000127

Since I am interested in the marginal effect of endogenous, I think I can calculate it by (referring to endogenous by X now): Var(b_1+2Xb_2|X) = Var(b_1) + 4X^2 Var(b_2) + 4X Cov(b_1,b_2|X), which simplifies to Var(b_1+2Xb_2|X) = Var(b_1) when X=0.

Given the values above and taking advantage of the fact that Cov(b_1,b_2|X) <= se_b_1 * se_b_2 , where se_b_1 and se_b_2 are the standard deviations of b_1 and b_2, respectively; I can bound the maximum value of Var(b_1+2Xb_2|X). In particular, for X=0, Var(b_1+2Xb_2|X) = Var(b_1) = 0.156600333^2, which implies that a 95% confidence interval around the marginal effect at 0 should have width 21.960.156600333 = 0.6138733.

When I run marginaleffects::predictions(model, newdata = datagrid(endogenous = c(0, 1))) I get the following output.

radius_500m Estimate Std. Error CI 2.5 % CI 97.5 %
0 9.04 0.165 8.71 9.36
1 9.03 0.203 8.64 9.43

which implies that the width of the 95% confidence interval at X=0 is 9.36-8.71=0.65, which is larger than the 0.6138733 I calculated previously.

What could be causing this? Thanks for your help!

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