Functions to perform stepwise estimations in fixest models.
Details
To include multiple independent variables, you need to use the stepwise functions.
There are 5 stepwise functions: sw, sw0, csw, csw0 and mvsw. Let's explain that.
Assume you have the following formula: fml = y ~ x1 + sw(x2, x3). The stepwise
function sw will estimate the following two models: y ~ x1 + x2 and y ~ x1 + x3.
That is, each element in sw() is sequentially, and separately, added to the formula.
Would have you used sw0 in lieu of sw, then the model y ~ x1 would also have
been estimated. The 0 in the name implies that the model without any stepwise
element will also be estimated.
Finally, the prefix c means cumulative: each stepwise element is added to the next.
That is, fml = y ~ x1 + csw(x2, x3) would lead to the following models y ~ x1 + x2
and y ~ x1 + x2 + x3. The 0 has the same meaning and would also lead to the model
without the stepwise elements to be estimated: in other words,
fml = y ~ x1 + csw0(x2, x3) leads to the following three models: y ~ x1,
y ~ x1 + x2 and y ~ x1 + x2 + x3.
The last stepwise function, mvsw, refers to 'multiverse' stepwise. It will estimate
as many models as there are unique combinations of stepwise variables. For example
fml = y ~ x1 + mvsw(x2, x3) will estimate y ~ x1, y ~ x1 + x2, y ~ x1 + x3,
y ~ x1 + x2 + x3. Beware that the number of estimations grows pretty fast (2^n,
with n the number of stewise variables)!
Examples
base = setNames(iris, c("y", "x1", "x2", "x3", "species"))
# Regular stepwise
feols(y ~ sw(x1, x2, x3), base)
#> Standard-errors: IID
#> Expl. vars.: x1
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 6.526223 0.478896 13.62763 < 2.2e-16 ***
#> x1 -0.223361 0.155081 -1.44029 0.1519
#> ---
#> Expl. vars.: x2
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 4.306603 0.078389 54.9389 < 2.2e-16 ***
#> x2 0.408922 0.018891 21.6460 < 2.2e-16 ***
#> ---
#> Expl. vars.: x3
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 4.777629 0.072935 65.5055 < 2.2e-16 ***
#> x3 0.888580 0.051374 17.2965 < 2.2e-16 ***
# Cumulative stepwise
feols(y ~ csw(x1, x2, x3), base)
#> Standard-errors: IID
#> Expl. vars.: x1
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 6.526223 0.478896 13.62763 < 2.2e-16 ***
#> x1 -0.223361 0.155081 -1.44029 0.1519
#> ---
#> Expl. vars.: x1 + x2
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 2.249140 0.247970 9.07022 7.0385e-16 ***
#> x1 0.595525 0.069328 8.58994 1.1633e-14 ***
#> x2 0.471920 0.017118 27.56916 < 2.2e-16 ***
#> ---
#> Expl. vars.: x1 + x2 + x3
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 1.855997 0.250777 7.40098 9.8539e-12 ***
#> x1 0.650837 0.066647 9.76538 < 2.2e-16 ***
#> x2 0.709132 0.056719 12.50248 < 2.2e-16 ***
#> x3 -0.556483 0.127548 -4.36293 2.4129e-05 ***
# Using the 0
feols(y ~ x1 + x2 + sw0(x3), base)
#> Standard-errors: IID
#> Expl. vars.: x1 + x2
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 2.249140 0.247970 9.07022 7.0385e-16 ***
#> x1 0.595525 0.069328 8.58994 1.1633e-14 ***
#> x2 0.471920 0.017118 27.56916 < 2.2e-16 ***
#> ---
#> Expl. vars.: x1 + x2 + x3
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 1.855997 0.250777 7.40098 9.8539e-12 ***
#> x1 0.650837 0.066647 9.76538 < 2.2e-16 ***
#> x2 0.709132 0.056719 12.50248 < 2.2e-16 ***
#> x3 -0.556483 0.127548 -4.36293 2.4129e-05 ***
# Multiverse stepwise
feols(y ~ x1 + mvsw(x2, x3), base)
#> Standard-errors: IID
#> Expl. vars.: x1
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 6.526223 0.478896 13.62763 < 2.2e-16 ***
#> x1 -0.223361 0.155081 -1.44029 0.1519
#> ---
#> Expl. vars.: x1 + x2
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 2.249140 0.247970 9.07022 7.0385e-16 ***
#> x1 0.595525 0.069328 8.58994 1.1633e-14 ***
#> x2 0.471920 0.017118 27.56916 < 2.2e-16 ***
#> ---
#> Expl. vars.: x1 + x3
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 3.457333 0.309188 11.18199 < 2.2e-16 ***
#> x1 0.399071 0.091110 4.38012 2.2416e-05 ***
#> x3 0.972130 0.052099 18.65937 < 2.2e-16 ***
#> ---
#> Expl. vars.: x1 + x2 + x3
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 1.855997 0.250777 7.40098 9.8539e-12 ***
#> x1 0.650837 0.066647 9.76538 < 2.2e-16 ***
#> x2 0.709132 0.056719 12.50248 < 2.2e-16 ***
#> x3 -0.556483 0.127548 -4.36293 2.4129e-05 ***