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)
#> x.1 x.2 x.3
#> Dependent Var.: y y y
#>
#> Constant 6.526*** (0.4789) 4.307*** (0.0784) 4.778*** (0.0729)
#> x1 -0.2234 (0.1551)
#> x2 0.4089*** (0.0189)
#> x3 0.8886*** (0.0514)
#> _______________ _________________ __________________ __________________
#> S.E. type IID IID IID
#> Observations 150 150 150
#> R2 0.01382 0.75995 0.66903
#> Adj. R2 0.00716 0.75833 0.66679
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Cumulative stepwise
feols(y ~ csw(x1, x2, x3), base)
#> x.1 x.2 x.3
#> Dependent Var.: y y y
#>
#> Constant 6.526*** (0.4789) 2.249*** (0.2480) 1.856*** (0.2508)
#> x1 -0.2234 (0.1551) 0.5955*** (0.0693) 0.6508*** (0.0667)
#> x2 0.4719*** (0.0171) 0.7091*** (0.0567)
#> x3 -0.5565*** (0.1275)
#> _______________ _________________ __________________ ___________________
#> S.E. type IID IID IID
#> Observations 150 150 150
#> R2 0.01382 0.84018 0.85861
#> Adj. R2 0.00716 0.83800 0.85571
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Using the 0
feols(y ~ x1 + x2 + sw0(x3), base)
#> x.1 x.2
#> Dependent Var.: y y
#>
#> Constant 2.249*** (0.2480) 1.856*** (0.2508)
#> x1 0.5955*** (0.0693) 0.6508*** (0.0667)
#> x2 0.4719*** (0.0171) 0.7091*** (0.0567)
#> x3 -0.5565*** (0.1275)
#> _______________ __________________ ___________________
#> S.E. type IID IID
#> Observations 150 150
#> R2 0.84018 0.85861
#> Adj. R2 0.83800 0.85571
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Multiverse stepwise
feols(y ~ x1 + mvsw(x2, x3), base)
#> x.1 x.2 x.3
#> Dependent Var.: y y y
#>
#> Constant 6.526*** (0.4789) 2.249*** (0.2480) 3.457*** (0.3092)
#> x1 -0.2234 (0.1551) 0.5955*** (0.0693) 0.3991*** (0.0911)
#> x2 0.4719*** (0.0171)
#> x3 0.9721*** (0.0521)
#> _______________ _________________ __________________ __________________
#> S.E. type IID IID IID
#> Observations 150 150 150
#> R2 0.01382 0.84018 0.70724
#> Adj. R2 0.00716 0.83800 0.70325
#>
#> x.4
#> Dependent Var.: y
#>
#> Constant 1.856*** (0.2508)
#> x1 0.6508*** (0.0667)
#> x2 0.7091*** (0.0567)
#> x3 -0.5565*** (0.1275)
#> _______________ ___________________
#> S.E. type IID
#> Observations 150
#> R2 0.85861
#> Adj. R2 0.85571
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1