partialling.out

Partialling out is a package that allows to generate residualised variables of already existing linear or fixed effects models. So far it works with lm, felm (lfepackage) and feols (fixest package) for applications of the Frisch-Waugh-Lovell theorem, as explained in Lovell (2008). Whereas this algorithm has already been implemented in fwlplot, this package offers three new characteristics.

• It uses an already existing model instead of a formula.

• Works with lm and felm objects alongside feols.

• Returns a data.frame with residualised variables instead of a plot, thus offering more freedom of what to do with the results.

Installation

You can install the development version of partialling.out from GitHub with:

# install.packages("pak")
pak::pak("marcboschmatas/partialling.out")

Examples

The workflow for partialling.out is rather simple: first, create a linear or fixed effects model.

library(partialling.out)
library(tinytable)
library(tinyplot)
library(palmerpenguins)

model <- lm(bill_length_mm ~ bill_depth_mm + species, data = penguins)
summary(model)
#> 
#> Call:
#> lm(formula = bill_length_mm ~ bill_depth_mm + species, data = penguins)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -8.0300 -1.5828  0.0733  1.6925 10.0313 
#> 
#> Coefficients:
#>                  Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)       13.2164     2.2475    5.88 9.83e-09 ***
#> bill_depth_mm      1.3940     0.1220   11.43  < 2e-16 ***
#> speciesChinstrap   9.9390     0.3678   27.02  < 2e-16 ***
#> speciesGentoo     13.4033     0.5118   26.19  < 2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 2.518 on 338 degrees of freedom
#>   (2 observations deleted due to missingness)
#> Multiple R-squared:  0.7892, Adjusted R-squared:  0.7874 
#> F-statistic: 421.9 on 3 and 338 DF,  p-value: < 2.2e-16

Using the partialling_out function, you can get the residualised variable of interest (bill length) and of the first explanatory variable (bill_length), i.e. it would return the residuals of the following two regressions.

modely <- lm(bill_length_mm ~ species, data = penguins)
modelx <- lm(bill_depth_mm ~ species, data = penguins)

res <- partialling_out(model, data = penguins)

tt(head(res)) |>
  format_tt(digits = 2) |>
  style_tt(align = "c")

res_bill_length_mm	res_bill_depth_mm
0.31	0.35
0.71	-0.95
1.51	-0.35
-2.09	0.95
0.51	2.25
0.11	-0.55

Checking the results

The Frisch-Waugh-Lovell theorem states that for a linear model

Y = X_1 \beta_1 + X_2 \beta_2 + u

The coefficient \hat{\beta}_1 will be equivalent to the coefficient, \tilde{\beta}_1, from the regression of

M_{X_2} Y = M_{X_2} X_1 \beta_1 + M_{X_1} u

Where M_{X_2} Y are the residuals of the regression of Y on X_2 and M_{X_2}X_1 are the residuals of the regression of X_1 on X_2.

Accordingly, the coefficient of res_bill_depth_mm in the model lm(res_bill_length_mm ~ res_bill_depth_mm) will be the same of the coefficient of bill_depth_mm in the original model.

resmodel <- lm(res_bill_length_mm ~ res_bill_depth_mm, data = res)

print(c(model$coefficients[2], resmodel$coefficients[2]))
#>     bill_depth_mm res_bill_depth_mm 
#>          1.394011          1.394011

Contributing

Contributing instructions can be found here

Acknowledgements

To the authors of the fwlplot package, Kyle Butts and Grant McDermott, which has provided inspiration and ideas for this project.

To my colleague Andreu Arenas-Jal for his insight and guiding.