# partialling.out [](https://lifecycle.r-lib.org/articles/stages.html#experimental) [](https://CRAN.R-project.org/package=partialling.out) [](https://app.codecov.io/gh/ropensci/partialling.out) [](https://github.com/ropensci/partialling.out/actions/workflows/R-CMD-check.yaml) [](https://github.com/ropensci/software-review/issues/703) 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` (`lfe`package) and `feols` (`fixest` package) for applications of the Frisch-Waugh-Lovell theorem, as explained in Lovell ([2008](doi:10.3200/JECE.39.1.88-91)). Whereas this algorithm has already been implemented in [`fwlplot`](https://github.com/kylebutts/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. ## Using the Frisch-Waugh-Lovell theorem The Frisch-Waugh-Lovell theorem states that for a linear model ``` math Y = X_1 \beta_1 + X_2 \beta_2 + u ``` The coefficient  will be equivalent to the coefficient, , from the regression of ``` math M_{X_2} Y = M_{X_2} X_1 \beta_1 + M_{X_1} u ``` Where  are the residuals of the regression of  on  and  are the residuals of the regression of  on .
This theorem is designed to help simplifying linear and, particularly, fixed effects models for easier visualisation and interpretation, transforming a multiple regression into a simple one that can be easily visualised via a scatterplot or further used in other models. ## Installation The package can be installed with: ``` r install.packages("partialling.out") ``` You can install the development version of partialling.out from [GitHub](https://github.com/) with: ``` r # install.packages("pak") pak::pak("marcboschmatas/partialling.out") ``` Or, from R-Universe with ``` r install.packages("partialling.out", repos = c('https://ropensci.r-universe.dev', 'https://cloud.r-project.org')) ``` ## Examples The workflow for `partialling.out` is rather simple: first, create a linear or fixed effects model. ``` r library(partialling.out) library(tinytable) 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. ``` r modely <- lm(bill_length_mm ~ species, data = penguins) modelx <- lm(bill_depth_mm ~ species, data = penguins) ``` ``` r 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 As stated above, if we follow following the Frisch-Waugh-Lovell theorem 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. ``` r 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](https://github.com/ropensci/partialling.out/blob/main/.github/contributing.md) Please note that this package is released with a [Contributor Code of Conduct](https://ropensci.org/code-of-conduct/). By contributing to this project, you agree to abide by its terms. ## Acknowledgements To the authors of the [fwlplot](https://github.com/kylebutts/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. To the ROpensci editors Mark Padgham and Nima Hejazi and to the reviewers Christian Testa, Kyle Butts, and Adam Loy.