In mattblackwell/qsslearnr: Learnr tutorials based on Quantitative Social Science

library(gradethis)
library(learnr)
library(qsslearnr)
library(tidyverse)
library(modelr)
tutorial_options(exercise.checker = gradethis::grade_learnr)
knitr::opts_chunk$set(echo = FALSE)
tut_reptitle <- "QSS Tidyverse Tutorial 6: Output Report"
n <- 10
data(progresa, package = "qss")

Extending Linear Regression

Conceptual questions

quiz(caption = "",
     question("How can regression models be used to draw causal inference?",
              answer("by predicting counterfactual outcomes", correct = TRUE),
              answer("by randomizing outcomes"),
              answer("by fitting a line")),
     question("Even if the average treatment effect is positive, the same treatment may not affect everyone in the positive direction. This is an example of:",
              answer("heterogenous treatment effects", correct = TRUE),
              answer("homogenous treatment effects"),
              answer("both of these"))
     )

First regression

Today we will use a data set designed to investigate the impact of Mexico's conditional cash transfer program, Progresa, on political outcomes such as voter turnout. See Section 4.5.2 in QSS for more information on this study. We have loaded the progresa data into this tutorial session. First, run a regression of turnout (t2000) on treatment status (treatment) to get a sense for the estimated effect of receiving the program earlier versus later. Save the regression to the object fit and print that object.

fit <- lm(_y_ ~ _x_, data = _dataname_)
fit

grade_result(
  pass_if(~ isTRUE(all.equal(.result, lm(t2000 ~ treatment, data = progresa)))),
  pass_if(~ isTRUE(all.equal(.result, lm(progresa$t2000 ~ progresa$treatment, data = progresa))),
          "Right! Remember that when you pass the `data` argument, you don't need to explicitly refer to the data frame in the formula."),
  pass_if(~ isTRUE(all.equal(.result, lm(progresa$t2000 ~ progresa$treatment))),
          "Good job! You might try using the `data` argument next time.")
)

Coefficients

• A coefficient tells you the estimated effect of $x$ on $y$ in your fitted model. You can use the coef function to view the coefficient(s) and the intercept.

fit <- lm(t2000 ~ treatment, data = progresa)

fit <- lm(t2000 ~ treatment, data = progresa)

coef(fit)

grade_code()

Add predictions and residuals to the original data set

• Besides the coefficients, predicted values and residuals also give us a sense of our fitted model. It is sometimes useful to add them to the original data set as new columns so plots can be made more easily. This can be done by the add_predictions and add_residuals functions. Let's experiment with add_predictions first, and then view the variables in progresa by the glimpse function.

fit <- lm(t2000 ~ treatment, data = progresa)

# Pass your fitted model to the add_predictions function
progresa <- progresa %>%
  add_predictions(_model_) 

# View the variables in progresa 

fit <- lm(t2000 ~ treatment, data = progresa)

progresa <- progresa %>%
  add_predictions(fit) 

glimpse(progresa)

grade_code()

• Then do the same with the add_residuals function, and view with glimpse.

fit <- lm(t2000 ~ treatment, data = progresa)

progresa <- progresa %>%

# View the variables in progresa 

fit <- lm(t2000 ~ treatment, data = progresa)

progresa <- progresa %>%
  add_residuals(fit)

glimpse(progresa)

grade_code()

Add another covariate

Now, add the variable avgpoverty as an additional control variable to the regression (saving it as fit_2var) and print that new model.

fit_2var <- lm(t2000 ~ treatment + avgpoverty, data = progresa)
fit_2var

grade_result(
  pass_if(~ isTRUE(all.equal(.result, lm(t2000 ~ treatment + avgpoverty, data = progresa)))),
  pass_if(~ isTRUE(all.equal(.result, lm(progresa$t2000 ~ progresa$treatment + progresa$avgpoverty, data = progresa))),
          "Right! Remember that when you pass the `data` argument, you don't need to explicitly refer to the data frame in the formula."),
  pass_if(~ isTRUE(all.equal(.result, coef(lm(progresa$t2000 ~ progresa$treatment + progresa$avgpoverty)))),
          "Good job! You might try using the `data` argument next time.")
)

Estimating interactions

Now, let's see how the effect of treatment varies by the average level of poverty. To do this, specify an interaction between treatment and avgpoverty using the : or * operators. Save this new model as fit_int and print it after running it.

fit_int <- lm(t2000 ~ treatment * avgpoverty, data = progresa)
fit_int

grade_result(
  pass_if(~ isTRUE(all.equal(.result, lm(t2000 ~ treatment + avgpoverty +  treatment:avgpoverty, data = progresa)))),
  pass_if(~ isTRUE(all.equal(.result, lm(t2000 ~ treatment * avgpoverty, data = progresa)))),
  pass_if(~ isTRUE(all.equal(.result, lm(t2000 ~ treatment + avgpoverty + treatment * avgpoverty, data = progresa)))),
  pass_if(~ isTRUE(all.equal(.result, lm(progresa$t2000 ~ progresa$treatment * progresa$avgpoverty, data = progresa))),
          "Right! Remember that when you pass the `data` argument, you don't need to explicitly refer to the data frame in the formula."),
  pass_if(~ isTRUE(all.equal(.result, coef(lm(progresa$t2000 ~ progresa$treatment * progresa$avgpoverty)))),
          "Good job! You might try using the `data` argument next time.")
)

Nonlinearities

Finally, let's investigate the relationship between poverty and turnout. Run a regression of turnout on avgpoverty and it squared term to account for any possible nonlinearities. Save the output as fit_sq and print it out.

fit_sq <- lm(t2000 ~ avgpoverty + I(avgpoverty ^ 2), data = progresa)
fit_sq

grade_code()

Submit

submission_ui

submission_server()

mattblackwell/qsslearnr documentation built on Sept. 17, 2022, 6:25 p.m.