[SOLVED] Socga2332 – problem set 3

Contents
Instructions 1
Prerequisite 1
Part 1 Multivariate Regression 2
Part 2 Logistic Regression 2
Part 3 Causality 3
Instructions
1. Submit two files for each problem set. The first is a R Markdown (.Rmd) file that can be run without error from start to end. The second is a PDF rendered from your R Markdown file or created using LATEX.
2. Name your files following this convention: [Last Name]_ps3.Rmd and [Last Name]_ps3.pdf (for example, Jiang_ps3.Rmd).
4. You are encouraged to discuss the problems with your classmates. But the R Markdown and PDF files that you submit have to be created on your own. Please do not ask for solutions from students in earlier cohorts.
5. Comment on your code wherever possible and explain your ideas in detail. You will get credits for showing the steps you take and for explaining your reasoning, even if you do not get the correct final result.

Prerequisite
Load multiple packages to your environment.
knitr::opts_chunk$set(echo = TRUE)
## load packages here library(dplyr)
##
## Attaching package: ‘dplyr’
## The following objects are masked from ‘package:stats’:
##
## filter, lag
## The following objects are masked from ‘package:base’:
##
## intersect, setdiff, setequal, union
Part 1 Multivariate Regression
gss.csv contains a dataset of the following variables:
Variable Name Variable Detail
id A respondent’s unique ID
abortion A respondent’s answer to the question “Should a Woman be Able to Have
Legal Abortion”; -1 = No, 0 = It depends, and 1 = Yes
pid A respondent’s party identification; 0 = Strong Democrat, 1 = Democrat,
2 = Democrat Leaning, 3 = Independent, 4 = Republican Leaning, 5 = Republican, 6 = Strong Republican
linc A respondent’s income (logged)
female A dummy variable of sex; 1 = Female, 0 = Male
mar A dummy variable of marital status; 1 = Married, 0 = Not married
1. [5pts]Plot the distribution of abortion using a bar plot
• Hint: treat both abortion and pid as continuous variables and fit regular OLS
3. [5pts]Calculate heteroskedasticity-robust standard errors for Model 2; call this model Model 3.
4. [5pts]Create a regression table with three columns: Model 1, Model 2, and Model 3.
5. [10pts]Plot the predicted value of abortion of male and female respondents with different pid values.
Be clear about which variables you fix at what values when generating the plot.
6. [5pts]Using both the tables and the plot, interpret the results.
Part 2 Logistic Regression
1. [5pts]Replicate the linear probability model and logistic model fitted in Lab 8, then fit a new logistic regression model using the same set of predictors but treat pid as an ordered categorical variable.
• Hint: by ordered categorical variable, I mean you need to factorize pid, or create dummy categories
2. [5pts]Create a regression table with three columns: Model 1 (linear probability model), Model 2 (logistic regression with pid as a numeric variable), and Model 3 (logistic regression with pid as an ordered categorical variable).
Part 3 Causality
A study on COVID-19 constructed a “COVID risk factor” score based on the COVID infection rate of a given area (defined by zip code).
A researcher wants to estimate the effect of having a vaccination center in the area on that area’s COVID risk factor score. She compiled a dataset that contains each area’s COVID risk factor score and whether the area has a vaccination center. She then estimated the effect of having a vaccination center using the “naive estimator” we discussed in class.
You noted that the quality of information residents have about COVID and the vaccine can be a confounding variable that affects both the area’s infection rate and whether there is a vaccination center in the area.
Assume that you are able to estimate the relationships this “informedness” confounder (info) and the original
“vaccination center” predictor (vaccine) have with the COVID risk factor score (covid_risk), which can be simulated using the following code (n is sample size):
library(“scales”)
set.seed(1234) # set the same seed to ensure identical results e = rnorm(n, 0, 0.5)
covid_risk = rescale( 0 – 7*vaccine – 2*info + e, to = c(0, 100))
1. [5pts]Import the data covid.csv. According to the potential outcome framework, create two new variables y_c and y_t where y_c is the value of the potential outcome of “risk factor” when the individual is not treated, and y_t is the value of the potential outcome of “risk factor” when the individual is treated. Explain your steps.
2. [5pts]Fill out the table below (round to 1 decimal points):
Group YT YC
Treatment Group (D = 1) E[YT|D = 1] =? E[YC|D = 1] =?
Control Group (D = 0) E[YT|D = 0] =? E[YC|D = 0] =?
3. [15pts]Estimate/calculate the following (write down the formula/equation you use):
i. The Naive Estimator of ATE
ii. The “true” Average Treatment Effect
iii. The “true” Treatment Effect on the Treated iv. The “true” Treatment Effect on the Control
v. Selection Bias