---
title: "Propensity Score Analysis"
output:
html_document:
df_print: paged
editor_options:
chunk_output_type: inline
---
*code for Chapter 5 "Propensity Score Matching" of book:*
*Leite, W. L. (2017). Practical propensity score methods using R. *
*Thousand Oaks, CA: Sage. *
As the R software and the R packages used in this example are updated frequently some incompatibilities between the current code and new R versions or package versions may appear.
Any updates to the code will be posted at:
http://www.practicalpropensityscore.com
This example estimates the effect of mothers having a job that provides or subsidizes child care on the length that they breastfeed their children National Longitudinal Survey of Youth 1979 (NLSY79) and the NLSY79 Children and Youth
# STEP 1 - DATA PREPARATION
*load dataset*
```{r, echo=FALSE}
load("Chapter5_data_breastfeeding_example.rData")
```
*Select covariates*
```{r, echo=F}
covariateNames <- c(
"C0005300", #RACE OF CHILD (MOTHER'S RACIAL/ETHNIC COHORT FROM SCREENER)
"C0005400", #SEX OF CHILD
"C0270300", #NUMBER OF JOBS HELD BY MOTHER IN 4TH QTR BEFORE BIRTH OF CHILD
"C0270600", #USUAL HOURS WORKED BY MOTHER AT ALL JOBS IN 4TH QTR BEFORE BIRTH OF CHILD
"C0270700", #USUAL EARNINGS OF MOTHER AT ALL JOBS IN 4TH QTR BEFORE BIRTH OF CHILD
"C0271800", # COLLECTIVE BARGAINING SET MOTHER'S MAIN JOB WAGES, 4TH QTR BEFORE BIRTH OF CHILD
"C0328000", #LENGTH OF GESTATION OF CHILD IN WEEKS
"C0328400", #CHILD DELIVERED BY CESAREAN SECTION?
"C0329000", # DAYS MOTHER STAYED IN HOSPITAL AT BIRTH OF CHILD
"C0329100", # DAYS CHILD STAYED IN HOSPITAL AFTER DELIVERY
"R0000700", #COUNTRY OF BIRTH OF MOTHER
"R0618300", #PROFILES ARMED FORCES QUALIFICATION TEST (AFQT) PERCENTILE SCORE - REVISED 1989 AFQT-2
"C0270200", #weeks after birth that mother returned to work (restricted to 12 weeks or less)
"motherAge", #age of mother at child's birth
"classWorker", #CLASS OF WORKER AT CURRENT JOB/MOST RECENT JOB
"familySize" , #FAMILY SIZE
"highestGrade" , #HIGHEST GRADE COMPLETED AS OF MAY 1 SURVEY YEAR (REVISED)
"jobsEver" , #NUMBER OF DIFFERENT JOBS EVER REPORTED AS OF INTERVIEW DATE
"maritalStatus" , #MARITAL STATUS (COLLAPSED)
"residenceRegion", #REGION OF CURRENT RESIDENCE
"ruralUrban" , #IS R'S CURRENT RESIDENCE URBAN/RURAL?
"totalWelfare", # TOTAL AMOUNT AFDC FOOD STAMPS OR OTH WELFARE/SSI RECEIVED DURING CAL YR
"weeksWorked", #NUMBER OF WEEKS WORKED IN PAST CALENDAR YEAR
"hoursPerWeek", #hours per week worked in the last calendar year
"maternityLeave", #FRINGE BENEFITS CURRENT JOB/MOST RECENT JOB - MATERNITY/PATERNITY LEAVE
"flexibleSchedule", #job allows flexible schedule
"argueChores",#FREQUENCY R & HUSBAND/PARTNER ARGUE ABOUT-CHORES & RESPONSIBILITIES
"dentalInsurance", #company provides dental insurance
"lifeInsurance", #company provides life insurance
"profitSharing", #company provides profit sharing
"retirement", #company provided retirement plan
"training") #company provided training opportunities
```
*Handle missing data*
This dataset was previously imputed
There are dummy variables indicating which values were imputed
The names of these dummy variables end with NA
It is important to include them in the propensity score model to account for potential imbalance in proportion of missing data between tereated and control groups
*Select dummy missing value indicators for variables with at least 5% of missing data
```{r}
covariateNamesNA <- paste(covariateNames,"NA",sep="")
covariateNamesNA <- covariateNamesNA[apply(data[,covariateNamesNA],2,mean)>=0.05]
```
*Combine covariate names with names of dummy missing indicator variables*
```{r}
covariateNames <- c(covariateNames, covariateNamesNA)
```
# STEP 2 - ESTIMATE PROPENSITY SCORES
*obtain the propensity score formula*
```{r}
psFormula <- paste(covariateNames, collapse="+")
psFormula <- formula(paste("childCare~",psFormula, sep=""))
print(psFormula)
```
*estimate propensity scores with logistic regression*
```{r, echo=F}
psModel <- glm(psFormula, data, family=binomial())
```
*save propensity scores and logit of propensity scores to dataset*
```{r, echo=F}
data$PScores <- fitted(psModel)
data$logitPScores <- with(data, log(PScores/(1-PScores)))
```
*estimate propensity scores with random forests*
```{r, echo=F, warning=F}
library(ranger)
ps_ranger = ranger(psFormula, data, probability=T, num.trees = 1000,
mtry = 7)
```
*save logit of propensity score to dataset*
```{r}
prediction_ranger = predict(ps_ranger, data=data)
data$PScores_RF = prediction_ranger$predictions[,1]
data$logitPScores_RF = with(data, log(PScores_RF/(1-PScores_RF)))
```
*evaluate common support of propensity score from logistic regression with histogram*
```{r}
hist(data$PScores[data$childCare==0], density = 10, angle = 45, main="Propensity Scores",
xlab="Shaded = Untreated | Gray = Treated")
hist(data$PScores[data$childCare==1], col=gray(0.4,0.25), add=T)
```
*evaluate common support of propensity score with box-and-wisker plots*
Random forests resulted in propensity scores with poor common support
```{r}
library(lattice)
bwplot( PScores~childCare, data = data,
ylab = "Propensity Scores with logistic regression", auto.key = TRUE)
bwplot( PScores_RF~childCare, data = data,
ylab = "Propensity Scores with random forest", auto.key = TRUE)
```
*obtain descriptive statistics of propensity scores*
```{r}
by(data$PScores, INDICES=data$childCare, summary)
```
---
# STEP 3 - PROPENSITY SCORE IMPLEMENTATION
*Propensity score matching*
*Variable ratio genetic matching*
Variable ratio is obtained by performing matching with replacement
```{r, echo=F, warning=F}
library(MatchIt)
Matching <- matchit(psFormula,distance=data$logitPScores,
data = data,
method = "genetic",ratio=1,replace=T,caliper=0.25)
summary(Matching)
```
# STEP 4 - COVARIATE BALANCE EVALUATION
```{r}
library(cobalt)
covariate.balance = bal.tab(Matching)
print(covariate.balance)
```
*Using the criterion of d < 0.05 for adequate covariate balance, check if any variable did not meet the criterion
```{r}
rownames(covariate.balance[[1]])[(abs(covariate.balance[[1]][,3]) > 0.05)]
```
*Using the criterion of d < 0.25 for adequate covariate balance, check if any variable did not meet the criterion
```{r}
rownames(covariate.balance[[1]])[(abs(covariate.balance[[1]][,3]) > 0.25)]
```
# STEP 5 - TREATMENT EFFECT ESTIMATION
*Obtain matched data*
```{r}
matchedData <- match.data(Matching)
```
*Because variable ratio matching results in weights, the survey package will be used for treatment effect estimation*
the survey package can be used for propensity score weighting, marginal mean weighting through stratification, and propensity score matching
*set up the survey design to declare what variable contains weights*
If the data had clusters, they would also be declared in this step with the ids argument
```{r, echo=F, warning=F}
library(survey)
design.Matching <- svydesign(ids=~1, weights=~weights,
data=matchedData)
```
*Fit a linear regression model using the weights to estimate the average treatment effect on treated (ATT)*
This model has the treatment indicator as the single predictor
the treatment effect is not statistically significant
```{r}
model.Matching <- svyglm(C0338600~childCare, design.Matching, family=gaussian())
summary(model.Matching)
```
*Fit a linear regression model to estimate the ATT controlling for variables with balance above 0.05*
the treatment effect is not statistically significant
```{r}
model.Matching2 <- svyglm(C0338600~childCare+C0270600+C0270700+C0328000+motherAge+familySize+highestGrade+totalWelfare+weeksWorked, design.Matching, family=gaussian())
summary(model.Matching2)
```
# STEP 6 - SENSITIVITY ANALYSIS
*run Frank et al. (2013) method*
```{r}
library(konfound)
sensitivity = pkonfound(est_eff=coef(model.Matching2)[2],std_err = SE(model.Matching2)[2], n_obs=nrow(matchedData), n_covariates=8)
```