--- title: "10 Discrete IVs and Other" author: "Colin Kuehl" date: "`r format(Sys.time(), '%B %d, %Y')`" output: html_document editor_options: chunk_output_type: console --- ## Set-Up Packages ```{r} library(foreign) library(ggcorrplot) library(tidyverse) library(stargazer) library(modelsummary) ``` Set your working directory and load the height wage data(HeightWage_MenWomenUS_HW.csv). ```{r} setwd("~/Dropbox/POLS 641/CMU Su26/cmucourse26/ClassCode/Day 10") hw <- read.csv("HeightWage_MenWomenUS_HW.csv") ``` ###Codebook in html - knit now to show in viewer 31b8e172-b470-440e-83d8-e6b185028602:t y p e : O A B l A G Y A N Q B h A D c A N w A y A C 0 A Z A B k A D Y A M w A t A D Q A N g A y A D I A L Q A 4 A D Q A Y g B m A C 0 A Y Q B m A D E A O Q A 5 A D U A Y Q A x A G I A M g B i A D k A 
 p o s i t i o n : N Q A 0 A D k A 
 p r e f i x : 
 s o u r c e : P A B 0 A G E A Y g B s A G U A I A B j A G w A Y Q B z A H M A P Q A i A H Q A Y Q B i A G w A Z Q A g A H Q A Y Q B i A G w A Z Q A t A G I A b w B y A G Q A Z Q B y A G U A Z A A g A H Q A Y Q B i A G w A Z Q A t A G g A b w B 2 A G U A c g A g A H Q A Y Q B i A G w A Z Q A t A G M A b w B u A G Q A Z Q B u A H M A Z Q B k A C I A P g A K A D w A d A B i A G 8 A Z A B 5 A D 4 A P A B 0 A H I A P g A K A D w A d A B k A D 4 A V g B h A H I A a Q B h A G I A b A B l A C A A b g B h A G 0 A Z Q A 8 A C 8 A d A B k A D 4 A C g A 8 A H Q A Z A A + A E Q A Z Q B z A G M A c g B p A H A A d A B p A G 8 A b g A 8 A C 8 A d A B k A D 4 A C g A 8 A C 8 A d A B y A D 4 A C g A 8 A H Q A c g A + A A o A P A B 0 A G Q A P g B t A G E A b A B l A D w A L w B 0 A G Q A P g A K A D w A d A B k A D 4 A T Q B h A G w A Z Q A g A C g A M Q A g A D 0 A I A B 5 A G U A c w A s A C A A M A A g A D 0 A I A B u A G 8 A K Q A 8 A C 8 A d A B k A D 4 A C g A 8 A C 8 A d A B y A D 4 A C g A 8 A H Q A c g A + A A o A P A B 0 A G Q A P g B 3 A G g A a Q B 0 A G U A P A A v A H Q A Z A A + A A o A P A B 0 A G Q A P g B X A G g A a Q B 0 A G U A I A A o A D E A I A A 9 A C A A e Q B l A H M A L A A g A D A A I A A 9 A C A A b g B v A C k A P A A v A H Q A Z A A + A A o A P A A v A H Q A c g A + A A o A P A B 0 A H I A P g A K A D w A d A B k A D 4 A Y g B s A G E A Y w B r A D w A L w B 0 A G Q A P g A K A D w A d A B k A D 4 A Q g B s A G E A Y w B r A C A A K A A x A C A A P Q A g A H k A Z Q B z A C w A I A A w A C A A P Q A g A G 4 A b w A p A D w A L w B 0 A G Q A P g A K A D w A L w B 0 A H I A P g A K A D w A d A B y A D 4 A C g A 8 A H Q A Z A A + A G g A a Q B z A H A A Y Q B u A G k A Y w A 8 A C 8 A d A B k A D 4 A C g A 8 A H Q A Z A A + A E g A a Q B z A H A A Y Q B u A G k A Y w A g A C g A M Q A g A D 0 A I A B 5 A G U A c w A s A C A A M A A g A D 0 A I A B u A G 8 A K Q A 8 A C 8 A d A B k A D 4 A C g A 8 A C 8 A d A B y A D 4 A C g A 8 A H Q A c g A + A A o A P A B 0 A G Q A P g B 3 A G E A Z w B l A D k A N g A 8 A C 8 A d A B k A D 4 A C g A 8 A H Q A Z A A + A E E A Z A B 1 A G w A d A A g A G g A b w B 1 A H I A b A B 5 A C A A d w B h A G c A Z Q B z A C A A K A B k A G 8 A b A B s A G E A c g B z A C k A I A B y A G U A c A B v A H I A d A B l A G Q A I A B p A G 4 A I A A x A D k A O Q A 2 A C A A K A B z A G E A b A B h A H I A e Q A g A G E A b g B k A C A A d w B h A G c A Z Q B z A C A A a Q B u A C A A c A B h A H M A d A A g A G M A Y Q B s A G U A b g B k A G E A c g A g A H k A Z Q B h A H I A I A B k A G k A d g B p A G Q A Z Q B k A C A A Y g B 5 A C A A a A B v A H U A c g B z A C A A d w B v A H I A a w B l A G Q A I A B p A G 4 A I A B w A G E A c w B 0 A C A A Y w B h A G w A Z Q B u A G Q A Y Q B y A C A A e Q B l A G E A c g A p A D w A L w B 0 A G Q A P g A K A D w A L w B 0 A H I A P g A K A D w A d A B y A D 4 A C g A 8 A H Q A Z A A + A G g A Z Q B p A G c A a A B 0 A D g A N Q A 8 A C 8 A d A B k A D 4 A C g A 8 A H Q A Z A A + A E E A Z A B 1 A G w A d A A g A G g A Z Q B p A G c A a A B 0 A C A A K A B p A G 4 A Y w B o A G U A c w A p A C w A I A B z A G U A b A B m A C 0 A c g B l A H A A b w B y A H Q A Z Q B k A C A A a Q B u A C A A M Q A 5 A D g A N Q A 8 A C 8 A d A B k A D 4 A C g A 8 A C 8 A d A B y A D 4 A C g A 8 A H Q A c g A + A A o A P A B 0 A G Q A P g B o A G U A a Q B n A G g A d A A 4 A D E A P A A v A H Q A Z A A + A A o A P A B 0 A G Q A P g B B A G Q A b w B s A G U A c w B j A G U A b g B 0 A C A A a A B l A G k A Z w B o A H Q A I A A o A G k A b g B j A G g A Z Q B z A C k A L A A g A H M A Z Q B s A G Y A L Q B y A G U A c A B v A H I A d A B l A G Q A I A B p A G 4 A I A A x A D k A O A A x A D w A L w B 0 A G Q A P g A K A D w A L w B 0 A H I A P g A K A D w A d A B y A D 4 A C g A 8 A H Q A Z A A + A G E A d A B o A G w A Z Q B 0 A H M A P A A v A H Q A Z A A + A A o A P A B 0 A G Q A P g B Q A G E A c g B 0 A G k A Y w B p A H A A Y Q B 0 A G k A b w B u A C A A a Q B u A C A A a A B p A G c A a A A g A H M A Y w B o A G 8 A b w B s A C A A Y Q B 0 A G g A b A B l A H Q A a Q B j A H M A I A A o A D E A I A A 9 A C A A e Q B l A H M A L A A g A D A A I A A 9 A C A A b g B v A C k A P A A v A H Q A Z A A + A A o A P A A v A H Q A c g A + A A o A P A B 0 A H I A P g A K A D w A d A B k A D 4 A Y w B s A H U A Y g B u A H U A b Q A 8 A C 8 A d A B k A D 4 A C g A 8 A H Q A Z A A + A E 4 A d Q B t A G I A Z Q B y A C A A b w B m A C A A Y w B s A H U A Y g A g A G 0 A Z Q B t A G I A Z Q B y A H M A a A B p A H A A c w A g A G k A b g A g A G g A a Q B n A G g A I A B z A G M A a A B v A G 8 A b A A s A C A A Z Q B 4 A G M A b A B 1 A G Q A a Q B u A G c A I A B h A H Q A a A B s A G U A d A B p A G M A c w A s A C A A Y Q B j A G E A Z A B l A G 0 A a Q B j A C 8 A a A B v A G 4 A b w B y A C A A c w B v A G M A a Q B l A H Q A e Q A g A G M A b A B 1 A G I A c w A s A C A A Y Q B u A G Q A I A B 2 A G 8 A Y w B h A H Q A a Q B v A G 4 A Y Q B s A C A A Y w B s A H U A Y g B z A D w A L w B 0 A G Q A P g A K A D w A L w B 0 A H I A P g A K A D w A d A B y A D 4 A C g A 8 A H Q A Z A A + A G 0 A b w B t A G U A Z A A 3 A D k A P A A v A H Q A Z A A + A A o A P A B 0 A G Q A P g B N A G 8 A d A B o A G U A c g A Z I H M A I A B 5 A G U A Y Q B y A H M A I A B v A G Y A I A B l A G Q A d Q B j A G E A d A B p A G 8 A b g A 8 A C 8 A d A B k A D 4 A C g A 8 A C 8 A d A B y A D 4 A C g A 8 A H Q A c g A + A A o A P A B 0 A G Q A P g B k A G E A Z A B l A G Q A N w A 5 A D w A L w B 0 A G Q A P g A K A D w A d A B k A D 4 A R g B h A H Q A a A B l A H I A G S B z A C A A e Q B l A G E A c g B z A C A A b w B m A C A A Z Q B k A H U A Y w B h A H Q A a Q B v A G 4 A P A A v A H Q A Z A A + A A o A P A A v A H Q A c g A + A A o A P A B 0 A H I A P g A K A D w A d A B k A D 4 A b Q B v A G 0 A c A B y A G 8 A M g A 8 A C 8 A d A B k A D 4 A C g A 8 A H Q A Z A A + A E 0 A b w B 0 A G g A Z Q B y A C A A a Q B u A C A A Y Q A g A H A A c g B v A G Y A Z Q B z A H M A a Q B v A G 4 A Y Q B s A C 8 A b Q B h A G 4 A Y Q B n A G U A c g B p A G E A b A A g A G 8 A Y w B j A H U A c A B h A H Q A a Q B v A G 4 A I A A o A D E A I A A 9 A C A A e Q B l A H M A L A A g A D A A I A A 9 A C A A b g B v A C k A P A A v A H Q A Z A A + A A o A P A A v A H Q A c g A + A A o A P A B 0 A H I A P g A K A D w A d A B k A D 4 A c A B v A H A A c A B y A G 8 A M g A 8 A C 8 A d A B k A D 4 A C g A 8 A H Q A Z A A + A E Y A Y Q B 0 A G g A Z Q B y A C A A a Q B u A C A A Y Q A g A H A A c g B v A G Y A Z Q B z A H M A a Q B v A G 4 A Y Q B s A C 8 A b Q B h A G 4 A Y Q B n A G U A c g B p A G E A b A A g A G 8 A Y w B j A H U A c A B h A H Q A a Q B v A G 4 A I A A o A D E A I A A 9 A C A A e Q B l A H M A L A A g A D A A I A A 9 A C A A b g B v A C k A P A A v A H Q A Z A A + A A o A P A A v A H Q A c g A + A A o A P A B 0 A H I A P g A K A D w A d A B k A D 4 A c w B p A G I A b A B p A G 4 A Z w B z A C A A P A A v A H Q A Z A A + A A o A P A B 0 A G Q A P g B O A H U A b Q B i A G U A c g A g A G 8 A Z g A g A H M A a Q B i A G w A a Q B u A G c A c w A 8 A C 8 A d A B k A D 4 A C g A 8 A C 8 A d A B y A D 4 A C g A 8 A H Q A c g A + A A o A P A B 0 A G Q A P g B h A G c A Z Q A 8 A C 8 A d A B k A D 4 A C g A 8 A H Q A Z A A + A E E A Z w B l A C A A K A B 5 A G U A Y Q B y A H M A K Q A g A G k A b g A g A D E A O Q A 5 A D Y A P A A v A H Q A Z A A + A A o A P A A v A H Q A c g A + A A o A P A B 0 A H I A P g A K A D w A d A B k A D 4 A Z Q B z A H Q A Z Q B l A G 0 A O A A w A D w A L w B 0 A G Q A P g A K A D w A d A B k A D 4 A U w B j A G 8 A c g B l A C A A b w B u A C A A U g B v A H M A Z Q B u A G I A Z Q B y A G c A I A B T A G U A b A B m A C 0 A R Q B z A H Q A Z Q B l A G 0 A I A B T A G M A Y Q B s A G U A I A B h A H M A I A B h A G 4 A I A B h A G Q A b w B s A G U A c w B j A G U A b g B 0 A C A A a Q B u A C A A M Q A 5 A D g A M A A g A C g A a A B p A G c A a A B l A H I A I A B 2 A G E A b A B 1 A G U A c w A g A G k A b g B k A G k A Y w B h A H Q A Z Q A g A G g A a Q B n A G g A Z Q B y A C A A c w B l A G w A Z g A t A G U A c w B 0 A G U A Z Q B t A C k A P A A v A H Q A Z A A + A A o A P A A v A H Q A c g A + A A o A P A B 0 A H I A P g A K A D w A d A B k A D 4 A a A B n A G M A O Q A 2 A D w A L w B 0 A G Q A P g A K A D w A d A B k A D 4 A S A B p A G c A a A B l A H M A d A A g A G c A c g B h A G Q A Z Q A g A G 8 A Z g A g A G U A Z A B 1 A G M A Y Q B 0 A G k A b w B u A C A A Y w B v A G 0 A c A B s A G U A d A B l A G Q A I A B p A G 4 A I A A x A D k A O Q A 2 A D w A L w B 0 A G Q A P g A K A D w A L w B 0 A H I A P g A K A D w A d A B y A D 4 A C g A 8 A H Q A Z A A + A F I A R Q B H A E k A T w B O A D w A L w B 0 A G Q A P g A K A D w A d A B k A D 4 A I A A 8 A C 8 A d A B k A D 4 A C g A 8 A C 8 A d A B y A D 4 A C g A 8 A H Q A c g A + A A o A P A B 0 A G Q A P g B u A G 8 A c g B l A H M A d A A 5 A D Y A P A A v A H Q A Z A A + A A o A P A B 0 A G Q A P g B O A G 8 A c g B 0 A G g A Z Q B h A H M A d A A g A C g A M Q A g A D 0 A I A B 5 A G U A c w A s A C A A M A A g A D 0 A I A B u A G 8 A K Q A 8 A C 8 A d A B k A D 4 A C g A 8 A C 8 A d A B y A D 4 A C g A 8 A H Q A c g A + A A o A P A B 0 A G Q A P g B u A G 8 A c g B j A G U A b g A 5 A D Y A P A A v A H Q A Z A A + A A o A P A B 0 A G Q A P g B O A G 8 A c g B 0 A G g A I A B D A G U A b g B 0 A H I A Y Q B s A C A A K A A x A C A A P Q A g A H k A Z Q B z A C w A I A A w A C A A P Q A g A G 4 A b w A p A D w A L w B 0 A G Q A P g A K A D w A L w B 0 A H I A P g A K A D w A d A B y A D 4 A C g A 8 A H Q A Z A A + A H M A b w B 1 A H Q A a A A 5 A D Y A P A A v A H Q A Z A A + A A o A P A B 0 A G Q A P g B T A G 8 A d Q B 0 A G g A I A A o A D E A I A A 9 A C A A e Q B l A H M A L A A g A D A A I A A 9 A C A A b g B v A C k A P A A v A H Q A Z A A + A A o A P A A v A H Q A c g A + A A o A P A B 0 A H I A P g A K A D w A d A B k A D 4 A d w B l A H M A d A A 5 A D Y A P A A v A H Q A Z A A + A A o A P A B 0 A G Q A P g B X A G U A c w B 0 A C A A K A A x A C A A P Q A g A H k A Z Q B z A C w A I A A w A C A A P Q A g A G 4 A b w A p A D w A L w B 0 A G Q A P g A K A D w A L w B 0 A H I A P g A K A D w A L w B 0 A G I A b w B k A H k A P g A 8 A C 8 A d A B h A G I A b A B l A D 4 A 
 s u f f i x : :31b8e172-b470-440e-83d8-e6b185028602 ## Exploring Wage Explore the data, we are mostly interested in wage: ```{r} ``` ```{r} summary(hw$wage96) hist(hw$wage96) summary(lm(wage96 ~ esteem80, data=hw)) ``` Using just continuous variables, create a multivariate model predicting wage. Practice our interpretation. ```{r} ``` ## Dummy Variables Can add to our multivariate regression ```{r} table(hw$white) table(hw$male) ck1a <- (lm(wage96~male, data=hw))#Tells us average for males and non-males summary(ck1a) hw %>% group_by(male) %>% summarise(mean=mean(wage96, na.rm=T)) 13.37+1.51 t.test(hw$wage96[hw$male==1], hw$wage96[hw$male==0], var.equal = FALSE) plot(hw$male,hw$wage96, ylim=c(0,25)) #Really zooming in. Black lines are just a bunch of dots abline(h=13.37, col="red") abline(h=13.37+1.51, col="blue") abline(abline(ck1a, lty=6, col="purple")) plot(hw$wage96~jitter(hw$male, 1), ylim=c(0,25)) #jitter will spread out your data a bit. in some cases with super large N I will take a random sample to get a better feel for the data. abline(h=13.37, col="red") abline(h=13.37+1.51, col="blue") abline(abline(ck1a, lty=6, col="purple")) ``` Indicate dummy on Multivariate Regression plot ```{r} ck3 <- lm(wage96~ age + male, data=hw) #Shows differences between males and females summary(ck3) plot(jitter(hw$age[hw$male==0]),(hw$wage96[hw$male==0]), col="red", pch=1, xlab="Age", ylab="Hourly Wage", main="Age as a Determinent of \n Wage by Gender", ylim=c(0,100)) #plots female note: \n creats new line #Shorten ylim to show difference points(jitter(hw$age[hw$male==1]), hw$wage96[hw$male==1], col="blue", pch=1) #plots male legend(50,90, legend=c("Female", "Male"), col=c("red", "blue"), pch=c(1, 16), bty="n") abline(a=11.405, b=.052, col="red") # intercept and slope from above abline(a=(11.405+1.708), b=.052, col="blue") ``` ## More Multivariate Models ```{r} ck2 <- lm(wage96~ male+ height85 + siblings + age, data=hw) #Shows differences between males and females summary(ck2) ck2a <- lm(wage96~ male+ height85 + siblings + age, data=hw) summary(ck2a) ``` Question: Does participation in high school athletics(athlets) have an affect on wage? ```{r} summary(lm(wage96~athlets, data=hw)) summary(lm(wage96~athlets+hgc96+siblings+height85+white+clubnum, data=hw)) ``` # Categorical Variables ```{r} #Use region variables, these have already been converted into dummy variables reg1 <-lm(wage96~norest96+norcen96+west96+south96, data=hw) #why is south NA? . . .. perfect multicollinearity. We need a reference category summary(reg1) reg2 <-lm(wage96~norcen96+west96+south96, data=hw) #Take south out to compare to summary(reg2)#remember we interpret these coefficients as the difference between each region and the reference category. reg3 <-lm(wage96~hgc96+norest96+norcen96+west96, data=hw) #add in education summary(reg3) plot(hw$hgc96, hw$wage96, xlab="Education level", ylab="Hourly Wage", main="Education as a Determinent of \n Wage by Region", ylim=c(0,100)) abline(a=-9.073, b=1.634, col="red") # The South abline(a=(-9.073+3.97), b=1.634, col="blue") #Northeast abline(a=(-9.073+1.613), b=1.634, col="hotpink") #NorthCentral abline(a=(-9.073+2.739), b=1.634, col="green") #West legend(0,95, legend=c("South", "Northeast", "North Central", "West"), col=c("red", "blue", "hotpink", "green"),lty=1, bty="n") ``` ```{r} #Racial category cat1 <- lm(wage96~ black + hispanic, data=hw) #Wage difference compared to white summary(cat1) sink <- lm(wage96~ male+ norcen96+west96+south96+ black + hispanic, data=hw) summary(sink) ``` Summarizing regression models ```{r} #Yesterday we used model summary, today we will use stargazer to create nice regression tables library("stargazer") stargazer(ck1a,reg3, sink, type="text", title = "Multivariate Regression Models") #We can also use the coefplot package. library(coefplot)#New Package. Will need to install. Also makes coefficient plots coefplot(ck1a)#point is equal to coefficient. Lines are confidence interval. When CI does not overlap 0 coefficient is significant coefplot(reg2) coefplot(sink, intercept = FALSE, newNames=c(hispanic="Hispanic", black="Black", south96="South", west96="West", norcen96="North Central", male="Male"), title="Predictors of Wage \n 1996", xlab="") multiplot(sink, reg2, intercept=FALSE) coefplot(ck2, intercept = FALSE)#remember comparing size of effect only makes sense when range is the same. ``` Bonus: Based on your extensive knowledge of American wages and statistics create your version of the best regression model(or models) Double Bonus: Create a table using stargazer ```{r} ``` ############################# Lets play a bit more with regression assumptions and transforming variables ```{r} # Restrict to employed respondents with complete height data hwdata2 <- subset(hw, !is.na(wage96) & wage96 > 0 & !is.na(height85)) hwdata2$lwage <- log(hwdata2$wage96) # log hourly wage ``` ## Why Log Wages? ```{r} #| fig-height: 3.2 par(mfrow = c(1, 2)) hist(hwdata2$wage96, main = "Raw Wage", xlab = "Hourly Wage (USD)") hist(hwdata2$lwage, main = "log(Wage)", xlab = "Log Hourly Wage") ``` - Raw wages are **right-skewed** — a few very high earners pull the tail - Log transformation compresses the scale and produces an approximately normal distribution - Interpretation shifts: a 1-inch increase in height is associated with a **percentage change** in wages ## Scatter Plot: Height and Log Wages ```{r} #| fig-height: 3.8 plot(hwdata2$lwage ~ hwdata2$height85, xlab = "Height in 1985 (inches)", ylab = "Log Hourly Wage (1996)") abline(lm(lwage ~ height85, data = hwdata2), col = "red") ``` - Is there a positive relationship? Does it look roughly linear? - Outliers at the extremes are worth noting ## Compare: Logged vs. Unlogged Outcome ```{r} model.wage.orig <- lm(wage96 ~ height85, data = hwdata2) model.wage <- lm(lwage ~ height85, data = hwdata2) modelsummary( list("Original" = model.wage.orig, "Log Outcome" = model.wage), stars = c("*" = .1, "**" = .05, "***" = .01), output = "kableExtra" ) ``` - Compare $R^2$, residual standard error, and residual patterns - Logged model: coefficient interpreted as *"a 1-inch increase in height is associated with a* $\hat{\beta} \times 100\%$ change in wages" # Regression Diagnostics {.center} ## The Four Diagnostic Plots ```{r} par(mfrow = c(2, 2)) plot(model.wage, labels.id = rownames(hwdata2)) ``` Four plots, four questions: 1. **Residuals vs. Fitted** — is the relationship linear? Should hug the dashed line 2. **Normal Q-Q** — are errors normally distributed? Points should follow the diagonal 3. **Scale-Location** — is variance constant (homoskedasticity)? Should be flat, no V-shape 4. **Residuals vs. Leverage** — are any observations disproportionately influential? (Cook's distance) ## Reading Each Plot ::::: columns ::: {.column width="50%"} **Residuals vs. Fitted** - Curve or U-shape → **non-linearity** (try a transformation) - Fan shape → **heteroskedasticity** (use robust SE) - Should be random scatter around zero ::: ::: {.column width="50%"} **Residuals vs. Leverage** - Points outside Cook's distance contour are **high-influence** - High leverage $\neq$ bad, but worth inspecting - Ask: does the result change substantially if I drop this case? ::: ::::: ## Removing Outliers — With Caution ```{r} # Identify high-wage outliers (e.g., top 1%) wage_cutoff <- quantile(hwdata2$wage96, 0.99, na.rm = TRUE)#fance way to take out outleirs hwdata4 <- subset(hwdata2, wage96 < wage_cutoff) model2.wage <- lm(lwage ~ height85, data = hwdata4) summary(model2.wage) par(mfrow = c(2, 2)) plot(model2.wage, labels.id = rownames(hwdata4)) ``` ::: alertblock **Warning:** Only remove observations if you have a **substantive theoretical reason**. Removing outliers to improve fit is data manipulation. Here we may want to keep high earners — they are real data points. ::: # Part 3: Multicollinearity {.center} ## A Richer Model ```{r} # Predict log wages with height plus controls model6 <- lm(lwage ~ height85 + hgc96 + male + daded79 + momed79, data = hwdata2) modelsummary(model6) ``` - Unit of analysis: **individual respondent** - Are father's education (`daded79`) and mother's education (`momed79`) correlated with each other? ## The Problem: Correlated Predictors ```{r} par(mfrow = c(1, 1)) #back to one pane plot(hwdata2$daded79, hwdata2$momed79, xlab = "Father's Education (years)", ylab = "Mother's Education (years)") cor(hwdata2$daded79, hwdata2$momed79, use = "complete") ``` - Parents' education levels tend to be correlated — assortative mating - Putting both in the same model asks OLS to separate effects it cannot easily distinguish ## Fit the Model and Check VIF ```{r} library(car) vif(model6) ``` - VIF $>$ 5: warrants inspection - VIF $>$ 10: serious problem — coefficients are unreliable - Note how individual coefficients may be insignificant even when the overall model fits well ## Inspect the Diagnostics ```{r} par(mfrow = c(2, 2)) plot(model6, labels.id = rownames(hwdata2)) ``` Also compare single-predictor models to the joint model: ```{r} summary(lm(lwage ~ daded79, data = hwdata2)) summary(lm(lwage ~ momed79, data = hwdata2)) ``` If each predictor is significant alone but not together, that is a classic **multicollinearity signature.** # All-in-one Regression Diagnostic package ```{r} model9 <- lm(lwage ~ height85 + hgc96 + male + daded79 + momed79 + esteem80, data = hwdata2) # install.packages("gvlma") library(gvlma) model9 <- lm(lwage ~ height85 + hgc96 + male + daded79 + momed79 + esteem80, data = hwdata2) summary(gvlma(model9)) ``` | Test | Null hypothesis ($H_0$) | |--------------------|------------------------------------| | Global Stat | Relationship is linear | | Skewness | Errors are not skewed | | Kurtosis | Errors are not kurtotic | | Link Function | DV is continuous (not categorical) | | Heteroscedasticity | Residual variance is constant | Reject ($p < .05$) = assumption violated. ## `performance` — Modern Alternative # install.packages("performance") ```{r} library(performance) check_autocorrelation(model9) check_normality(model9) check_collinearity(model9) check_heteroskedasticity(model9) model_performance(model9) ``` | Check | Tool | |----|----| | Right-skewed outcome or predictor? | `hist()` $\to$ log-transform | | Non-linearity? | Residuals vs. Fitted plot | | Heteroskedasticity? | Scale-Location plot; `bptest()` | | Influential outliers? | Residuals vs. Leverage; Cook's distance | | Multicollinearity? | `cor()`; `vif()` | | Autocorrelation? | `durbinWatsonTest()` | | All at once? | `check_model()` or `summary(gvlma())` | ------------------------------------------------------------------------ Remember: violating these assumptions does not always mean **bias** — it usually means your **standard errors are wrong**, which corrupts inference even when coefficients look reasonable. ###### Some Experiments Basics # Experiments Set working directory and unpack packages ```{r} #install.packages("pwr") #install.packages("AER") library(haven) library(tidyverse) library(pwr) library(AER) #More info here: https://www.statmethods.net/stats/power.html ``` Recall, with experiments we're focused more on design than statistical analysis. #Practice data from the textbook. ```{r} GGD <- read_csv("GerberGreenData.csv") summary(GGD) #check balance across wards b1 <- table(GGD$Ward, GGD$ContactAssigned) prop.table(b1, 1) #Balance looks good. summary(lm(GGD$ContactAssigned~GGD$Ward)) # Can run T-test or regression to see if sig dif. Ward is not correlated with treatment assignment #across # of people in household b2 <- table(GGD$PeopleHH, GGD$ContactAssigned) prop.table(b2, 1) #use dplyr balance <- GGD %>% group_by(ContactAssigned)%>% summarise(People=mean(PeopleHH), Ward=mean(Ward)) t(balance) #Experimental results: Does talking to people increase likelihood of voting? #ITT does being assigned to treatment actually effect the likilood of voting(regardless of compliance)? ITT <-(lm(GGD$Voted~GGD$ContactAssigned)) summary(ITT) #Voting is dummy variable and this is experimental. When we use OLS on a dummy we call it a linear probablity model and it is interpreted as percentage change in Y from a one unit change in X. An advanced class would talk about the advantages of LPM vs logit or probit for binary DVs. #What variables are we missing from our model? summary(lm(Voted ~ ContactAssigned+Ward+PeopleHH, data=GGD))#adding controls does not change coefficient, only signifigance #Compliance: #ATE model ATE <-(lm(GGD$Voted~GGD$ContactObserved)) #The effect of actually being treated summary(ATE) #percentage of those assigned to treatment actually treated summary(lm(ContactObserved ~ ContactAssigned, data=GGD))#table 10.2 in book. twosls <- ivreg(Voted ~ ContactObserved | ContactAssigned, data=GGD) summary(twosls) stargazer(ATE,ITT, twosls, type="text", title = "Comparison of Experimental Models") multiplot(ATE,ITT, twosls, title = "Comparison of Experimental Models", xlab="Effect Size(Percentage)", intercept=FALSE) ``` Heterogeneous Treatment Effects ```{r} #We have limited data, but say we were interested in if the effect of contact was dependent on the number of people in the household hhe <- (lm(Voted~ContactObserved*PeopleHH, data=GGD)) summary(hhe) ``` I haven't used it much, but DeclareDesign has good stuff on thinking through experimental designs ()