library(tidyverse)
math_score<-read.csv("ECLSK_98_99_math.csv")math_score<-filter(math_score,!( P1DISABL ==1), !( C1R4MSCL ==-1), RACE %in%c(1, 3, 4) ) subset_math_hisp<-math_score[c(1, 2, 138:140, 260, 533:537, 800:801, 809, 812:813, 822, 961, 1270:1272, 1276, 1537, 1823, 2000)]subset_math_hisp$ R1_KAGE [subset_math_hisp$ R1_KAGE == -9] <- NA
subset_math_hisp$ P1LEARN [subset_math_hisp$ P1LEARN == -9] <- NA
subset_math_hisp$ C1R4MSCL [subset_math_hisp$ C1R4MSCL == -9] <- NA
subset_math_hisp$ P1CONTRO [subset_math_hisp$ P1CONTRO == -9] <- NA
subset_math_hisp$ P1SOCIAL [subset_math_hisp$ P1SOCIAL == -9] <- NA
subset_math_hisp$ P1SADLON [subset_math_hisp$ P1SADLON == -9] <- NA
subset_math_hisp$ P1IMPULS [subset_math_hisp$ P1IMPULS == -9] <- NA
subset_math_hisp$ P1DISABL [subset_math_hisp$ P1DISABL == -9] <- NA
subset_math_hisp$ P1CENTER [subset_math_hisp$ P1CENTER == -9] <- NA
subset_math_hisp$ P1FIRKDG [subset_math_hisp$ P1FIRKDG <= -8] <- NA
subset_math_hisp$ P1YYINT [subset_math_hisp$ P1YYINT <= -8] <- NA
subset_math_hisp$ P1CHLBOO [subset_math_hisp$ P1CHLBOO <= -7] <- NA
subset_math_hisp$ P1DIAGNO [subset_math_hisp$ P1DIAGNO <= -8] <- NAsubset_math_hisp<-na.omit(subset_math_hisp)subset_math_hisp<-subset_math_hisp%>%
mutate(race =sjmisc::rec(RACE, rec = "1=1; 3=2; 4=2"))%>%
mutate(learning_difficulty =sjmisc::rec( P1DIAGNO, rec = "-1=2; 1=1; 2=2")) %>%
mutate(home_lang=sjmisc::rec( C1SCREEN, rec = "1=2; 2=1")) %>%
mutate(Home_language_binary=sjmisc::rec( home_lang, rec = "1=1; 2=0")) %>%
mutate(c_age=R1_KAGE-mean(R1_KAGE))%>%
mutate(Center_binary=sjmisc::rec( P1CENTER, rec = "1=1; 2=0"))subset_math_hisp$gender<-factor(subset_math_hisp$GENDER, levels = c(1, 2),
labels = c("Male","Female"))
subset_math_hisp$race<-factor(subset_math_hisp$race, levels = c (1, 2),
labels = c("White", "Hispanic"))
subset_math_hisp$center<-factor(subset_math_hisp$P1CENTER, levels = c(1, 2),
labels = c("Yes","No"))
subset_math_hisp$family_type<-factor(subset_math_hisp$P1HFAMIL, levels = c(1, 2, 3, 4, 5),
labels = c("Both parents & sib","Both parents & no sib", "Single parent & sib", " Single parent & no sib", "Other"))
subset_math_hisp$kindergarten<-factor(subset_math_hisp$P1FIRKDG , levels = c(1, 2),
labels = c("Yes","No"))
subset_math_hisp$assess_spanish<-factor(subset_math_hisp$C1SPASMT , levels = c(1, 2),
labels = c("Yes","No"))
subset_math_hisp$home_lang<-factor(subset_math_hisp$home_lang , levels = c(1, 2),
labels = c("English","Non-English"))
subset_math_hisp$learning_difficulty<-factor(subset_math_hisp$learning_difficulty , levels = c(1, 2),
labels = c("Yes","No"))
subset_math_hisp$SES<-factor(subset_math_hisp$W1SESQ5 , levels = c(1, 2, 3, 4, 5),
labels = c("First quintile", "Second quintile", "Third quintile", "Fourth quintile", "Fifth quintile"))my_mathdata<-subset_math_hisp[c(5:11, 14:15, 24, 26:37 )]library(reshape2)
names(my_mathdata)<-c("Child_Age", "Math_score", "Approach_to_Learning", "Self_control", "Social_interaction", "Sad_alone", "Impulsive", "Number_of_sibling", "Total_household_member", "Number_of_book", "Race", "Learning difficulty","Home_language","Home_language_binary", "Child_assessment_age", "Center_binary", "Gender", "Center", "Types_family" , "Kindergarten", "Spanish_assessment ","SES" )
head(my_mathdata)## Child_Age Math_score Approach_to_Learning Self_control
## 1 77.20 44.44 3.00 3.0
## 2 64.10 28.57 3.67 3.0
## 3 74.53 40.88 3.50 3.2
## 4 63.60 19.65 2.67 2.8
## 5 70.63 26.85 3.00 2.8
## 6 62.63 22.27 3.33 2.0
## Social_interaction Sad_alone Impulsive Number_of_sibling
## 1 3.00 1.50 2.0 2
## 2 4.00 1.50 1.5 2
## 3 4.00 1.25 2.5 1
## 4 3.00 1.75 2.0 1
## 5 3.67 1.67 1.5 1
## 6 4.00 1.75 2.0 1
## Total_household_member Number_of_book Race Learning difficulty
## 1 5 100 White No
## 2 5 40 White No
## 3 4 75 White No
## 4 4 100 White No
## 5 4 200 White No
## 6 4 200 White No
## Home_language Home_language_binary Child_assessment_age Center_binary
## 1 English 1 8.744793 1
## 2 English 1 -4.355207 1
## 3 English 1 6.074793 1
## 4 English 1 -4.855207 1
## 5 English 1 2.174793 1
## 6 English 1 -5.825207 1
## Gender Center Types_family Kindergarten Spanish_assessment
## 1 Female Yes Both parents & sib Yes No
## 2 Female Yes Both parents & sib Yes No
## 3 Female Yes Both parents & sib Yes No
## 4 Male Yes Both parents & sib Yes No
## 5 Female Yes Both parents & sib Yes No
## 6 Male Yes Both parents & sib Yes No
## SES
## 1 Fifth quintile
## 2 Fifth quintile
## 3 Fifth quintile
## 4 Fifth quintile
## 5 Fifth quintile
## 6 Fifth quintilesummary(my_mathdata)## Child_Age Math_score Approach_to_Learning Self_control
## Min. :56.90 Min. :10.60 Min. :1.170 Min. :1.00
## 1st Qu.:65.20 1st Qu.:20.81 1st Qu.:2.830 1st Qu.:2.60
## Median :68.27 Median :26.03 Median :3.170 Median :2.80
## Mean :68.46 Mean :27.50 Mean :3.148 Mean :2.86
## 3rd Qu.:71.53 3rd Qu.:32.26 3rd Qu.:3.500 3rd Qu.:3.20
## Max. :79.00 Max. :95.44 Max. :4.000 Max. :4.00
## Social_interaction Sad_alone Impulsive Number_of_sibling
## Min. :1.330 Min. :1.000 Min. :1.000 Min. : 0.000
## 1st Qu.:3.000 1st Qu.:1.250 1st Qu.:1.500 1st Qu.: 1.000
## Median :3.330 Median :1.500 Median :2.000 Median : 1.000
## Mean :3.354 Mean :1.514 Mean :1.873 Mean : 1.424
## 3rd Qu.:3.670 3rd Qu.:1.750 3rd Qu.:2.000 3rd Qu.: 2.000
## Max. :4.000 Max. :3.750 Max. :4.000 Max. :10.000
## Total_household_member Number_of_book Race
## Min. : 2.000 Min. : 0.00 White :6804
## 1st Qu.: 4.000 1st Qu.: 40.00 Hispanic:1958
## Median : 4.000 Median : 75.00
## Mean : 4.477 Mean : 84.18
## 3rd Qu.: 5.000 3rd Qu.:100.00
## Max. :13.000 Max. :200.00
## Learning difficulty Home_language Home_language_binary
## Yes: 0 English :7627 Min. :0.0000
## No :8762 Non-English:1135 1st Qu.:1.0000
## Median :1.0000
## Mean :0.8705
## 3rd Qu.:1.0000
## Max. :1.0000
## Child_assessment_age Center_binary Gender Center
## Min. :-11.5552 Min. :0.0000 Male :4306 Yes:6623
## 1st Qu.: -3.2552 1st Qu.:1.0000 Female:4456 No :2139
## Median : -0.1852 Median :1.0000
## Mean : 0.0000 Mean :0.7559
## 3rd Qu.: 3.0748 3rd Qu.:1.0000
## Max. : 10.5448 Max. :1.0000
## Types_family Kindergarten Spanish_assessment
## Both parents & sib :6503 Yes:8460 Yes: 621
## Both parents & no sib : 900 No : 302 No :8141
## Single parent & sib : 844
## Single parent & no sib: 437
## Other : 78
##
## SES
## First quintile :1115
## Second quintile:1522
## Third quintile :1712
## Fourth quintile:2027
## Fifth quintile :2386
## ##Descriptive Analysis of Data
library(dplyr)
library(knitr)
library(DT)
library(xtable)
library(devtools)
library(ggplot2)
library(pastecs)
library(kableExtra)
library(ztable)T1.1<-sapply(my_mathdata[,1:10], min)
T1.2<-sapply(my_mathdata[,1:10], mean)
T1.3<-sapply(my_mathdata[,1:10], median)
T1.4<-sapply(my_mathdata[,1:10], sd)
T1.5<-sapply(my_mathdata[,1:10], max)
kable(cbind(Min=T1.1, Max=T1.5, Mean=T1.2, Median=T1.3, Sd=T1.4), format = "html", caption = "Table 1: Descriptive Analysis of Continuous Variables", booktabs = T) | Min | Max | Mean | Median | Sd | |
|---|---|---|---|---|---|
| Child_Age | 56.90 | 79.00 | 68.455207 | 68.27 | 4.1941982 |
| Math_score | 10.60 | 95.44 | 27.501615 | 26.03 | 9.4071097 |
| Approach_to_Learning | 1.17 | 4.00 | 3.148142 | 3.17 | 0.4624071 |
| Self_control | 1.00 | 4.00 | 2.859770 | 2.80 | 0.4765388 |
| Social_interaction | 1.33 | 4.00 | 3.354468 | 3.33 | 0.5367221 |
| Sad_alone | 1.00 | 3.75 | 1.513802 | 1.50 | 0.3656078 |
| Impulsive | 1.00 | 4.00 | 1.873145 | 2.00 | 0.6180660 |
| Number_of_sibling | 0.00 | 10.00 | 1.423648 | 1.00 | 1.0795026 |
| Total_household_member | 2.00 | 13.00 | 4.477060 | 4.00 | 1.2545040 |
| Number_of_book | 0.00 | 200.00 | 84.182949 | 75.00 | 60.5478430 |
T2.1 <- my_mathdata$Gender
cbind(freq=table(T2.1), percentage=prop.table(table(T2.1))*100)## freq percentage
## Male 4306 49.14403
## Female 4456 50.85597T2.2 <- my_mathdata$Race
cbind(freq=table(T2.2), percentage=prop.table(table(T2.2))*100)## freq percentage
## White 6804 77.6535
## Hispanic 1958 22.3465T2.3 <- my_mathdata$Types_family
cbind(freq=table(T2.3), percentage=prop.table(table(T2.3))*100)## freq percentage
## Both parents & sib 6503 74.2182150
## Both parents & no sib 900 10.2716275
## Single parent & sib 844 9.6325040
## Single parent & no sib 437 4.9874458
## Other 78 0.8902077 T2.4 <- my_mathdata$SES
cbind(freq=table(T2.4), percentage=prop.table(table(T2.4))*100)## freq percentage
## First quintile 1115 12.72541
## Second quintile 1522 17.37046
## Third quintile 1712 19.53892
## Fourth quintile 2027 23.13399
## Fifth quintile 2386 27.23123 T2.5 <- my_mathdata$Home_language
cbind(freq=table(T2.5), percentage=prop.table(table(T2.5))*100)## freq percentage
## English 7627 87.04634
## Non-English 1135 12.95366 T2.6 <- my_mathdata$Center
cbind(freq=table(T2.6), percentage=prop.table(table(T2.6))*100)## freq percentage
## Yes 6623 75.58777
## No 2139 24.41223 T2.7 <- my_mathdata$Kindergarten
cbind(freq=table(T2.7), percentage=prop.table(table(T2.7))*100)## freq percentage
## Yes 8460 96.553298
## No 302 3.446702c1<-table( my_mathdata$Race, my_mathdata$Gender)
c2<-table( my_mathdata$Race, my_mathdata$SES)
c3<-table( my_mathdata$Race, my_mathdata$Home_language)
c4<-table( my_mathdata$Race, my_mathdata$Types_family)
c5<-table( my_mathdata$Center, my_mathdata$Race)
c6<-table(my_mathdata$Race, my_mathdata$Kindergarten )
v1=round(prop.table(c1, 1), 2)
v2=round(prop.table(c2, 1), 2)
v3=round(prop.table(c3, 1), 2)
v4=round(prop.table(c4, 1), 2)
v5=round(prop.table(c5, 1), 2)
v6=round(prop.table(c6, 1), 2)
kable(v1, format = "html", caption = "Table 3.1: Percentage of Gender by Race", booktabs = T) | Male | Female | |
|---|---|---|
| White | 0.49 | 0.51 |
| Hispanic | 0.50 | 0.50 |
kable(v2, format = "html", caption = "Table 3.2: Percentage of SES by Race", booktabs = T) | First quintile | Second quintile | Third quintile | Fourth quintile | Fifth quintile | |
|---|---|---|---|---|---|
| White | 0.06 | 0.16 | 0.20 | 0.26 | 0.32 |
| Hispanic | 0.37 | 0.22 | 0.17 | 0.15 | 0.09 |
kable(v3, format = "html", caption = "Table 3.3: Percentage of Home Language by Race", booktabs = T) | English | Non-English | |
|---|---|---|
| White | 0.98 | 0.02 |
| Hispanic | 0.47 | 0.53 |
kable(v4, format = "html", caption = "Table 3.4: Percentage of Family Types by Race", booktabs = T) | Both parents & sib | Both parents & no sib | Single parent & sib | Single parent & no sib | Other | |
|---|---|---|---|---|---|
| White | 0.76 | 0.1 | 0.08 | 0.04 | 0.01 |
| Hispanic | 0.68 | 0.1 | 0.14 | 0.07 | 0.01 |
kable(v5, format = "html", caption = "Table 3.5: Percentage of Center-based Care by Race", booktabs = T) | White | Hispanic | |
|---|---|---|
| Yes | 0.82 | 0.18 |
| No | 0.64 | 0.36 |
kable(v6, format = "html", caption = "Table 3.6: Percentage of First-time at Kindergarten by Race", booktabs = T)| Yes | No | |
|---|---|---|
| White | 0.97 | 0.03 |
| Hispanic | 0.95 | 0.05 |
kable(v2, format = "html",caption = "Table 3.2: Percentage of Center-based care by Race", booktabs = T)| First quintile | Second quintile | Third quintile | Fourth quintile | Fifth quintile | |
|---|---|---|---|---|---|
| White | 0.06 | 0.16 | 0.20 | 0.26 | 0.32 |
| Hispanic | 0.37 | 0.22 | 0.17 | 0.15 | 0.09 |
kable(v3, format = "html",caption = "Table 3.3: Percentage of Gender by Race", booktabs = T)| English | Non-English | |
|---|---|---|
| White | 0.98 | 0.02 |
| Hispanic | 0.47 | 0.53 |
kable(v4, format = "html",caption = "Table 3.4: Percentage of Home language by Race", booktabs = T)| Both parents & sib | Both parents & no sib | Single parent & sib | Single parent & no sib | Other | |
|---|---|---|---|---|---|
| White | 0.76 | 0.1 | 0.08 | 0.04 | 0.01 |
| Hispanic | 0.68 | 0.1 | 0.14 | 0.07 | 0.01 |
kable(v5, format = "html",caption = "Table 3.5: Percentage of Family types by Race", booktabs = T)| White | Hispanic | |
|---|---|---|
| Yes | 0.82 | 0.18 |
| No | 0.64 | 0.36 |
kable(v6, format = "html",caption = "Table 3.6: Percentage of First time in Kindergarten by Race", booktabs = T)| Yes | No | |
|---|---|---|
| White | 0.97 | 0.03 |
| Hispanic | 0.95 | 0.05 |
library(pander)
des2 <- my_mathdata %>%
group_by(Race, Home_language, Center) %>%
summarize(N = length(Math_score),
Mean = mean(Math_score),
SD = sd(Math_score),
SE = SD/sqrt(N))
pander(des2, digit=2)| Race | Home_language | Center | N | Mean | SD | SE |
|---|---|---|---|---|---|---|
| White | English | Yes | 5349 | 30 | 9.5 | 0.13 |
| White | English | No | 1348 | 26 | 8.5 | 0.23 |
| White | Non-English | Yes | 77 | 29 | 8.6 | 0.98 |
| White | Non-English | No | 30 | 26 | 5.8 | 1.1 |
| Hispanic | English | Yes | 668 | 26 | 8.3 | 0.32 |
| Hispanic | English | No | 262 | 23 | 6.8 | 0.42 |
| Hispanic | Non-English | Yes | 529 | 21 | 6.2 | 0.27 |
| Hispanic | Non-English | No | 499 | 19 | 5.8 | 0.26 |
Linear Regression Model for Math Skills
mym1<-lm(Math_score~Child_assessment_age+Race+Gender+Approach_to_Learning+Self_control+Social_interaction+Sad_alone+Impulsive+Kindergarten+Center+Number_of_sibling+Total_household_member+Types_family+SES+Home_language+Number_of_book , data = my_mathdata)
mym2<-lm(Math_score~Child_assessment_age+Race*Center+Home_language*Race+Gender+Approach_to_Learning+Social_interaction+Self_control+Sad_alone+Impulsive+Kindergarten+Number_of_sibling+Total_household_member+Types_family+SES+Number_of_book, data = my_mathdata)
mym3<-lm(Math_score~Child_assessment_age+Race*Center*Home_language+Gender+Approach_to_Learning+Social_interaction+Self_control+Sad_alone+Impulsive+Kindergarten+Number_of_sibling+Total_household_member+Types_family+SES+Number_of_book, data = my_mathdata)
AIC(mym1, mym2, mym3)## df AIC
## mym1 24 60893.60
## mym2 26 60891.55
## mym3 28 60894.97Logistic regression model: Center-based care and race as predictor of home language
mylan1<-glm(Home_language_binary~Race+Center+Gender+Kindergarten+Number_of_sibling+Total_household_member+Types_family+SES+Number_of_book, data = my_mathdata)
mylan2<-glm(Home_language_binary~Race*Center+Gender+Kindergarten+Number_of_sibling+Total_household_member+Types_family+SES+Number_of_book, data = my_mathdata)
AIC(mylan1, mylan2)## df AIC
## mylan1 17 393.3411
## mylan2 18 251.1772Logistic regression model: Race as a predictor of Center-based care
myc1<-glm(Center_binary~Race+Gender+Number_of_sibling+Total_household_member+Types_family+SES, data = my_mathdata)
myc2<-glm(Center_binary~Race*SES+Gender+Number_of_sibling+Total_household_member+Types_family, data = my_mathdata)
AIC(myc1, myc2)## df AIC
## myc1 14 9236.458
## myc2 18 9232.393##Table-4: Best-fitted Regresstion models for Math skills, home language, and Center-based care
library(broom)
library(huxtable)
huxreg('Mathmatics skills'=mym2, 'Home language'=mylan2, 'Center-based care'= myc2, number_format = 2, note = 'White children were reference group, {stars}', error_pos = 'same') | Mathmatics skills | Home language | Center-based care | |
| (Intercept) | 20.58 *** (1.20) | 0.79 *** (0.02) | 0.77 *** (0.03) |
| Child_assessment_age | 0.61 *** (0.02) | ||
| RaceHispanic | -1.57 *** (0.30) | -0.36 *** (0.01) | -0.16 *** (0.03) |
| CenterNo | -1.59 *** (0.24) | 0.01 (0.01) | |
| Home_languageNon-English | -0.36 (0.76) | ||
| GenderFemale | -0.41 * (0.17) | -0.00 (0.01) | 0.00 (0.01) |
| Approach_to_Learning | 2.39 *** (0.20) | ||
| Social_interaction | -0.65 *** (0.18) | ||
| Self_control | 0.46 * (0.20) | ||
| Sad_alone | -0.16 (0.25) | ||
| Impulsive | -0.77 *** (0.15) | ||
| KindergartenNo | -0.97 * (0.47) | -0.02 (0.01) | |
| Number_of_sibling | -0.08 (0.16) | 0.02 *** (0.00) | -0.03 *** (0.01) |
| Total_household_member | -0.41 ** (0.13) | -0.02 *** (0.00) | -0.02 ** (0.01) |
| Types_familyBoth parents & no sib | -0.03 (0.32) | 0.02 (0.01) | -0.00 (0.02) |
| Types_familySingle parent & sib | -1.17 *** (0.31) | 0.05 *** (0.01) | 0.04 ** (0.02) |
| Types_family Single parent & no sib | -0.89 * (0.42) | 0.04 ** (0.01) | 0.06 ** (0.02) |
| Types_familyOther | -1.03 (0.90) | 0.10 *** (0.03) | 0.04 (0.05) |
| SESSecond quintile | 1.56 *** (0.33) | 0.18 *** (0.01) | 0.02 (0.02) |
| SESThird quintile | 3.17 *** (0.34) | 0.20 *** (0.01) | 0.09 *** (0.02) |
| SESFourth quintile | 4.52 *** (0.34) | 0.19 *** (0.01) | 0.16 *** (0.02) |
| SESFifth quintile | 7.81 *** (0.35) | 0.18 *** (0.01) | 0.23 *** (0.02) |
| Number_of_book | 0.01 *** (0.00) | 0.00 *** (4.92e-05) | |
| RaceHispanic:CenterNo | 0.91 * (0.44) | -0.16 *** (0.01) | |
| RaceHispanic:Home_languageNon-English | -1.27 (0.85) | ||
| RaceHispanic:SESSecond quintile | 0.11 ** (0.03) | ||
| RaceHispanic:SESThird quintile | 0.07 (0.04) | ||
| RaceHispanic:SESFourth quintile | 0.08 * (0.04) | ||
| RaceHispanic:SESFifth quintile | 0.12 ** (0.04) | ||
| N | 8762 | 8762 | 8762 |
| R 2 | 0.31 | ||
| logLik | -30419.77 | -107.59 | -4598.20 |
| AIC | 60891.55 | 251.18 | 9232.39 |
| White children were reference group, *** p < 0.001; ** p < 0.01; * p < 0.05 | |||
##Best fitted models estimated by using Zelig
library(ZeligChoice)
library(Zelig)
z.out.math <- zelig(Math_score~Child_assessment_age+Race*Center+Home_language*Race+Gender+Approach_to_Learning+Social_interaction+Self_control+Sad_alone+Impulsive+Kindergarten+Number_of_sibling+Total_household_member+Types_family+SES+Number_of_book, model = "ls", data = my_mathdata, cite = FALSE)
summary(z.out.math)## Model:
##
## Call:
## z5$zelig(formula = Math_score ~ Child_assessment_age + Race *
## Center + Home_language * Race + Gender + Approach_to_Learning +
## Social_interaction + Self_control + Sad_alone + Impulsive +
## Kindergarten + Number_of_sibling + Total_household_member +
## Types_family + SES + Number_of_book, data = my_mathdata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -20.946 -5.157 -0.981 3.974 57.169
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 20.579781 1.199557 17.156
## Child_assessment_age 0.609541 0.020638 29.534
## RaceHispanic -1.565943 0.304408 -5.144
## CenterNo -1.590022 0.241401 -6.587
## Home_languageNon-English -0.357878 0.763822 -0.469
## GenderFemale -0.414212 0.169712 -2.441
## Approach_to_Learning 2.386975 0.204373 11.680
## Social_interaction -0.650842 0.179123 -3.633
## Self_control 0.462243 0.201140 2.298
## Sad_alone -0.162220 0.247378 -0.656
## Impulsive -0.774385 0.152605 -5.074
## KindergartenNo -0.966217 0.469149 -2.060
## Number_of_sibling -0.080765 0.156528 -0.516
## Total_household_member -0.411521 0.127971 -3.216
## Types_familyBoth parents & no sib -0.031293 0.322241 -0.097
## Types_familySingle parent & sib -1.170353 0.305181 -3.835
## Types_family Single parent & no sib -0.886677 0.423776 -2.092
## Types_familyOther -1.027808 0.898209 -1.144
## SESSecond quintile 1.562552 0.331274 4.717
## SESThird quintile 3.168882 0.337772 9.382
## SESFourth quintile 4.520057 0.338938 13.336
## SESFifth quintile 7.811676 0.346588 22.539
## Number_of_book 0.013381 0.001588 8.424
## RaceHispanic:CenterNo 0.909675 0.440747 2.064
## RaceHispanic:Home_languageNon-English -1.270735 0.849252 -1.496
## Pr(>|t|)
## (Intercept) < 2e-16
## Child_assessment_age < 2e-16
## RaceHispanic 2.74e-07
## CenterNo 4.76e-11
## Home_languageNon-English 0.639413
## GenderFemale 0.014680
## Approach_to_Learning < 2e-16
## Social_interaction 0.000281
## Self_control 0.021579
## Sad_alone 0.511997
## Impulsive 3.97e-07
## KindergartenNo 0.039475
## Number_of_sibling 0.605881
## Total_household_member 0.001306
## Types_familyBoth parents & no sib 0.922641
## Types_familySingle parent & sib 0.000126
## Types_family Single parent & no sib 0.036438
## Types_familyOther 0.252537
## SESSecond quintile 2.43e-06
## SESThird quintile < 2e-16
## SESFourth quintile < 2e-16
## SESFifth quintile < 2e-16
## Number_of_book < 2e-16
## RaceHispanic:CenterNo 0.039053
## RaceHispanic:Home_languageNon-English 0.134612
##
## Residual standard error: 7.801 on 8737 degrees of freedom
## Multiple R-squared: 0.3142, Adjusted R-squared: 0.3123
## F-statistic: 166.8 on 24 and 8737 DF, p-value: < 2.2e-16
##
## Next step: Use 'setx' method z.out.lan<- zelig(Home_language_binary~Race*Center+Gender+Kindergarten+Number_of_sibling+Total_household_member+Types_family+SES+Number_of_book, model = "logit", data = my_mathdata, cite = FALSE)
summary(z.out.lan)## Model:
##
## Call:
## z5$zelig(formula = Home_language_binary ~ Race * Center + Gender +
## Kindergarten + Number_of_sibling + Total_household_member +
## Types_family + SES + Number_of_book, data = my_mathdata)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.8137 0.0586 0.1421 0.2221 2.2255
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.012424 0.256016 7.861 3.82e-15
## RaceHispanic -3.355617 0.137627 -24.382 < 2e-16
## CenterNo -0.191977 0.222392 -0.863 0.38801
## GenderFemale -0.074282 0.091913 -0.808 0.41899
## KindergartenNo -0.311231 0.220436 -1.412 0.15798
## Number_of_sibling 0.201036 0.068596 2.931 0.00338
## Total_household_member -0.099815 0.050331 -1.983 0.04735
## Types_familyBoth parents & no sib 0.324000 0.177790 1.822 0.06840
## Types_familySingle parent & sib 0.700547 0.145811 4.804 1.55e-06
## Types_family Single parent & no sib 0.569943 0.207428 2.748 0.00600
## Types_familyOther 1.150867 0.448460 2.566 0.01028
## SESSecond quintile 1.032055 0.129463 7.972 1.56e-15
## SESThird quintile 1.302557 0.145914 8.927 < 2e-16
## SESFourth quintile 1.050792 0.152374 6.896 5.34e-12
## SESFifth quintile 0.926266 0.177212 5.227 1.72e-07
## Number_of_book 0.018497 0.001492 12.393 < 2e-16
## RaceHispanic:CenterNo -0.274122 0.245337 -1.117 0.26386
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 6755.6 on 8761 degrees of freedom
## Residual deviance: 3206.6 on 8745 degrees of freedom
## AIC: 3240.6
##
## Number of Fisher Scoring iterations: 7
##
## Next step: Use 'setx' method z.out.center <- zelig(Center_binary~Race*SES+Gender+Number_of_sibling+Total_household_member+Types_family, model = "ls", data = my_mathdata, cite = FALSE)
summary(z.out.center)## Model:
##
## Call:
## z5$zelig(formula = Center_binary ~ Race * SES + Gender + Number_of_sibling +
## Total_household_member + Types_family, data = my_mathdata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.02989 0.00837 0.15283 0.25274 0.90231
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.770807 0.031685 24.327 < 2e-16
## RaceHispanic -0.162518 0.025827 -6.292 3.28e-10
## SESSecond quintile 0.017171 0.024128 0.712 0.476693
## SESThird quintile 0.092407 0.023549 3.924 8.77e-05
## SESFourth quintile 0.159819 0.023079 6.925 4.68e-12
## SESFifth quintile 0.231921 0.022720 10.208 < 2e-16
## GenderFemale 0.002062 0.008755 0.236 0.813792
## Number_of_sibling -0.027524 0.008183 -3.363 0.000773
## Total_household_member -0.018264 0.006704 -2.724 0.006454
## Types_familyBoth parents & no sib -0.003179 0.016836 -0.189 0.850227
## Types_familySingle parent & sib 0.042584 0.015932 2.673 0.007536
## Types_family Single parent & no sib 0.061631 0.022159 2.781 0.005425
## Types_familyOther 0.041734 0.047117 0.886 0.375768
## RaceHispanic:SESSecond quintile 0.105982 0.034630 3.060 0.002217
## RaceHispanic:SESThird quintile 0.067929 0.035755 1.900 0.057483
## RaceHispanic:SESFourth quintile 0.079729 0.036817 2.166 0.030374
## RaceHispanic:SESFifth quintile 0.116561 0.040895 2.850 0.004379
##
## Residual standard error: 0.4094 on 8745 degrees of freedom
## Multiple R-squared: 0.09366, Adjusted R-squared: 0.092
## F-statistic: 56.48 on 16 and 8745 DF, p-value: < 2.2e-16
##
## Next step: Use 'setx' method##Table-5: White-Hispanic Difference in Math skills, home language, and center-based care
###Math skills
x.math_w <- setx(z.out.math, Race="White")
x.math_his <- setx(z.out.math, Race="Hispanic")
s.w.his <- sim(z.out.math, x = x.math_w, x1=x.math_his)
summary(s.w.his)##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 32.1006 0.1957422 32.10272 31.73689 32.48205
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 31.91969 7.711393 32.13008 17.51948 47.25856
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 30.53356 0.3508173 30.51894 29.86826 31.22913
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 30.78719 7.802699 31.01172 14.58959 45.96568
## fd
## mean sd 50% 2.5% 97.5%
## 1 -1.567045 0.308383 -1.576511 -2.135768 -0.9368095plot(s.w.his)
###Home language
x.l_w <- setx(z.out.lan, Race="White")
x.l_his <- setx(z.out.lan, Race="Hispanic")
s.l.w.his <- sim(z.out.lan, x = x.l_w , x1=x.l_his)
summary(s.l.w.his)##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## [1,] 0.9858749 0.002306249 0.9860427 0.9810921 0.9899962
## pv
## 0 1
## [1,] 0.011 0.989
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## [1,] 0.7108612 0.03080715 0.711925 0.6499192 0.7679808
## pv
## 0 1
## [1,] 0.262 0.738
## fd
## mean sd 50% 2.5% 97.5%
## [1,] -0.2750137 0.02946264 -0.2735908 -0.3333681 -0.2206657plot(s.l.w.his)
###Center-based care
x.c.w <- setx(z.out.center, Race="White")
x.c.his <- setx(z.out.center, Race="Hispanic")
s.c.w.his <- sim(z.out.center, x = x.c.w , x1=x.c.his)
summary(s.c.w.his)##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 0.8832465 0.01017769 0.8833186 0.8646198 0.9032662
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 0.9002213 0.3931954 0.9123816 0.1426104 1.66667
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 0.836611 0.03120618 0.8369688 0.7743973 0.8976316
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 0.8335882 0.4026554 0.8345641 0.05607799 1.680856
## fd
## mean sd 50% 2.5% 97.5%
## 1 -0.04663552 0.0319186 -0.04627316 -0.1085466 0.01300679##Center-based care as a predictor of home language
x.l_his.cy <- setx(z.out.lan, Race="Hispanic", Center="Yes")
x.l_his.cn <- setx(z.out.lan, Race="Hispanic", Center="No")
s.l.his.cyn <- sim(z.out.lan, x = x.l_his.cy , x1=x.l_his.cn)
summary(s.l.his.cyn)##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## [1,] 0.7120602 0.03238202 0.7134157 0.644844 0.7713082
## pv
## 0 1
## [1,] 0.262 0.738
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## [1,] 0.6081503 0.04331983 0.6080602 0.5192793 0.690639
## pv
## 0 1
## [1,] 0.38 0.62
## fd
## mean sd 50% 2.5% 97.5%
## [1,] -0.1039098 0.02616043 -0.1041059 -0.15292 -0.05185476plot(s.l.his.cyn)
x.l_w.cy <- setx(z.out.lan, Race="White", Center="Yes")
x.l_w.cn <- setx(z.out.lan, Race="White", Center="No")
s.l.w.cyn <- sim(z.out.lan, x = x.l_w.cy , x1=x.l_w.cn)
summary(s.l.w.cyn)##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## [1,] 0.9859132 0.002318563 0.9860919 0.9807919 0.9899759
## pv
## 0 1
## [1,] 0.017 0.983
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## [1,] 0.9829438 0.003902609 0.9833417 0.9742012 0.9895962
## pv
## 0 1
## [1,] 0.014 0.986
## fd
## mean sd 50% 2.5% 97.5%
## [1,] -0.002969379 0.003626362 -0.002667761 -0.01128016 0.003042756plot(s.l.w.cyn)
x.l_w.cy <- setx(z.out.lan, Race="White", Center="Yes")
x.l_his.cn <- setx(z.out.lan, Race="Hispanic", Center="No")
s.l.w.his.cyn <- sim(z.out.lan, x = x.l_w.cy , x1=x.l_his.cn)
summary(s.l.w.his.cyn)##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## [1,] 0.9859195 0.002276966 0.9862105 0.9810538 0.9897421
## pv
## 0 1
## [1,] 0.025 0.975
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## [1,] 0.6061789 0.04093127 0.6058145 0.5281883 0.6825027
## pv
## 0 1
## [1,] 0.417 0.583
## fd
## mean sd 50% 2.5% 97.5%
## [1,] -0.3797407 0.03967391 -0.3807568 -0.4576849 -0.3054714x.l_w.cy <- setx(z.out.lan, Race="White", Center="Yes")
x.l_his.cy <- setx(z.out.lan, Race="Hispanic", Center="Yes")
s.l.w.his.cyy <- sim(z.out.lan, x = x.l_w.cy , x1=x.l_his.cy)
summary(s.l.w.his.cyy)##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## [1,] 0.9858908 0.002270797 0.9860832 0.9811529 0.9897006
## pv
## 0 1
## [1,] 0.013 0.987
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## [1,] 0.7116791 0.03156291 0.712244 0.6457582 0.7739639
## pv
## 0 1
## [1,] 0.266 0.734
## fd
## mean sd 50% 2.5% 97.5%
## [1,] -0.2742118 0.03015369 -0.2738557 -0.3376053 -0.2150196##Effect of Home language on White-Hispanic Gap of Math score
x.his.ma.le <- setx(z.out.math, Race="Hispanic", Home_language="English")
x.his.ma.lne <- setx(z.out.math, Race="Hispanic", Home_language="Non-English")
s.his.ma.le.lne <- sim(z.out.math, x = x.his.ma.le, x.his.ma.lne)
summary(s.his.ma.le.lne )##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 30.54537 0.3327017 30.54918 29.88369 31.18767
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 30.36505 7.741376 29.87659 15.33498 45.08538
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 28.92916 0.3888702 28.9214 28.18625 29.6525
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 29.38963 7.89886 29.30863 14.31814 45.19803
## fd
## mean sd 50% 2.5% 97.5%
## 1 -1.616211 0.3935906 -1.625579 -2.363111 -0.8338916x.w.ma.le <- setx(z.out.math, Race="White", Home_language="English")
x.his.ma.lne <- setx(z.out.math, Race="Hispanic", Home_language="Non-English")
s.w.his.ma.le.lne <- sim(z.out.math, x = x.w.ma.le , x.his.ma.lne)
summary(s.w.his.ma.le.lne )##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 32.10592 0.194666 32.10797 31.7061 32.49096
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 32.0925 7.888016 31.97545 16.13821 47.27745
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 28.92268 0.3890252 28.92469 28.18245 29.70115
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 28.96399 7.71642 29.10733 13.55458 43.82159
## fd
## mean sd 50% 2.5% 97.5%
## 1 -3.183243 0.3694282 -3.186903 -3.891855 -2.504496x.w.ma.le <- setx(z.out.math, Race="White", Home_language="English")
x.his.ma.le <- setx(z.out.math, Race="Hispanic", Home_language="English")
s.w.his.ma.le.le <- sim(z.out.math, x = x.w.ma.le, x.his.ma.le)
summary(s.w.his.ma.le.le )##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 32.09518 0.1991704 32.09438 31.7097 32.48545
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 31.90703 7.673923 31.89444 17.02879 46.91994
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 30.52838 0.3459793 30.51018 29.87153 31.19354
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 30.20586 7.810606 30.1323 15.35409 45.51627
## fd
## mean sd 50% 2.5% 97.5%
## 1 -1.566806 0.3028893 -1.559413 -2.173274 -0.9933738##Effect of Center on White-Hispanic Gap of Math score
x.his.ma.cy <- setx(z.out.math, Race="Hispanic", Center="Yes")
x.his.ma.cn <- setx(z.out.math, Race="Hispanic", Center="No")
s.his.ma.c <- sim(z.out.math, x = x.his.ma.cy, x1=x.his.ma.cn)
summary(s.his.ma.c )##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 30.55368 0.3337743 30.54288 29.90156 31.1899
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 30.68524 7.647597 30.86213 15.49687 44.85698
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 29.86597 0.4403972 29.86526 28.99291 30.75265
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 29.80594 7.803051 29.86831 13.25428 44.93023
## fd
## mean sd 50% 2.5% 97.5%
## 1 -0.6877054 0.384792 -0.6769337 -1.453861 0.03342578x.w.ma.cy <- setx(z.out.math, Race="White", Center="Yes")
x.his.ma.cn <- setx(z.out.math, Race="Hispanic", Center="No")
s.w.his.ma.c <- sim(z.out.math, x = x.w.ma.cy, x1=x.his.ma.cn)
summary(s.w.his.ma.c )##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 32.10105 0.1980098 32.10623 31.70056 32.45915
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 32.17057 7.79026 32.40657 17.00888 46.67234
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 29.85266 0.4349433 29.8821 29.0071 30.69187
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 29.68881 7.600956 29.4041 14.74816 44.77908
## fd
## mean sd 50% 2.5% 97.5%
## 1 -2.248393 0.4020441 -2.24582 -3.016757 -1.47203x.w.ma.cy <- setx(z.out.math, Race="White", Center="Yes")
x.his.ma.cy <- setx(z.out.math, Race="Hispanic", Center="Yes")
s.w.his.ma.cy <- sim(z.out.math, x = x.w.ma.cy, x1=x.his.ma.cy)
summary(s.w.his.ma.cy )##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 32.10581 0.2000318 32.10892 31.68511 32.47204
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 31.6972 7.570976 31.92307 17.2055 46.36756
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 30.55552 0.3297788 30.554 29.9239 31.18123
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 30.7262 7.773733 30.82127 16.15298 45.78373
## fd
## mean sd 50% 2.5% 97.5%
## 1 -1.550289 0.2962703 -1.538372 -2.139303 -0.9881587x.w.ma.cn <- setx(z.out.math, Race="White", Center="No")
x.his.ma.cy <- setx(z.out.math, Race="Hispanic", Center="Yes")
s.w.his.ma.cny <- sim(z.out.math, x = x.w.ma.cn, x1=x.his.ma.cy)
summary(s.w.his.ma.cny )##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 30.51049 0.284965 30.50816 29.95095 31.09067
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 30.58303 7.778024 30.53294 14.89264 45.08588
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 30.53832 0.3458717 30.54363 29.85929 31.20401
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 30.50429 7.641836 30.48463 16.63039 46.12865
## fd
## mean sd 50% 2.5% 97.5%
## 1 0.02783073 0.3612707 0.02328402 -0.640659 0.7652891##Effect of home language on the association of Center-based care and math skills
x.math1 <- setx(z.out.math, Race="Hispanic", Center="Yes", Home_language="English")
x.math2<- setx(z.out.math, Race="Hispanic", Center="Yes", Home_language="Non-English")
s.his2 <- sim(z.out.math, x = x.math1, x1=x.math2)
summary(s.his2)##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 30.51374 0.3455776 30.51575 29.85564 31.19588
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 30.49554 7.69326 30.42948 15.20718 44.64617
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 28.91677 0.3922084 28.90938 28.20484 29.72466
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 28.94195 7.960025 29.16835 13.48229 44.4704
## fd
## mean sd 50% 2.5% 97.5%
## 1 -1.596966 0.3882095 -1.612538 -2.351803 -0.8360668x.math11 <- setx(z.out.math, Race="White", Center="Yes", Home_language="English")
x.math22<- setx(z.out.math, Race="White", Center="Yes", Home_language="Non-English")
s.w2 <- sim(z.out.math, x = x.math11, x1=x.math22)
summary(s.w2)##
## sim x :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 32.09214 0.2034766 32.09629 31.69948 32.47487
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 32.07852 7.65389 32.0739 17.04747 46.92753
##
## sim x1 :
## -----
## ev
## mean sd 50% 2.5% 97.5%
## 1 31.72826 0.752917 31.73112 30.29667 33.15327
## pv
## mean sd 50% 2.5% 97.5%
## [1,] 32.38714 7.733448 32.62307 17.68402 47.59528
## fd
## mean sd 50% 2.5% 97.5%
## 1 -0.3638834 0.7576926 -0.3585656 -1.824768 1.133592