#install.packages("dplyr")
cities <- read.csv('C:/Users/canda/DEM7903 Causal Inference/Homeownership FC.csv')
View(cities)
cities$Proximity <- as.numeric(cities$Proximity)
class(cities$Proximity)
## [1] "numeric"
View(cities)
plot(cities$Dbw2000,cities$pctbown00,pch=20,
xlab='D index',ylab='Percent Black Homeowners',
main='Cities by Residential segregtaion and Black homeownership in Year 2000')
cor(cities$Dbw2000,cities$pctbown00)
## [1] 0.2205872
cor.test(cities$Dbw2000,cities$pctbown00)
##
## Pearson's product-moment correlation
##
## data: cities$Dbw2000 and cities$pctbown00
## t = 3.1904, df = 199, p-value = 0.001651
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.08478066 0.34834751
## sample estimates:
## cor
## 0.2205872
cit2 <- lm(t_00~Dbw2000+pctbown00,data=cities)
summary(cit2)
##
## Call:
## lm(formula = t_00 ~ Dbw2000 + pctbown00, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -223690 -72106 -23687 21499 1729889
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -46559.0 28694.4 -1.623 0.106
## Dbw2000 3879.6 840.7 4.615 7.07e-06 ***
## pctbown00 -663.9 2051.1 -0.324 0.747
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 183100 on 198 degrees of freedom
## Multiple R-squared: 0.09918, Adjusted R-squared: 0.09009
## F-statistic: 10.9 on 2 and 198 DF, p-value: 3.228e-05
library(lme4)
## Loading required package: Matrix
city3<-lmer(Dbw2000~pctbown00+(1|pctbown00),data=cities)
summary(city3)
## Linear mixed model fit by REML ['lmerMod']
## Formula: Dbw2000 ~ pctbown00 + (1 | pctbown00)
## Data: cities
##
## REML criterion at convergence: 1665.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.66924 -0.61415 -0.00613 0.53549 2.00319
##
## Random effects:
## Groups Name Variance Std.Dev.
## pctbown00 (Intercept) 93.95 9.693
## Residual 146.51 12.104
## Number of obs: 201, groups: pctbown00, 175
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 28.2803 1.4344 19.716
## pctbown00 0.5231 0.1716 3.049
##
## Correlation of Fixed Effects:
## (Intr)
## pctbown00 -0.610
#library(mediation)
#install.packages("lavaan")
library(lavaan)
## This is lavaan 0.6-11
## lavaan is FREE software! Please report any bugs.
str(cities)
## 'data.frame': 201 obs. of 13 variables:
## $ statefp20: int 48 48 48 48 48 48 48 48 48 48 ...
## $ placefp20: int 26544 48804 41212 20092 13492 58820 7000 46776 41116 48772 ...
## $ cityname : chr "Forest Hill" "Missouri City" "Lancaster" "DeSoto" ...
## $ Proximity: num 0 1 0 0 0 0 0 1 1 0 ...
## $ b_20 : int 5630 31255 27716 40012 26719 21645 55824 8650 5803 10287 ...
## $ t_20 : int 13955 74259 41275 56145 49148 56039 115282 23392 18030 36914 ...
## $ pb_20 : num 40.3 42.1 67.2 71.3 54.4 ...
## $ dbw_20 : num 17.6 41.2 40 21.3 32.4 ...
## $ b_00 : int 7414 20486 13814 17242 10918 25360 52461 9263 4767 6770 ...
## $ t_00 : int 12949 52913 25894 37646 32093 57755 113866 23935 13682 30831 ...
## $ pb_00 : num 57.3 38.7 53.4 45.8 34 ...
## $ Dbw2000 : num 28.8 52.9 44.8 15.9 32.9 ...
## $ pctbown00: num 50.4 32.9 29.6 28.8 26 ...
fit.totaleffect=lm(pctbown00~Dbw2000,cities)
summary(fit.totaleffect)
##
## Call:
## lm(formula = pctbown00 ~ Dbw2000, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.160 -3.365 -1.672 1.167 45.725
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.08965 0.98057 2.131 0.03431 *
## Dbw2000 0.09042 0.02834 3.190 0.00165 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.328 on 199 degrees of freedom
## Multiple R-squared: 0.04866, Adjusted R-squared: 0.04388
## F-statistic: 10.18 on 1 and 199 DF, p-value: 0.001651
fit.realeffect=lm(Dbw2000~pctbown00,cities)
summary(fit.realeffect)
##
## Call:
## lm(formula = Dbw2000 ~ pctbown00, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -33.204 -11.181 -0.123 10.735 39.794
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 28.1832 1.3646 20.65 < 2e-16 ***
## pctbown00 0.5382 0.1687 3.19 0.00165 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.44 on 199 degrees of freedom
## Multiple R-squared: 0.04866, Adjusted R-squared: 0.04388
## F-statistic: 10.18 on 1 and 199 DF, p-value: 0.001651
fit.othereffect=lm(pb_00~pctbown00,cities)
summary(fit.othereffect)
##
## Call:
## lm(formula = pb_00 ~ pctbown00, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -23.369 -2.798 -1.130 1.829 28.382
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.90820 0.43823 6.636 2.98e-10 ***
## pctbown00 1.54146 0.05417 28.455 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.958 on 199 degrees of freedom
## Multiple R-squared: 0.8027, Adjusted R-squared: 0.8017
## F-statistic: 809.7 on 1 and 199 DF, p-value: < 2.2e-16
fit.mediator=lm(Proximity~pctbown00,cities)
summary(fit.mediator)
##
## Call:
## lm(formula = Proximity ~ pctbown00, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8475 -0.2685 -0.2401 0.6402 0.7700
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.228730 0.039628 5.772 2.97e-08 ***
## pctbown00 0.012272 0.004899 2.505 0.013 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4483 on 199 degrees of freedom
## Multiple R-squared: 0.03057, Adjusted R-squared: 0.0257
## F-statistic: 6.276 on 1 and 199 DF, p-value: 0.01304
fit.new=lm(Proximity~pb_00,cities)
summary(fit.new)
##
## Call:
## lm(formula = Proximity ~ pb_00, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8219 -0.2438 -0.1947 0.5260 0.8288
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.169865 0.042295 4.016 8.38e-05 ***
## pb_00 0.011388 0.002777 4.101 5.99e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4373 on 199 degrees of freedom
## Multiple R-squared: 0.07793, Adjusted R-squared: 0.0733
## F-statistic: 16.82 on 1 and 199 DF, p-value: 5.992e-05
fit.newnew=lm(Proximity~dbw_20,cities)
summary(fit.newnew)
##
## Call:
## lm(formula = Proximity ~ dbw_20, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6196 -0.3110 -0.2159 0.5593 0.8615
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.033497 0.085210 0.393 0.6947
## dbw_20 0.009172 0.002850 3.219 0.0015 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.444 on 199 degrees of freedom
## Multiple R-squared: 0.04948, Adjusted R-squared: 0.0447
## F-statistic: 10.36 on 1 and 199 DF, p-value: 0.001504
fit.other=lm(pb_00~Dbw2000,cities)
summary(fit.other)
##
## Call:
## lm(formula = pb_00 ~ Dbw2000, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.682 -6.951 -2.864 3.652 47.282
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.55271 1.64089 2.165 0.0316 *
## Dbw2000 0.22301 0.04743 4.702 4.8e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.59 on 199 degrees of freedom
## Multiple R-squared: 0.1, Adjusted R-squared: 0.09548
## F-statistic: 22.11 on 1 and 199 DF, p-value: 4.8e-06
fit.dv=lm(pctbown00~Dbw2000+Proximity,cities)
summary(fit.dv)
##
## Call:
## lm(formula = pctbown00 ~ Dbw2000 + Proximity, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.801 -3.289 -1.650 0.724 46.221
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.97488 0.97732 2.021 0.04466 *
## Dbw2000 0.07719 0.02914 2.649 0.00873 **
## Proximity 1.80977 1.01302 1.787 0.07555 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.294 on 198 degrees of freedom
## Multiple R-squared: 0.06375, Adjusted R-squared: 0.05429
## F-statistic: 6.741 on 2 and 198 DF, p-value: 0.001472
fit.main=lm(Dbw2000~Proximity+pctbown00,cities)
summary(fit.main)
##
## Call:
## lm(formula = Dbw2000 ~ Proximity + pctbown00, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -32.639 -10.831 -0.328 9.328 41.569
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 26.4159 1.4405 18.338 < 2e-16 ***
## Proximity 7.7264 2.3849 3.240 0.00140 **
## pctbown00 0.4433 0.1674 2.649 0.00873 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.08 on 198 degrees of freedom
## Multiple R-squared: 0.09655, Adjusted R-squared: 0.08743
## F-statistic: 10.58 on 2 and 198 DF, p-value: 4.31e-05
specmod <- "#Path c
Dbw2000 ~ c*pctbown00
#Path a
Proximity ~ a*Dbw2000
#Path b
Proximity ~ b*pctbown00
#Indirect effect (a*b)
ab :=a*b
"
fitmod<- sem(specmod, data=cities)
## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan
## WARNING: some observed variances are (at least) a factor 1000 times larger than
## others; use varTable(fit) to investigate
summary(fitmod,fit.measures=TRUE, rsquare=TRUE)
## lavaan 0.6-11 ended normally after 1 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 5
##
## Number of observations 201
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 26.650
## Degrees of freedom 3
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -952.092
## Loglikelihood unrestricted model (H1) -952.092
##
## Akaike (AIC) 1914.185
## Bayesian (BIC) 1930.701
## Sample-size adjusted Bayesian (BIC) 1914.860
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value RMSEA <= 0.05 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## Dbw2000 ~
## pctbown00 (c) 0.538 0.168 3.206 0.001
## Proximity ~
## Dbw2000 (a) 0.007 0.002 3.264 0.001
## pctbown00 (b) 0.009 0.005 1.800 0.072
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .Dbw2000 235.999 23.541 10.025 0.000
## .Proximity 0.189 0.019 10.025 0.000
##
## R-Square:
## Estimate
## Dbw2000 0.049
## Proximity 0.079
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## ab 0.000 0.000 1.748 0.081
set.seed(2000)
fitmod2 <- sem(specmod, data=cities, se="bootstrap", bootstrap=3000)
## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan
## WARNING: some observed variances are (at least) a factor 1000 times larger than
## others; use varTable(fit) to investigate
parameterEstimates(fitmod2, ci = TRUE, level=0.95, boot.ci.type="perc")
## lhs op rhs label est se z pvalue ci.lower ci.upper
## 1 Dbw2000 ~ pctbown00 c 0.538 0.218 2.463 0.014 0.222 1.075
## 2 Proximity ~ Dbw2000 a 0.007 0.002 3.315 0.001 0.003 0.010
## 3 Proximity ~ pctbown00 b 0.009 0.007 1.334 0.182 0.000 0.026
## 4 Dbw2000 ~~ Dbw2000 235.999 21.544 10.955 0.000 192.447 276.757
## 5 Proximity ~~ Proximity 0.189 0.014 13.346 0.000 0.156 0.212
## 6 pctbown00 ~~ pctbown00 41.678 0.000 NA NA 41.678 41.678
## 7 ab := a*b ab 0.000 0.000 1.410 0.159 0.000 0.000
summary(fitmod2)
## lavaan 0.6-11 ended normally after 1 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 5
##
## Number of observations 201
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 3000
## Number of successful bootstrap draws 3000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## Dbw2000 ~
## pctbown00 (c) 0.538 0.218 2.463 0.014
## Proximity ~
## Dbw2000 (a) 0.007 0.002 3.315 0.001
## pctbown00 (b) 0.009 0.007 1.334 0.182
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .Dbw2000 235.999 21.544 10.955 0.000
## .Proximity 0.189 0.014 13.346 0.000
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## ab 0.000 0.000 1.410 0.159