Social Capital

Importing Data

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

Data Cleaning

Final cleaning and rename

Error in tbl_vars(y) : object 'finaldata' not found

Error: unexpected ']' in "data[5:]"

Hierarchical clustering

res.pca <- PCA(df, ncp = 6, graph = FALSE)
# Compute hierarchical clustering on principal components
res.hcpc <- HCPC(res.pca, graph = FALSE)

fviz_dend(res.hcpc, show_labels = FALSE)

library(Rtsne)
fviz_cluster(res.hcpc, geom = "point", main = "Factor map")

res.hcpc$desc.var$quanti

t-SNE

library(Rtsne)
tsne <- Rtsne(data[c(23,24,28,29,31)], dims = 2, perplexity=50, verbose=FALSE, max_iter = 500)
tsne_data <- tsne$Y %>%
  data.frame() %>%
  setNames(c("X", "Y")) %>%
  mutate(cluster = factor(res.hcpc$data.clust$clust))
ggplot(aes(x = X, y = Y), data = tsne_data) +
  geom_point(aes(color = cluster))

data exploration after clustering

d=res.hcpc$data.clust
d$clust=as.factor(d$clust)

ggplot(d, aes(x=clust, y=education)) +geom_violin(trim=FALSE)
ggplot(d, aes(x=clust, y=sk09)) +geom_violin(trim=FALSE)
ggplot(d, aes(x=clust, y=income)) +geom_violin(trim=FALSE)
ggplot(d, aes(x=clust, y=white)) +geom_violin(trim=FALSE)
ggplot(d, aes(x=clust, y=black)) +geom_violin(trim=FALSE)
ggplot(d, aes(x=clust, y=rural_percent)) +geom_violin(trim=FALSE)

RUCC

library(cluster) 
gower_dist <- daisy(data[c(23,24,28,29,31)], metric = "gower")
gower_mat <- as.matrix(gower_dist)
sil_width <- c(NA)
for(i in 2:8){  
  pam_fit <- pam(data[c(23,24,28,29,31)], k = i)  
  sil_width[i] <- pam_fit$silinfo$avg.width  
}
plot(1:8, sil_width,
     xlab = "Number of clusters",
     ylab = "Silhouette Width")
lines(1:8, sil_width)

gower

library(cluster) 
gower_dist <- daisy(data[c(2,23,24,28,29)], metric = "gower")
gower_mat <- as.matrix(gower_dist)
sil_width <- c(NA)
for(i in 2:8){  
  pam_fit <- pam(gower_dist, diss = TRUE, k = i)  
  sil_width[i] <- pam_fit$silinfo$avg.width  
}
plot(1:8, sil_width,
     xlab = "Number of clusters",
     ylab = "Silhouette Width")
lines(1:8, sil_width)

k <- 4
pam_fit <- pam(gower_dist, diss = TRUE, k)
pam_results <- data %>%
  mutate(cluster = pam_fit$clustering) %>%
  group_by(cluster) %>%
  do(the_summary = summary(.))
pam_results$the_summary
tsne_obj <- Rtsne(gower_dist, is_distance = TRUE,pca_scale=TRUE)
tsne_data <- tsne_obj$Y %>%
  data.frame() %>%
  setNames(c("X", "Y")) %>%
  mutate(cluster = factor(pam_fit$clustering))
ggplot(aes(x = X, y = Y), data = tsne_data) +
  geom_point(aes(color = cluster))

Mutilevel Model

Overall EQI

model1 <- lmer(air_EQI_22July2013 ~ sk09+ (1 |state)+cat_rucc+education+black+income, data=data,REML=F)
summary(model1)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
air_EQI_22July2013 ~ sk09 + (1 | state) + cat_rucc + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  4444.3   4504.8  -2212.2   4424.3     3098 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.4461 -0.6132  0.0368  0.6398  5.1351 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.2542   0.5042  
 Residual             0.2285   0.4780  
Number of obs: 3108, groups:  state, 49

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.46598    0.07517   6.199
sk09        -0.22650    0.01299 -17.439
cat_rucc2   -0.08711    0.03224  -2.702
cat_rucc3   -0.53989    0.02523 -21.401
cat_rucc4   -1.14784    0.03128 -36.699
education    0.14457    0.01480   9.768
black        0.15412    0.01305  11.806
income       0.08422    0.01353   6.223

Correlation of Fixed Effects:
          (Intr) sk09   ct_rc2 ct_rc3 ct_rc4 eductn black 
sk09       0.066                                          
cat_rucc2 -0.130 -0.056                                   
cat_rucc3 -0.189 -0.250  0.413                            
cat_rucc4 -0.173 -0.407  0.354  0.603                     
education -0.059 -0.392  0.038  0.224  0.220              
black     -0.034 -0.098  0.071  0.143  0.175  0.095       
income    -0.088  0.060  0.223  0.310  0.285 -0.443  0.161

model2 <- lmer(water_EQI_22July2013 ~ sk09+ (1 |state)+cat_rucc+education+black+income, data=data,REML=F)
summary(model2)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
water_EQI_22July2013 ~ sk09 + (1 | state) + cat_rucc + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  5763.9   5824.4  -2872.0   5743.9     3098 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.0632 -0.2854  0.1306  0.5485  3.2417 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.6477   0.8048  
 Residual             0.3466   0.5887  
Number of obs: 3108, groups:  state, 49

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.12797    0.11808   1.084
sk09        -0.09265    0.01602  -5.783
cat_rucc2    0.05545    0.03972   1.396
cat_rucc3    0.03094    0.03108   0.995
cat_rucc4   -0.17255    0.03854  -4.478
education    0.04708    0.01825   2.580
black       -0.02885    0.01613  -1.789
income       0.03058    0.01670   1.831

Correlation of Fixed Effects:
          (Intr) sk09   ct_rc2 ct_rc3 ct_rc4 eductn black 
sk09       0.051                                          
cat_rucc2 -0.102 -0.056                                   
cat_rucc3 -0.148 -0.250  0.413                            
cat_rucc4 -0.135 -0.407  0.354  0.603                     
education -0.046 -0.391  0.038  0.224  0.220              
black     -0.028 -0.097  0.071  0.142  0.174  0.092       
income    -0.070  0.061  0.223  0.309  0.285 -0.443  0.162

model3 <- lmer(land_EQI_22July2013 ~ sk09+ (1 |state)+cat_rucc+education+black+income, data=data,REML=F)
summary(model3)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
land_EQI_22July2013 ~ sk09 + (1 | state) + cat_rucc + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  5892.2   5952.6  -2936.1   5872.2     3098 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-8.4960 -0.3826  0.0644  0.5070  3.0536 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.2992   0.5470  
 Residual             0.3658   0.6048  
Number of obs: 3108, groups:  state, 49

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.24062    0.08264   2.912
sk09         0.04893    0.01641   2.981
cat_rucc2   -0.02405    0.04079  -0.590
cat_rucc3   -0.13029    0.03191  -4.083
cat_rucc4   -0.23730    0.03956  -5.998
education   -0.06309    0.01871  -3.373
black       -0.02487    0.01647  -1.510
income       0.11247    0.01710   6.578

Correlation of Fixed Effects:
          (Intr) sk09   ct_rc2 ct_rc3 ct_rc4 eductn black 
sk09       0.077                                          
cat_rucc2 -0.149 -0.056                                   
cat_rucc3 -0.218 -0.250  0.413                            
cat_rucc4 -0.199 -0.408  0.354  0.603                     
education -0.069 -0.392  0.037  0.223  0.220              
black     -0.039 -0.098  0.072  0.144  0.176  0.097       
income    -0.100  0.060  0.223  0.310  0.285 -0.443  0.160

model4 <- lmer(sociod_EQI_22July2013 ~ sk09+ (1 |state)+cat_rucc+education+black+income, data=data,REML=F)
summary(model4)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
sociod_EQI_22July2013 ~ sk09 + (1 | state) + cat_rucc + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  2814.3   2874.8  -1397.2   2794.3     3098 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-8.1763 -0.5236  0.0483  0.6158  3.1107 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.08391  0.2897  
 Residual             0.13645  0.3694  
Number of obs: 3108, groups:  state, 49

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.07613    0.04446   1.712
sk09         0.03720    0.01001   3.716
cat_rucc2   -0.07570    0.02491  -3.040
cat_rucc3   -0.14387    0.01948  -7.385
cat_rucc4   -0.38094    0.02415 -15.772
education    0.30210    0.01141  26.470
black       -0.07883    0.01003  -7.859
income       0.60189    0.01042  57.746

Correlation of Fixed Effects:
          (Intr) sk09   ct_rc2 ct_rc3 ct_rc4 eductn black 
sk09       0.088                                          
cat_rucc2 -0.169 -0.056                                   
cat_rucc3 -0.247 -0.251  0.413                            
cat_rucc4 -0.226 -0.408  0.354  0.602                     
education -0.078 -0.393  0.037  0.223  0.219              
black     -0.044 -0.098  0.072  0.145  0.177  0.099       
income    -0.112  0.060  0.223  0.311  0.286 -0.443  0.160

model5 <- lmer(built_EQI_22July2013 ~ sk09+ (1 |state)+cat_rucc+education+black+income, data=data,REML=F)
summary(model5)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
built_EQI_22July2013 ~ sk09 + (1 | state) + cat_rucc + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  7458.6   7519.1  -3719.3   7438.6     3098 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.2991 -0.4847  0.0818  0.6186  4.2431 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.08751  0.2958  
 Residual             0.62073  0.7879  
Number of obs: 3108, groups:  state, 49

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.22625    0.05332   4.244
sk09         0.10929    0.02104   5.194
cat_rucc2    0.38232    0.05299   7.215
cat_rucc3    0.03574    0.04138   0.864
cat_rucc4   -0.94362    0.05129 -18.396
education    0.24623    0.02403  10.246
black        0.07270    0.02069   3.514
income      -0.02441    0.02181  -1.119

Correlation of Fixed Effects:
          (Intr) sk09   ct_rc2 ct_rc3 ct_rc4 eductn black 
sk09       0.164                                          
cat_rucc2 -0.296 -0.059                                   
cat_rucc3 -0.437 -0.257  0.412                            
cat_rucc4 -0.402 -0.416  0.354  0.601                     
education -0.138 -0.405  0.033  0.218  0.217              
black     -0.079 -0.095  0.078  0.156  0.187  0.125       
income    -0.185  0.059  0.225  0.315  0.290 -0.444  0.154

RUCC 1

model1.1 <- lmer(RUCC1_air_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model1.1)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC1_air_EQI_22July2013 ~ sk09 + (1 | state) + education + black +  
    income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  2711.4   2746.4  -1348.7   2697.4     1078 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.4414 -0.6389  0.0713  0.6558  2.9951 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.3002   0.5479  
 Residual             0.6389   0.7993  
Number of obs: 1085, groups:  state, 49

Fixed effects:
            Estimate Std. Error t value
(Intercept) -0.31262    0.08931  -3.500
sk09        -0.25408    0.04084  -6.222
education    0.25387    0.04692   5.411
black        0.40058    0.03370  11.887
income       0.14484    0.03215   4.505

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09       0.178                     
education -0.132 -0.315              
black     -0.077 -0.137  0.080       
income    -0.094  0.098 -0.593  0.148

model1.2 <- lmer(RUCC1_water_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model1.2)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC1_water_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  1959.1   1994.0   -972.5   1945.1     1078 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.0704 -0.1863  0.0844  0.4767  3.4794 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.6637   0.8147  
 Residual             0.2999   0.5476  
Number of obs: 1085, groups:  state, 49

Fixed effects:
             Estimate Std. Error t value
(Intercept)  0.078527   0.120546   0.651
sk09        -0.088252   0.028378  -3.110
education    0.094215   0.032613   2.889
black       -0.064913   0.023614  -2.749
income       0.001459   0.022467   0.065

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09       0.084                     
education -0.068 -0.304              
black     -0.038 -0.131  0.056       
income    -0.050  0.096 -0.597  0.163

model1.3 <- lmer(RUCC1_land_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model1.3)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC1_land_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  2192.3   2227.2  -1089.2   2178.3     1078 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-8.8502 -0.3919  0.0765  0.5253  4.1780 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.3566   0.5972  
 Residual             0.3856   0.6210  
Number of obs: 1085, groups:  state, 49

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.14276    0.09205   1.551
sk09         0.05923    0.03197   1.853
education   -0.09580    0.03676  -2.606
black       -0.06848    0.02652  -2.582
income       0.13654    0.02526   5.404

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09       0.130                     
education -0.100 -0.309              
black     -0.057 -0.135  0.066       
income    -0.072  0.096 -0.595  0.156

model1.4 <- lmer(RUCC1_sociod_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model1.4)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC1_sociod_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  1410.1   1445.0   -698.0   1396.1     1078 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.9816 -0.5849 -0.0655  0.4491  8.0322 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.1371   0.3703  
 Residual             0.1894   0.4352  
Number of obs: 1085, groups:  state, 49

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.50286    0.05807   8.659
sk09        -0.01827    0.02235  -0.817
education   -0.26102    0.02569 -10.159
black        0.20647    0.01851  11.154
income      -0.59995    0.01764 -34.006

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09       0.146                     
education -0.111 -0.311              
black     -0.063 -0.136  0.071       
income    -0.080  0.097 -0.594  0.153

model1.5 <- lmer(RUCC1_built_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model1.5)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC1_built_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  2808.4   2843.3  -1397.2   2794.4     1078 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.7613 -0.5660  0.1271  0.6305  4.4819 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.1655   0.4069  
 Residual             0.7165   0.8465  
Number of obs: 1085, groups:  state, 49

Fixed effects:
            Estimate Std. Error t value
(Intercept) -0.01665    0.07264  -0.229
sk09         0.15397    0.04278   3.599
education    0.40089    0.04900   8.181
black        0.22162    0.03494   6.342
income      -0.01117    0.03340  -0.334

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09       0.239                     
education -0.168 -0.327              
black     -0.106 -0.140  0.102       
income    -0.119  0.102 -0.588  0.135

RUCC 2

model2.1 <- lmer(RUCC2_air_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model2.1)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC2_air_EQI_22July2013 ~ sk09 + (1 | state) + education + black +  
    income
   Data: data

     AIC      BIC   logLik deviance df.resid 
   742.0    768.4   -364.0    728.0      312 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.6511 -0.5417  0.0642  0.5809  2.3070 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.5832   0.7637  
 Residual             0.4226   0.6501  
Number of obs: 319, groups:  state, 45

Fixed effects:
            Estimate Std. Error t value
(Intercept) -0.13412    0.12618  -1.063
sk09         0.09009    0.09525   0.946
education    0.14424    0.06820   2.115
black        0.15114    0.07103   2.128
income      -0.09245    0.08095  -1.142

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09       0.197                     
education -0.177 -0.517              
black     -0.011 -0.162  0.129       
income     0.041  0.085 -0.361  0.292

model2.2 <- lmer(RUCC2_water_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model2.2)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC2_water_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
   542.9    569.2   -264.4    528.9      312 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.4962 -0.1765  0.0193  0.2852  2.8883 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.7072   0.8409  
 Residual             0.2011   0.4484  
Number of obs: 319, groups:  state, 45

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.10835    0.13121   0.826
sk09        -0.02734    0.06758  -0.405
education    0.03613    0.04758   0.759
black       -0.01992    0.05145  -0.387
income       0.06365    0.05783   1.101

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09       0.131                     
education -0.120 -0.513              
black     -0.006 -0.171  0.113       
income     0.019  0.087 -0.357  0.291

model2.3 <- lmer(RUCC2_land_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model2.3)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC2_land_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
   652.4    678.7   -319.2    638.4      312 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-6.7082 -0.3555  0.0813  0.4729  2.7411 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.2369   0.4867  
 Residual             0.3457   0.5880  
Number of obs: 319, groups:  state, 45

Fixed effects:
             Estimate Std. Error t value
(Intercept)  0.144963   0.086741   1.671
sk09         0.142783   0.083325   1.714
education    0.004104   0.060780   0.068
black       -0.047979   0.060412  -0.794
income       0.099979   0.070444   1.419

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09       0.256                     
education -0.226 -0.522              
black     -0.017 -0.154  0.148       
income     0.070  0.081 -0.365  0.293

model2.4 <- lmer(RUCC2_sociod_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model2.4)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC2_sociod_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
   382.2    408.6   -184.1    368.2      312 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.6802 -0.4660  0.0135  0.6162  2.1651 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.1511   0.3887  
 Residual             0.1410   0.3755  
Number of obs: 319, groups:  state, 45

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.04130    0.06575   0.628
sk09         0.18677    0.05442   3.432
education    0.36299    0.03920   9.259
black       -0.06514    0.04023  -1.619
income       0.78296    0.04616  16.963

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09       0.218                     
education -0.194 -0.518              
black     -0.013 -0.159  0.135       
income     0.050  0.084 -0.362  0.292

model2.5 <- lmer(RUCC2_built_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model2.5)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC2_built_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
   798.5    824.9   -392.3    784.5      312 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.7727 -0.5109  0.0567  0.5298  2.9185 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.1588   0.3986  
 Residual             0.5980   0.7733  
Number of obs: 319, groups:  state, 45

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.19405    0.08382   2.315
sk09         0.60434    0.10347   5.841
education    0.18332    0.07767   2.360
black       -0.20405    0.07090  -2.878
income      -0.07050    0.08730  -0.808

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09       0.334                     
education -0.294 -0.533              
black     -0.025 -0.145  0.183       
income     0.124  0.074 -0.371  0.295

RUCC 3

model3.1 <- lmer(RUCC3_air_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model3.1)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC3_air_EQI_22July2013 ~ sk09 + (1 | state) + education + black +  
    income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  2179.9   2214.6  -1082.9   2165.9     1041 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.8569 -0.5920 -0.0162  0.6385  3.2613 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.6776   0.8232  
 Residual             0.3999   0.6324  
Number of obs: 1048, groups:  state, 44

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.04170    0.12740   0.327
sk09        -0.38356    0.04002  -9.584
education    0.31160    0.03314   9.402
black        0.08819    0.03020   2.920
income       0.07591    0.04162   1.824

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09      -0.031                     
education  0.006 -0.434              
black      0.041 -0.138  0.101       
income     0.073 -0.028 -0.315  0.212

model3.2 <- lmer(RUCC3_water_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model3.2)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC3_water_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  2039.0   2073.7  -1012.5   2025.0     1041 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.8947 -0.2268  0.1626  0.5279  2.8749 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.7098   0.8425  
 Residual             0.3470   0.5890  
Number of obs: 1048, groups:  state, 44

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.04668    0.12983   0.360
sk09        -0.09007    0.03735  -2.411
education    0.08062    0.03089   2.610
black       -0.05058    0.02820  -1.794
income      -0.04312    0.03883  -1.110

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09      -0.029                     
education  0.006 -0.434              
black      0.037 -0.139  0.100       
income     0.066 -0.026 -0.315  0.211

model3.3 <- lmer(RUCC3_land_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model3.3)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC3_land_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  2076.2   2110.9  -1031.1   2062.2     1041 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-8.0744 -0.3723  0.0571  0.4614  2.5967 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.4098   0.6402  
 Residual             0.3684   0.6069  
Number of obs: 1048, groups:  state, 44

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.16920    0.10032   1.687
sk09         0.04255    0.03819   1.114
education   -0.03411    0.03173  -1.075
black       -0.05140    0.02876  -1.787
income       0.08884    0.03976   2.234

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09      -0.038                     
education  0.008 -0.437              
black      0.049 -0.136  0.106       
income     0.091 -0.031 -0.316  0.214

model3.4 <- lmer(RUCC3_sociod_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model3.4)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC3_sociod_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  1132.7   1167.4   -559.3   1118.7     1041 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-8.4568 -0.5611  0.0543  0.6302  3.7975 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.09431  0.3071  
 Residual             0.15316  0.3914  
Number of obs: 1048, groups:  state, 44

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.34238    0.04945   6.923
sk09         0.11890    0.02433   4.886
education    0.36709    0.02036  18.028
black       -0.09469    0.01825  -5.189
income       0.71355    0.02542  28.075

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09      -0.050                     
education  0.011 -0.443              
black      0.064 -0.133  0.116       
income     0.124 -0.037 -0.318  0.219

model3.5 <- lmer(RUCC3_built_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model3.5)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC3_built_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  2275.6   2310.3  -1130.8   2261.6     1041 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.8311 -0.5406  0.0620  0.6246  4.3945 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.1040   0.3225  
 Residual             0.4726   0.6875  
Number of obs: 1048, groups:  state, 44

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.11256    0.05683   1.981
sk09         0.37849    0.04133   9.157
education    0.23360    0.03522   6.632
black       -0.10146    0.03049  -3.328
income      -0.01539    0.04367  -0.352

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09      -0.078                     
education  0.021 -0.460              
black      0.096 -0.123  0.147       
income     0.204 -0.050 -0.325  0.232

RUCC 4

model4.1 <- lmer(RUCC4_air_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model4.1)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC4_air_EQI_22July2013 ~ sk09 + (1 | state) + education + black +  
    income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  1021.7   1053.1   -503.8   1007.7      649 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.4180 -0.6065 -0.0306  0.6109  3.7516 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.7340   0.8568  
 Residual             0.2181   0.4670  
Number of obs: 656, groups:  state, 41

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.39988    0.13849   2.887
sk09        -0.19556    0.02097  -9.325
education    0.13213    0.03365   3.927
black        0.06358    0.03177   2.001
income       0.09724    0.03555   2.736

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09      -0.081                     
education -0.007 -0.367              
black      0.050 -0.081  0.162       
income     0.093  0.005 -0.447  0.085

model4.2 <- lmer(RUCC4_water_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model4.2)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC4_water_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  1520.8   1552.2   -753.4   1506.8      649 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-3.05989 -0.58308  0.06681  0.66507  2.58322 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.5369   0.7328  
 Residual             0.4981   0.7058  
Number of obs: 656, groups:  state, 41

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.19988    0.12561   1.591
sk09        -0.11678    0.03138  -3.721
education    0.04929    0.05020   0.982
black        0.01909    0.04688   0.407
income       0.08930    0.05340   1.672

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09      -0.135                     
education -0.007 -0.373              
black      0.084 -0.077  0.179       
income     0.157  0.003 -0.449  0.084

model4.3 <- lmer(RUCC4_land_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model1.3)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC1_land_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  2192.3   2227.2  -1089.2   2178.3     1078 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-8.8502 -0.3919  0.0765  0.5253  4.1780 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.3566   0.5972  
 Residual             0.3856   0.6210  
Number of obs: 1085, groups:  state, 49

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.14276    0.09205   1.551
sk09         0.05923    0.03197   1.853
education   -0.09580    0.03676  -2.606
black       -0.06848    0.02652  -2.582
income       0.13654    0.02526   5.404

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09       0.130                     
education -0.100 -0.309              
black     -0.057 -0.135  0.066       
income    -0.072  0.096 -0.595  0.156

model4.4 <- lmer(RUCC4_sociod_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model4.4)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC4_sociod_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
   911.8    943.2   -448.9    897.8      649 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.5427 -0.4525  0.0575  0.5875  2.4639 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.09776  0.3127  
 Residual             0.20533  0.4531  
Number of obs: 656, groups:  state, 41

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.19876    0.05825   3.412
sk09         0.11786    0.01985   5.937
education    0.36624    0.03163  11.578
black       -0.11695    0.02913  -4.015
income       0.59014    0.03399  17.365

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09      -0.190                     
education -0.002 -0.382              
black      0.117 -0.072  0.199       
income     0.219 -0.001 -0.452  0.086

model4.5 <- lmer(RUCC4_built_EQI_22July2013 ~ sk09+ (1 |state)+education+black+income, data=data,REML=F)
summary(model4.5)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
RUCC4_built_EQI_22July2013 ~ sk09 + (1 | state) + education +  
    black + income
   Data: data

     AIC      BIC   logLik deviance df.resid 
  1744.6   1776.0   -865.3   1730.6      649 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.5640 -0.4689  0.1504  0.6488  2.7310 

Random effects:
 Groups   Name        Variance Std.Dev.
 state    (Intercept) 0.08265  0.2875  
 Residual             0.77661  0.8813  
Number of obs: 656, groups:  state, 41

Fixed effects:
            Estimate Std. Error t value
(Intercept) -0.06991    0.07185  -0.973
sk09         0.09493    0.03669   2.588
education    0.19878    0.05772   3.444
black       -0.13814    0.05112  -2.702
income      -0.11418    0.06401  -1.784

Correlation of Fixed Effects:
          (Intr) sk09   eductn black 
sk09      -0.324                     
education  0.030 -0.409              
black      0.178 -0.053  0.248       
income     0.348 -0.025 -0.454  0.094