County Characteristics on Juvenile Justice System Involvement Outcomes in WI US

# data management
library(haven)
library(dplyr)
library(tidyverse)
library(tidycensus)
library(corrr)

# spatial analysis
library(sf)
library(spatialreg)
library(spdep)
library(spaMM)

# plot
library(ggplot2)
library(tigris)
library(maps)
library(tmap)
library(rmapshaper)
library(tidyrgeoda)
library(corrplot)

# table
library(flextable)
library(stargazer)
library(DT)

Import Contextual and Geo Data

yj <- read.csv("wi_county_data.csv")
wi_poly <- read_sf("County_Boundaries_24K/County_Boundaries_24K.shp")
yj$COUNTY_FIP <- as.factor(yj$COUNTY_FIP)
yj_dat <- left_join(wi_poly, yj, by = "COUNTY_FIP")

Global Moran’s I

### queen method
nb_q<-poly2nb(st_geometry(yj_dat),queen = T)
nb_q

## Neighbour list object:
## Number of regions: 72 
## Number of nonzero links: 370 
## Percentage nonzero weights: 7.137346 
## Average number of links: 5.138889

moran.test(yj_dat$Court_Rate, nb2listw(nb_q,style = "B"))

## 
##  Moran I test under randomisation
## 
## data:  yj_dat$Court_Rate  
## weights: nb2listw(nb_q, style = "B")    
## 
## Moran I statistic standard deviate = 0.27743, p-value = 0.3907
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.005379915      -0.014084507       0.004922432

moran.test(yj_dat$Close_Rate, nb2listw(nb_q,style = "B"))

## 
##  Moran I test under randomisation
## 
## data:  yj_dat$Close_Rate  
## weights: nb2listw(nb_q, style = "B")    
## 
## Moran I statistic standard deviate = 1.939, p-value = 0.02625
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.122443597      -0.014084507       0.004957724

moran.test(yj_dat$DPA_Rate, nb2listw(nb_q,style = "B"))

## 
##  Moran I test under randomisation
## 
## data:  yj_dat$DPA_Rate  
## weights: nb2listw(nb_q, style = "B")    
## 
## Moran I statistic standard deviate = 4.3053, p-value = 8.336e-06
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.283585951      -0.014084507       0.004780303

moran.test(yj_dat$Youth_Services_100y, nb2listw(nb_q,style = "B"))

## 
##  Moran I test under randomisation
## 
## data:  yj_dat$Youth_Services_100y  
## weights: nb2listw(nb_q, style = "B")    
## 
## Moran I statistic standard deviate = 4.2198, p-value = 1.223e-05
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##        0.25500091       -0.01408451        0.00406627

moran.test(yj_dat$RUCS, nb2listw(nb_q,style = "B"))

## 
##  Moran I test under randomisation
## 
## data:  yj_dat$RUCS  
## weights: nb2listw(nb_q, style = "B")    
## 
## Moran I statistic standard deviate = 4.5526, p-value = 2.65e-06
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.306504984      -0.014084507       0.004958886

moran.test(yj_dat$WISH_Urban, nb2listw(nb_q,style = "B"))

## 
##  Moran I test under randomisation
## 
## data:  yj_dat$WISH_Urban  
## weights: nb2listw(nb_q, style = "B")    
## 
## Moran I statistic standard deviate = 2.4178, p-value = 0.007806
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.157805297      -0.014084507       0.005054117

moran.test(yj_dat$DA_Rep, nb2listw(nb_q,style = "B"))

## 
##  Moran I test under randomisation
## 
## data:  yj_dat$DA_Rep  
## weights: nb2listw(nb_q, style = "B")    
## 
## Moran I statistic standard deviate = 0.71065, p-value = 0.2386
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.036341399      -0.014084507       0.005034889

moran.test(yj_dat$Voter_Rep, nb2listw(nb_q,style = "B"))

## 
##  Moran I test under randomisation
## 
## data:  yj_dat$Voter_Rep  
## weights: nb2listw(nb_q, style = "B")    
## 
## Moran I statistic standard deviate = 1.5542, p-value = 0.06007
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.092569304      -0.014084507       0.004709127

moran.test(yj_dat$Child_Poverty, nb2listw(nb_q,style = "B"))

## 
##  Moran I test under randomisation
## 
## data:  yj_dat$Child_Poverty  
## weights: nb2listw(nb_q, style = "B")    
## 
## Moran I statistic standard deviate = 0.026049, p-value = 0.4896
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      -0.012263548      -0.014084507       0.004886718

moran.test(yj_dat$White_Race, nb2listw(nb_q,style = "B"))

## 
##  Moran I test under randomisation
## 
## data:  yj_dat$White_Race  
## weights: nb2listw(nb_q, style = "B")    
## 
## Moran I statistic standard deviate = 0.68157, p-value = 0.2478
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.021370919      -0.014084507       0.002706073

moran.test(yj_dat$House_Turnover, nb2listw(nb_q,style = "B"))

## 
##  Moran I test under randomisation
## 
## data:  yj_dat$House_Turnover  
## weights: nb2listw(nb_q, style = "B")    
## 
## Moran I statistic standard deviate = 0.076489, p-value = 0.4695
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      -0.008746125      -0.014084507       0.004871090

moran.test(yj_dat$Delinquency_100y, nb2listw(nb_q,style = "B"))

## 
##  Moran I test under randomisation
## 
## data:  yj_dat$Delinquency_100y  
## weights: nb2listw(nb_q, style = "B")    
## 
## Moran I statistic standard deviate = 2.1416, p-value = 0.01611
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.131006222      -0.014084507       0.004589853

moran.test(yj_dat$Detention_Facilities, nb2listw(nb_q,style = "B"))

## 
##  Moran I test under randomisation
## 
## data:  yj_dat$Detention_Facilities  
## weights: nb2listw(nb_q, style = "B")    
## 
## Moran I statistic standard deviate = 2.423, p-value = 0.007697
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.154594595      -0.014084507       0.004846491

## 
##  Welch Two Sample t-test
## 
## data:  yj_dat$DA_Rep and yj_dat$White_Race
## t = -10.073, df = 79.062, p-value = 7.896e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.6862891 -0.4598220
## sample estimates:
## mean of x mean of y 
## 0.3194444 0.8925000

## 
##  Welch Two Sample t-test
## 
## data:  yj_dat$WISH_Urban and yj_dat$White_Race
## t = -9.0815, df = 78.6, p-value = 7.036e-14
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.6478665 -0.4149113
## sample estimates:
## mean of x mean of y 
## 0.3611111 0.8925000

## 
##  Welch Two Sample t-test
## 
## data:  yj_dat$Detention_Facilities and yj_dat$White_Race
## t = -15.725, df = 83.56, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.8176312 -0.6340355
## sample estimates:
## mean of x mean of y 
## 0.1666667 0.8925000

court.ols.1 <- lm (Court_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep +  Delinquency_100y + Detention_Facilities,
                     data = yj_dat)
court.ols.2 <- lm (Court_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep +  Delinquency_100y + Detention_Facilities +
                     Child_Poverty + White_Race + House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat)
dpa.ols.1 <- lm (DPA_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep +  Delinquency_100y + Detention_Facilities,
                     data = yj_dat)
dpa.ols.2 <- lm (DPA_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep +  Delinquency_100y + Detention_Facilities +
                     Child_Poverty + White_Race + House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat)
close.ols.1 <- lm (Close_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities,
                     data = yj_dat)
close.ols.2 <- lm (Close_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities +
                     Child_Poverty + White_Race + House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat)

wiw <- nb2listw(nb_q, style = "W", zero.policy = TRUE)
court.err.1 <- errorsarlm (Court_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep +  Delinquency_100y + Detention_Facilities,
                     data = yj_dat,                         listw=wiw)
court.err.2 <- errorsarlm (Court_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities +
                     Child_Poverty + White_Race + House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)
dpa.err.1 <- errorsarlm (DPA_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities,
                     data = yj_dat,                         listw=wiw)
dpa.err.2 <- errorsarlm (DPA_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities +
                     Child_Poverty + White_Race + House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)
close.err.1 <- errorsarlm (Close_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities,
                     data = yj_dat,                         listw=wiw)
close.err.2 <- errorsarlm (Close_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities +
                     Child_Poverty + White_Race + House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)

# construct spatial lag for predictors: Youth_Services_100y, RUCS
yj_dat$lag_Youth_Services_100y <- lag.listw(wiw,yj_dat$Youth_Services_100y)

court.lag.1a <- lagsarlm (Court_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities,
                     data = yj_dat,                         listw=wiw)
court.lag.1b <- lagsarlm (Court_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities +                      lag_Youth_Services_100y,
                     data = yj_dat,                         listw=wiw)
court.lag.2a <- lagsarlm (Court_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities + 
                     Child_Poverty + White_Race + House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)
court.lag.2b <- lagsarlm (Court_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep +  Delinquency_100y + Detention_Facilities +                      lag_Youth_Services_100y +  
                     Child_Poverty + White_Race + House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)

dpa.lag.1a <- lagsarlm (DPA_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities,
                     data = yj_dat,                         listw=wiw)
dpa.lag.1b <- lagsarlm (DPA_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities +                      lag_Youth_Services_100y   ,
                     data = yj_dat,                         listw=wiw)
dpa.lag.2a <- lagsarlm (DPA_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities +                      
                     Child_Poverty + White_Race + House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)
dpa.lag.2b <- lagsarlm (DPA_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y + Detention_Facilities +                      lag_Youth_Services_100y +  
                     Child_Poverty + White_Race + House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)

close.lag.1a <- lagsarlm (Close_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities,
                     data = yj_dat,                         listw=wiw)
close.lag.1b <- lagsarlm (Close_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities +                      lag_Youth_Services_100y   ,
                     data = yj_dat,                         listw=wiw)
close.lag.2a <- lagsarlm (Close_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep +Delinquency_100y + Detention_Facilities +                      
                     Child_Poverty + White_Race + House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)
close.lag.2b <- lagsarlm (Close_Rate ~ Youth_Services_100y + 
                     RUCS + DA_Rep + Delinquency_100y +  Detention_Facilities +                      lag_Youth_Services_100y +  
                     Child_Poverty + White_Race + House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)

Table 2. Regression Results for County Court Rate

	Dependent variable:
	Court_Rate
	OLS	Spatial Error Model	Spatial Lag Models
	(1)	(2)	(3)	(4)
	court.ols.2	court.err.2	court.lag.2a	court.lag.2b
Youth_Services_100y	0.278	0.224	0.262	0.309
	(0.322)	(0.246)	(0.291)	(0.335)
RUCS	0.001	-0.001	-0.003	-0.004
	(0.016)	(0.014)	(0.014)	(0.015)
DA_Rep	0.003	0.006	0.001	0.002
	(0.034)	(0.029)	(0.031)	(0.031)
Delinquency_100y	-0.027**	-0.023**	-0.027**	-0.026**
	(0.013)	(0.010)	(0.012)	(0.012)
Detention_Facilities	0.039	0.075*	0.044	0.044
	(0.052)	(0.045)	(0.047)	(0.047)
lag_Youth_Services_100y				-0.168
				(0.595)
Child_Poverty	0.306	0.317	0.279	0.283
	(0.294)	(0.249)	(0.266)	(0.267)
White_Race	-0.278*	-0.417***	-0.307**	-0.310**
	(0.158)	(0.128)	(0.143)	(0.144)
House_Turnover	0.976	0.759	0.871	0.831
	(0.611)	(0.521)	(0.555)	(0.574)
scale(Average_Youth_Pop)	0.038	0.033	0.040*	0.040*
	(0.023)	(0.021)	(0.021)	(0.021)
scale(Crime_Rate_2021)	0.0003	0.009	0.001	0.002
	(0.017)	(0.015)	(0.016)	(0.016)
Constant	0.468**	0.605***	0.598***	0.611***
	(0.187)	(0.150)	(0.182)	(0.190)
Observations	72	72	72	72
R2	0.379
Adjusted R2	0.277
Log Likelihood		56.644	54.185	54.225
sigma2		0.011	0.013	0.013
Akaike Inf. Crit.		-87.288	-82.369	-80.450
Residual Std. Error	0.125 (df = 61)
F Statistic	3.717*** (df = 10; 61)
Wald Test (df = 1)		10.525***	1.799	1.767
LR Test (df = 1)		6.715***	1.796	1.781
Note:	p<0.1; p<0.05; p<0.01

Table3. Regression Results for County DPA Rate

	Dependent variable:
	DPA_Rate
	OLS	Spatial Error Model	Spatial Lag Models
	(1)	(2)	(3)	(4)
	dpa.ols.2	dpa.err.2	dpa.lag.2a	dpa.lag.2b
Youth_Services_100y	0.544**	0.509**	0.492**	0.489*
	(0.270)	(0.248)	(0.228)	(0.261)
RUCS	0.015	0.006	0.011	0.011
	(0.013)	(0.011)	(0.011)	(0.011)
DA_Rep	0.030	0.020	0.024	0.024
	(0.028)	(0.023)	(0.024)	(0.024)
Delinquency_100y	-0.008	-0.019**	-0.015	-0.015
	(0.011)	(0.009)	(0.009)	(0.010)
Detention_Facilities	0.001	0.007	0.007	0.007
	(0.044)	(0.035)	(0.037)	(0.037)
lag_Youth_Services_100y				0.012
				(0.467)
Child_Poverty	-0.208	-0.155	-0.190	-0.190
	(0.247)	(0.194)	(0.208)	(0.208)
White_Race	0.292**	0.321***	0.304***	0.304***
	(0.133)	(0.112)	(0.112)	(0.112)
House_Turnover	-0.318	-0.517	-0.416	-0.413
	(0.512)	(0.412)	(0.431)	(0.445)
scale(Average_Youth_Pop)	-0.001	0.004	0.002	0.002
	(0.020)	(0.015)	(0.016)	(0.016)
scale(Crime_Rate_2021)	0.022	0.012	0.018	0.018
	(0.014)	(0.011)	(0.012)	(0.012)
Constant	-0.089	-0.026	-0.137	-0.137
	(0.157)	(0.134)	(0.134)	(0.138)
Observations	72	72	72	72
R2	0.281
Adjusted R2	0.163
Log Likelihood		71.321	70.894	70.894
sigma2		0.008	0.008	0.008
Akaike Inf. Crit.		-116.641	-115.787	-113.788
Residual Std. Error	0.105 (df = 61)
F Statistic	2.385** (df = 10; 61)
Wald Test (df = 1)		16.842***	11.019***	10.748***
LR Test (df = 1)		10.630***	9.776***	9.440***
Note:	p<0.1; p<0.05; p<0.01

Table4. Regression Results for County Close Case Rate

	Dependent variable:
	Close_Rate
	OLS	Spatial Error Model	Spatial Lag Models
	(1)	(2)	(3)	(4)
	close.ols.2	close.err.2	close.lag.2a	close.lag.2b
Youth_Services_100y	-0.926**	-0.825**	-0.849**	-0.815**
	(0.394)	(0.374)	(0.353)	(0.406)
RUCS	-0.020	-0.017	-0.022	-0.023
	(0.019)	(0.017)	(0.017)	(0.017)
DA_Rep	-0.034	-0.022	-0.032	-0.031
	(0.042)	(0.036)	(0.037)	(0.037)
Delinquency_100y	0.033**	0.048***	0.040***	0.040***
	(0.016)	(0.015)	(0.014)	(0.015)
Detention_Facilities	-0.039	-0.022	-0.037	-0.036
	(0.064)	(0.055)	(0.057)	(0.057)
lag_Youth_Services_100y				-0.126
				(0.718)
Child_Poverty	-0.110	-0.242	-0.163	-0.159
	(0.360)	(0.306)	(0.322)	(0.322)
White_Race	0.063	-0.062	0.020	0.019
	(0.194)	(0.173)	(0.173)	(0.174)
House_Turnover	-0.678	-0.804	-0.771	-0.799
	(0.748)	(0.645)	(0.669)	(0.690)
scale(Average_Youth_Pop)	-0.036	-0.039	-0.036	-0.035
	(0.029)	(0.024)	(0.026)	(0.026)
scale(Crime_Rate_2021)	-0.021	-0.008	-0.017	-0.016
	(0.021)	(0.018)	(0.019)	(0.019)
Constant	0.564**	0.644***	0.482**	0.494**
	(0.229)	(0.206)	(0.213)	(0.222)
Observations	72	72	72	72
R2	0.223
Adjusted R2	0.096
Log Likelihood		40.856	40.237	40.252
sigma2		0.018	0.019	0.019
Akaike Inf. Crit.		-55.712	-54.475	-52.504
Residual Std. Error	0.154 (df = 61)
F Statistic	1.754* (df = 10; 61)
Wald Test (df = 1)		7.035***	3.570*	3.394*
LR Test (df = 1)		4.341**	3.104*	2.844*
Note:	p<0.1; p<0.05; p<0.01

AICs<-c(AIC(court.ols.2),AIC(court.lag.2a), AIC(court.lag.2b), AIC(court.err.2))
BICs<-c(BIC(court.ols.2),BIC(court.lag.2a),BIC(court.lag.2b), BIC(court.err.2))
labels<-c("OLS", "SLM_DV", "SLM_DV_IV", "SEM" )
flextable(data.frame(Models=labels, AIC=round(AICs, 2), BIC=round(BICs, 2)))

Models	AIC	BIC
OLS	-82.57	-55.25
SLM_DV	-82.37	-52.77
SLM_DV_IV	-80.45	-48.58
SEM	-87.29	-57.69

AICs<-c(AIC(dpa.ols.2),AIC(dpa.lag.2a), AIC(dpa.lag.2b), AIC(dpa.err.2))
BICs<-c(BIC(dpa.ols.2),BIC(dpa.lag.2a),BIC(dpa.lag.2b), BIC(dpa.err.2))
labels<-c("OLS", "SLM_DV", "SLM_DV_IV", "SEM" )
flextable(data.frame(Models=labels, AIC=round(AICs, 2), BIC=round(BICs, 2)))

Models	AIC	BIC
OLS	-108.01	-80.69
SLM_DV	-115.79	-86.19
SLM_DV_IV	-113.79	-81.91
SEM	-116.64	-87.04

AICs<-c(AIC(close.ols.2),AIC(close.lag.2a), AIC(close.lag.2b), AIC(close.err.2))
BICs<-c(BIC(close.ols.2),BIC(close.lag.2a),BIC(close.lag.2b), BIC(close.err.2))
labels<-c("OLS", "SLM_DV", "SLM_DV_IV", "SEM" )
flextable(data.frame(Models=labels, AIC=round(AICs, 2), BIC=round(BICs, 2)))

Models	AIC	BIC
OLS	-53.37	-26.05
SLM_DV	-54.47	-24.88
SLM_DV_IV	-52.50	-20.63
SEM	-55.71	-26.12

court.ols.2.sa <- lm (Court_Rate ~ Youth_Services_100y + 
                     WISH_Urban + Voter_Rep +  Delinquency_100y + Detention_Facilities +
                     Child_Poverty +  House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat)
dpa.ols.2.sa <- lm (DPA_Rate ~ Youth_Services_100y + 
                     WISH_Urban + Voter_Rep +  Delinquency_100y + Detention_Facilities +
                     Child_Poverty + House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat)
close.ols.2.sa <- lm (Close_Rate ~ Youth_Services_100y + 
                     WISH_Urban + Voter_Rep + Delinquency_100y +  Detention_Facilities +
                     Child_Poverty + House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat)

wiw <- nb2listw(nb_q, style = "W", zero.policy = TRUE)
court.err.2.sa <- errorsarlm (Court_Rate ~ Youth_Services_100y + 
                     WISH_Urban + Voter_Rep + Delinquency_100y +  Detention_Facilities +
                     Child_Poverty +  House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)
dpa.err.2.sa <- errorsarlm (DPA_Rate ~ Youth_Services_100y + 
                     WISH_Urban + Voter_Rep + Delinquency_100y +  Detention_Facilities +
                     Child_Poverty +  House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)
close.err.2.sa <- errorsarlm (Close_Rate ~ Youth_Services_100y + 
                    WISH_Urban + Voter_Rep + Delinquency_100y +  Detention_Facilities +
                     Child_Poverty +  House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)

# construct spatial lag for predictors: Youth_Services_100y, RUCS
yj_dat$lag_Youth_Services_100y <- lag.listw(wiw,yj_dat$Youth_Services_100y)
court.lag.2a.sa <- lagsarlm (Court_Rate ~ Youth_Services_100y + 
                     WISH_Urban + Voter_Rep + Delinquency_100y +  Detention_Facilities + 
                     Child_Poverty +  House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)
court.lag.2b.sa <- lagsarlm (Court_Rate ~ Youth_Services_100y + 
                     WISH_Urban + Voter_Rep +  Delinquency_100y + Detention_Facilities +                      lag_Youth_Services_100y +  
                     Child_Poverty +  House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)
dpa.lag.2a.sa <- lagsarlm (DPA_Rate ~ Youth_Services_100y + 
                     WISH_Urban + Voter_Rep + Delinquency_100y +  Detention_Facilities +                      
                     Child_Poverty +  House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)
dpa.lag.2b.sa <- lagsarlm (DPA_Rate ~ Youth_Services_100y + 
                     WISH_Urban + Voter_Rep + Delinquency_100y + Detention_Facilities +                      lag_Youth_Services_100y +  
                     Child_Poverty +  House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)
close.lag.2a.sa <- lagsarlm (Close_Rate ~ Youth_Services_100y + 
                     WISH_Urban + Voter_Rep +Delinquency_100y + Detention_Facilities +                      
                     Child_Poverty +  House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)
close.lag.2b.sa <- lagsarlm (Close_Rate ~ Youth_Services_100y + 
                     WISH_Urban + Voter_Rep + Delinquency_100y +  Detention_Facilities +                      lag_Youth_Services_100y +  
                     Child_Poverty +  House_Turnover +
                     scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                     data = yj_dat,                         listw=wiw)

Table S1 Regression Results for County Court Rate

	Dependent variable:
	Court_Rate
	OLS	Spatial Error Model	Spatial Lag Models
	(1)	(2)	(3)	(4)
	court.ols.2.sa	court.err.2.sa	court.lag.2a.sa	court.lag.2b.sa
Youth_Services_100y	0.372	0.402	0.373	0.379
	(0.313)	(0.262)	(0.288)	(0.334)
WISH_Urban	-0.005	0.010	0.004	0.004
	(0.043)	(0.040)	(0.040)	(0.040)
Voter_Rep	-0.001	-0.002	-0.001	-0.001
	(0.002)	(0.002)	(0.002)	(0.002)
Delinquency_100y	-0.027**	-0.023**	-0.027**	-0.027**
	(0.013)	(0.011)	(0.012)	(0.012)
Detention_Facilities	0.046	0.066	0.048	0.048
	(0.054)	(0.049)	(0.050)	(0.050)
lag_Youth_Services_100y				-0.023
				(0.609)
Child_Poverty	0.431	0.478*	0.434	0.435
	(0.293)	(0.267)	(0.270)	(0.271)
House_Turnover	0.864	0.684	0.798	0.793
	(0.639)	(0.570)	(0.589)	(0.604)
scale(Average_Youth_Pop)	0.043*	0.042**	0.046**	0.046**
	(0.022)	(0.020)	(0.020)	(0.020)
scale(Crime_Rate_2021)	-0.005	-0.0003	-0.005	-0.005
	(0.017)	(0.015)	(0.015)	(0.016)
Constant	0.295*	0.295**	0.342**	0.342**
	(0.161)	(0.137)	(0.156)	(0.157)
Observations	72	72	72	72
R2	0.354
Adjusted R2	0.260
Log Likelihood		53.231	52.322	52.323
sigma2		0.013	0.014	0.014
Akaike Inf. Crit.		-82.462	-80.644	-78.646
Residual Std. Error	0.127 (df = 62)
F Statistic	3.769*** (df = 9; 62)
Wald Test (df = 1)		3.658*	0.918	0.907
LR Test (df = 1)		2.732*	0.914	0.911
Note:	p<0.1; p<0.05; p<0.01

Table S2 Regression Results for County DPA Rate

	Dependent variable:
	DPA_Rate
	OLS	Spatial Error Model	Spatial Lag Models
	(1)	(2)	(3)	(4)
	dpa.ols.2.sa	dpa.err.2.sa	dpa.lag.2a.sa	dpa.lag.2b.sa
Youth_Services_100y	0.402	0.439*	0.353	0.419
	(0.261)	(0.245)	(0.225)	(0.256)
WISH_Urban	-0.009	-0.002	-0.004	-0.002
	(0.036)	(0.029)	(0.031)	(0.031)
Voter_Rep	0.003**	0.003**	0.003***	0.004***
	(0.002)	(0.001)	(0.001)	(0.001)
Delinquency_100y	-0.010	-0.021**	-0.018**	-0.017*
	(0.011)	(0.009)	(0.009)	(0.009)
Detention_Facilities	-0.001	0.008	0.004	0.004
	(0.045)	(0.037)	(0.038)	(0.038)
lag_Youth_Services_100y				-0.242
				(0.472)
Child_Poverty	-0.202	-0.205	-0.207	-0.197
	(0.245)	(0.198)	(0.208)	(0.208)
House_Turnover	-0.039	-0.257	-0.139	-0.193
	(0.534)	(0.438)	(0.452)	(0.463)
scale(Average_Youth_Pop)	-0.010	0.0003	-0.006	-0.005
	(0.018)	(0.015)	(0.015)	(0.015)
scale(Crime_Rate_2021)	0.025*	0.015	0.020*	0.021*
	(0.014)	(0.011)	(0.012)	(0.012)
Constant	0.040	0.094	-0.015	-0.011
	(0.135)	(0.120)	(0.115)	(0.115)
Observations	72	72	72	72
R2	0.257
Adjusted R2	0.150
Log Likelihood		69.737	69.784	69.915
sigma2		0.008	0.008	0.008
Akaike Inf. Crit.		-115.474	-115.568	-113.830
Residual Std. Error	0.106 (df = 62)
F Statistic	2.387** (df = 9; 62)
Wald Test (df = 1)		15.956***	11.566***	11.939***
LR Test (df = 1)		9.803***	9.898***	10.154***
Note:	p<0.1; p<0.05; p<0.01

Table S3 Regression Results for County Close Case Rate

	Dependent variable:
	Close_Rate
	OLS	Spatial Error Model	Spatial Lag Models
	(1)	(2)	(3)	(4)
	close.ols.2.sa	close.err.2.sa	close.lag.2a.sa	close.lag.2b.sa
Youth_Services_100y	-0.909**	-0.804**	-0.815**	-0.807**
	(0.378)	(0.362)	(0.342)	(0.395)
WISH_Urban	0.020	0.030	0.032	0.032
	(0.052)	(0.044)	(0.047)	(0.048)
Voter_Rep	-0.002	-0.002	-0.002	-0.002
	(0.002)	(0.002)	(0.002)	(0.002)
Delinquency_100y	0.035**	0.050***	0.041***	0.041***
	(0.015)	(0.014)	(0.014)	(0.014)
Detention_Facilities	-0.047	-0.034	-0.046	-0.046
	(0.065)	(0.056)	(0.059)	(0.059)
lag_Youth_Services_100y				-0.028
				(0.719)
Child_Poverty	-0.301	-0.311	-0.300	-0.298
	(0.354)	(0.303)	(0.320)	(0.321)
House_Turnover	-0.852	-0.977	-0.923	-0.929
	(0.772)	(0.669)	(0.696)	(0.713)
scale(Average_Youth_Pop)	-0.032	-0.036	-0.029	-0.029
	(0.026)	(0.023)	(0.024)	(0.024)
scale(Crime_Rate_2021)	-0.017	-0.007	-0.014	-0.014
	(0.020)	(0.017)	(0.018)	(0.018)
Constant	0.667***	0.631***	0.509***	0.510***
	(0.195)	(0.180)	(0.194)	(0.195)
Observations	72	72	72	72
R2	0.214
Adjusted R2	0.100
Log Likelihood		40.861	39.745	39.745
sigma2		0.018	0.019	0.019
Akaike Inf. Crit.		-57.723	-55.489	-53.491
Residual Std. Error	0.153 (df = 62)
F Statistic	1.880* (df = 9; 62)
Wald Test (df = 1)		7.452***	3.380*	3.327*
LR Test (df = 1)		5.179**	2.945*	2.786*
Note:	p<0.1; p<0.05; p<0.01

delin.ols.2 <- lm (Delinquency_100y ~ Youth_Services_100y + 
                      RUCS + Detention_Facilities +
                      Child_Poverty + DA_Rep*White_Race + House_Turnover +
                      scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                      data = yj_dat)
delin.err.2 <- errorsarlm (Delinquency_100y ~ Youth_Services_100y + 
                     RUCS + Detention_Facilities +
                      Child_Poverty + DA_Rep*White_Race + House_Turnover +
                      scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                      data = yj_dat,  listw=wiw)
delin.lag.2a <- lagsarlm (Delinquency_100y ~ Youth_Services_100y + 
                      RUCS +Detention_Facilities +                      
                      Child_Poverty + DA_Rep*White_Race + House_Turnover +
                      scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                      data = yj_dat,                         listw=wiw)
delin.lag.2b <- lagsarlm (Delinquency_100y ~ Youth_Services_100y + 
                      RUCS + Detention_Facilities + 
                      lag_Youth_Services_100y +  
                      Child_Poverty + DA_Rep*White_Race + House_Turnover +
                      scale(Average_Youth_Pop) + scale(Crime_Rate_2021),
                      data = yj_dat,                         listw=wiw)

Title: Regression Results: Delinquency Cases Per 100 Youth - Model 2

	Dependent variable:
	Delinquency_100y
	OLS	Spatial Error Model	Spatial Lag Models
	(1)	(2)	(3)	(4)
	delin.ols.2	delin.err.2	delin.lag.2a	delin.lag.2b
Youth_Services_100y	-0.357	-1.799	-0.716	-3.561
	(3.094)	(2.942)	(2.800)	(3.126)
RUCS	0.214	0.176	0.165	0.201
	(0.148)	(0.133)	(0.136)	(0.133)
Detention_Facilities	-0.043	-0.261	-0.114	-0.135
	(0.527)	(0.467)	(0.475)	(0.466)
lag_Youth_Services_100y				10.519*
				(5.438)
Child_Poverty	2.410	2.706	2.734	2.357
	(2.826)	(2.477)	(2.547)	(2.499)
DA_Rep	6.031	6.492	6.585	7.151
	(5.076)	(4.534)	(4.579)	(4.497)
White_Race	1.179	1.417	1.376	1.544
	(1.564)	(1.410)	(1.410)	(1.385)
House_Turnover	8.214	10.074**	8.655*	10.451**
	(5.815)	(5.090)	(5.252)	(5.234)
scale(Average_Youth_Pop)	-0.159	-0.105	-0.131	-0.139
	(0.224)	(0.197)	(0.202)	(0.198)
scale(Crime_Rate_2021)	-0.100	-0.124	-0.117	-0.152
	(0.165)	(0.145)	(0.149)	(0.148)
DA_Rep:White_Race	-7.340	-7.818	-7.907	-8.563*
	(5.590)	(4.985)	(5.041)	(4.952)
Constant	-0.671	-0.846	-1.286	-1.955
	(1.805)	(1.647)	(1.651)	(1.672)
Observations	72	72	72	72
R2	0.198
Adjusted R2	0.067
Log Likelihood		-108.498	-108.548	-106.800
sigma2		1.170	1.179	1.130
Akaike Inf. Crit.		242.995	243.096	241.601
Residual Std. Error	1.205 (df = 61)
F Statistic	1.510 (df = 10; 61)
Wald Test (df = 1)		3.485*	2.499	1.252
LR Test (df = 1)		2.232	2.130	1.062
Note:	p<0.1; p<0.05; p<0.01