R Notebook

In this report, we will investigate whether or not the average amount of white population in a state has an effect on the average arrests rate in that state. In order to do so we will merge two datasets, one from social explorer on crime data and the other on the 2014 white population rate in each state.

library(nlme)
library(dplyr)

Attaching package: ‘dplyr’

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    collapse

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    filter, lag

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    intersect, setdiff, setequal, union

library(magrittr)
library(tidyr)

Attaching package: ‘tidyr’

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    extract

library(haven)
library(lmerTest)

Loading required package: Matrix

Attaching package: ‘Matrix’

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Loading required package: lme4

Attaching package: ‘lme4’

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Attaching package: ‘lmerTest’

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library(ggplot2)
library(texreg)

Version:  1.36.23
Date:     2017-03-03
Author:   Philip Leifeld (University of Glasgow)

Please cite the JSS article in your publications -- see citation("texreg").

Attaching package: ‘texreg’

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library(stringr)

Merging the Datasets

Populationbyrace <- read.csv("/Users/robertperez/Documents/Rstudio DataSets /population_race_2014.csv")
Crimedata <- read.csv("/Users/robertperez/Documents/Rstudio DataSets /crimedata.csv")
crimedatabyrace <- merge(Populationbyrace, Crimedata, 
                         by.x = "Geo_NAME",
                         by.y = "Geo_Name")
#Isolate the State Name from teh Geo_QName variable
X<-data.frame(str_locate(crimedatabyrace$Geo_QName,"County,"))
X2<-X%>%select(end)
crimedatabyrace$loc <- X2$end
crimedatabyrace1<-crimedatabyrace%>%
  mutate(statename = substr(Geo_QName, loc+1,length(Geo_QName)))
head(crimedatabyrace1)

Manipulating The Data

crimedatabyrace1 <- rename(crimedatabyrace1, county = Geo_NAME, Arrestsrate_per100k = SE_T011_001,
           white = SE_T020_002,
           black = SE_T020_003,
           native = SE_T020_004,
           asian = SE_T020_005,
           pacifisland= SE_T020_006,
           mixed = SE_T020_007)%>%
  select(statename, county, Arrestsrate_per100k, white, black, native, asian, pacifisland, mixed)
  head(crimedatabyrace1)

print(crimedatabyrace1)

crimedatabyrace1<-na.omit(crimedatabyrace1)
head(crimedatabyrace1)

Looking at the means

###Means, color = red
####Looking at aaverages for each state and race
crimedatabyrace1%>%
  group_by(statename)%>%
  summarize(Arrestsrate_per100k = mean(Arrestsrate_per100k), white = mean(white), black = mean(black))

State Level Analysis Ecological model

statenames <- crimedatabyrace1 %>% 
  group_by(statename) %>% 
  summarise(Arrestsrate_per100k = mean(Arrestsrate_per100k, na.rm = TRUE), white = mean(log(white), na.rm = TRUE))
head(statenames)

ecoreg <- lm(Arrestsrate_per100k ~ white, data = crimedatabyrace1)
summary(ecoreg)

Call:
lm(formula = Arrestsrate_per100k ~ white, data = crimedatabyrace1)

Residuals:
    Min      1Q  Median      3Q     Max 
-3198.4 -1177.1  -262.8   947.7 16228.0 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 3.163e+03  1.634e+01 193.656   <2e-16 ***
white       4.538e-05  8.838e-05   0.513    0.608    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1744 on 13251 degrees of freedom
Multiple R-squared:  1.99e-05,  Adjusted R-squared:  -5.557e-05 
F-statistic: 0.2637 on 1 and 13251 DF,  p-value: 0.6076

ggplot(data=crimedatabyrace1, aes(x=statename, y=Arrestsrate_per100k))+
  geom_col(color ="red", fill = "black")+coord_flip()

Regression Model Complete Pooling

AR<- lm(Arrestsrate_per100k ~ white, data = crimedatabyrace1)
summary(ARwhite)

Call:
lm(formula = Arrestsrate_per100k ~ white + black, data = crimedatabyrace1)

Residuals:
    Min      1Q  Median      3Q     Max 
-3196.6 -1177.2  -263.1   947.8 16228.3 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  3.163e+03  1.638e+01 193.170   <2e-16 ***
white        5.673e-05  1.242e-04   0.457    0.648    
black       -5.484e-05  4.216e-04  -0.130    0.897    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1744 on 13250 degrees of freedom
Multiple R-squared:  2.117e-05, Adjusted R-squared:  -0.0001298 
F-statistic: 0.1403 on 2 and 13250 DF,  p-value: 0.8691

ARwhite<- lm(Arrestsrate_per100k ~ white +  black, data = crimedatabyrace1)
summary(ARwhite)

Call:
lm(formula = Arrestsrate_per100k ~ white + black, data = crimedatabyrace1)

Residuals:
    Min      1Q  Median      3Q     Max 
-3196.6 -1177.2  -263.1   947.8 16228.3 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  3.163e+03  1.638e+01 193.170   <2e-16 ***
white        5.673e-05  1.242e-04   0.457    0.648    
black       -5.484e-05  4.216e-04  -0.130    0.897    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1744 on 13250 degrees of freedom
Multiple R-squared:  2.117e-05, Adjusted R-squared:  -0.0001298 
F-statistic: 0.1403 on 2 and 13250 DF,  p-value: 0.8691

Intercept

dcoef <- crimedatabyrace1 %>% 
    group_by(statename) %>% 
    do(mod = lm(Arrestsrate_per100k ~ white, data = .))
coef <- dcoef %>% do(data.frame(intc = coef(.$mod)[1]))
ggplot(coef, aes(x = intc)) + geom_histogram()

Slope

dcoef <- crimedatabyrace1 %>% 
    group_by(statename) %>% 
    do(mod = lm(Arrestsrate_per100k ~ white, data = .))
coef <- dcoef %>% do(data.frame(sexc = coef(.$mod)[2]))
ggplot(coef, aes(x = sexc)) + geom_histogram()

Random Intercept

m1_lme <- lme(Arrestsrate_per100k ~ white, data = crimedatabyrace1, random = ~1|statename, method = "ML")
summary(m1_lme)

Linear mixed-effects model fit by maximum likelihood
 Data: crimedatabyrace1 
       AIC      BIC    logLik
  231552.4 231582.3 -115772.2

Random effects:
 Formula: ~1 | statename
        (Intercept) Residual
StdDev:    908.1807  1494.13

Fixed effects: Arrestsrate_per100k ~ white 
               Value Std.Error    DF   t-value p-value
(Intercept) 3245.785 136.54066 13206 23.771565  0.0000
white          0.000   0.00008 13206 -0.279782  0.7796
 Correlation: 
      (Intr)
white -0.052

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max 
-3.2451978 -0.6331617 -0.1160736  0.5145651 10.6186223 

Number of Observations: 13253
Number of Groups: 46 

m2_lme <- lme(Arrestsrate_per100k ~ white, data = crimedatabyrace1, random = ~ white|statename, method = "ML")
summary(m2_lme)

Linear mixed-effects model fit by maximum likelihood
 Data: crimedatabyrace1 
     AIC      BIC  logLik
  231548 231592.9 -115768

Random effects:
 Formula: ~white | statename
 Structure: General positive-definite, Log-Cholesky parametrization
            StdDev       Corr  
(Intercept) 9.101732e+02 (Intr)
white       4.278992e-04 0.016 
Residual    1.492528e+03       

Fixed effects: Arrestsrate_per100k ~ white 
               Value Std.Error    DF   t-value p-value
(Intercept) 3244.624 136.91245 13206 23.698533  0.0000
white          0.000   0.00011 13206  0.398053  0.6906
 Correlation: 
      (Intr)
white -0.04 

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max 
-3.2501799 -0.6329070 -0.1188938  0.5100618 10.6371287 

Number of Observations: 13253
Number of Groups: 46 

AIC(AR, m1_lme, m2_lme)

Conclusion: As we can see the lowest AIC means best fit and in this report that is the random intercept model 2. In this report we see that race within states has very little effect on the average arrests rates per 100k population. Through further analysis one will be able to measure average arrests rate by sex and other races.