Afzal | SOC 712 | Home Work 5

(New) Binary Dependent Variable Models

I will use same dataset that i used last week that is stop and frisk data from 2018. But this time instead of finding likelihood of someone being arrested, i am interested in the likelihood of weapon(firearms) been found and use some new as well as some last week independent variables.Therefore, my binary dependent variable will be weapon found or not.

Reminder of data description:

Every time a police officer stops a person in NYC, the officer is require to fill out a form recording the details of the stop. The forms were filled out by hand and manually entered into an NYPD database. When the forms became electronic, database are available for download for public . Each row of the data set represent a stop by NYPD officer. Dataset also contain variable such as the age, race, weight, height of the person stopped, if a person was frisked (when an officer pass the hands over someone in a search for hidden weapons, drugs, or other items and the location of the stop.

Prepering Dataset for Binary Dependent Variable:

library(readxl)
# Reading the excel data
sqf<- read_excel("C:/Users/Afzal Hossain/Documents/A.Spring 2019/SOC 712/HW/HW4/sqf_2018.xlsx")
dim(sqf)

[1] 11008    83

library(dplyr)
#Keeping the variable that i am interested in.
sq<-select(sqf, 'STOP_FRISK_ID',"WEAPON_FOUND_FLAG",'SUMMONS_ISSUED_FLAG','OTHER_WEAPON_FLAG','SUSPECT_ARRESTED_FLAG','FRISKED_FLAG','SEARCHED_FLAG','SUSPECT_REPORTED_AGE':'SUSPECT_BODY_BUILD_TYPE')
# Lets look the Data
head(sq)

# Dealing with null values
sq$SUSPECT_SEX <- as.character(sq$SUSPECT_SEX)
sq$SUSPECT_SEX[sq$SUSPECT_SEX == "(null)"] <- NA
sq$SUSPECT_RACE_DESCRIPTION<-as.character(sq$SUSPECT_RACE_DESCRIPTION)
sq$SUSPECT_RACE_DESCRIPTION[sq$SUSPECT_RACE_DESCRIPTION == "(null)"]<- NA
sq$SUSPECT_BODY_BUILD_TYPE<-as.character(sq$SUSPECT_BODY_BUILD_TYPE)
sq$SUSPECT_BODY_BUILD_TYPE[sq$SUSPECT_BODY_BUILD_TYPE== "(null)"]<- NA
# Taking records that are only complete
sq<-sq[complete.cases(sq), ]
dim(sq)

[1] 10776    13

I can see that it reduce the data size by deleting incomplete dataset. Original data set had 11008 record, now we have 10776 record. This is acceptable since this data was collected by hand, therefore missing value are expected.

I will eecode the race and race variable in order to easy understanding and create bigger groups.

# Recoding Variable for bodu type
sq$SUSPECT_BODY_BUILD_TYPE[sq$SUSPECT_BODY_BUILD_TYPE=='EA' | 
                             sq$SUSPECT_BODY_BUILD_TYPE=='HEA' |
                             sq$SUSPECT_BODY_BUILD_TYPE=='THN'|
                             sq$SUSPECT_BODY_BUILD_TYPE=='U' |
                             sq$SUSPECT_BODY_BUILD_TYPE=='XXX'] <- "BIG/ATHLETETIC" 
sq$SUSPECT_BODY_BUILD_TYPE[sq$SUSPECT_BODY_BUILD_TYPE=='MED' |
                             sq$SUSPECT_BODY_BUILD_TYPE=='THN'] <- "Small" 
# Recoding Variable for Race
sq$SUSPECT_RACE_DESCRIPTION[sq$SUSPECT_RACE_DESCRIPTION=='ASIAN / PACIFIC ISLANDER' | 
                              sq$SUSPECT_RACE_DESCRIPTION=='BLACK HISPANIC'|
                              sq$SUSPECT_RACE_DESCRIPTION=='WHITE HISPANIC' |
                              sq$SUSPECT_RACE_DESCRIPTION=='AMERICAN INDIAN/ALASKAN NATIVE'] <- "LATINO/OTHER" 
# Making appropriate data type
sq$OTHER_WEAPON_FLAG<- as.factor(sq$OTHER_WEAPON_FLAG)
sq$FRISKED_FLAG<- as.factor(sq$FRISKED_FLAG)
sq$WEAPON_FOUND_FLAG<- as.factor(sq$WEAPON_FOUND_FLAG)
sq$SUSPECT_REPORTED_AGE<- as.double(sq$SUSPECT_REPORTED_AGE)
sq$SUSPECT_ARRESTED_FLAG<- as.factor(sq$SUSPECT_ARRESTED_FLAG)
sq$SUSPECT_SEX<- as.factor(sq$SUSPECT_SEX)
sq$SUSPECT_RACE_DESCRIPTION<- as.factor(sq$SUSPECT_RACE_DESCRIPTION)
sq$SUSPECT_BODY_BUILD_TYPE<- as.factor(sq$SUSPECT_BODY_BUILD_TYPE)
sq$SUSPECT_HEIGHT<- as.double(sq$SUSPECT_HEIGHT)
sq$SUSPECT_WEIGHT<- as.double(sq$SUSPECT_WEIGHT)

# Creating New Variables
sq <- sq %>% 
  mutate(weapon_found =as.integer(WEAPON_FOUND_FLAG),arrast = as.integer(SUSPECT_ARRESTED_FLAG),Frisk = as.integer(FRISKED_FLAG))
sq <- sq %>% 
  select(weapon_found ,arrast, Frisk,SEARCHED_FLAG,SUSPECT_SEX,SUSPECT_REPORTED_AGE,SUSPECT_RACE_DESCRIPTION, everything())
head(sq)

As before,I will now recode the variable to 0/1 instead of Y/N for my newly created variables which are Weapon_Found arrast, and Frisk. Also Filter any missing value.

sq <- sq %>% filter(!is.na(SUMMONS_ISSUED_FLAG),!is.na(SUSPECT_REPORTED_AGE),!is.na(SUSPECT_HEIGHT),!is.na(SUSPECT_WEIGHT),!is.na(SUSPECT_SEX),!is.na(weapon_found))%>%
  mutate(arrasted = sjmisc::rec(arrast, rec = "1=0; 2=1"), Frisked = sjmisc::rec(Frisk,   rec = "1=0; 2=1"),
         Weapon_Found = sjmisc::rec(weapon_found, rec = "1=0; 2=1")) %>% 
             select(Weapon_Found,WEAPON_FOUND_FLAG,arrasted, SUSPECT_ARRESTED_FLAG, Frisked,FRISKED_FLAG,   
                    SUSPECT_SEX,SUSPECT_REPORTED_AGE,
                          SUSPECT_RACE_DESCRIPTION, everything()) %>% 
                                select(-weapon_found)
sq$arrasted<- as.factor(sq$arrasted)
sq$Weapon_Found<- as.factor(sq$Weapon_Found)
sq$Frisked<- as.factor(sq$Frisked)
head(sq)

Logistic Regression

Lets create our first simple model where we predict using our bineary dependent variable Weapon_Found and a independent continuas variable Age of the suspect stop by officer, SUSPECT_REPORTED_AGE

m0 <- glm(Weapon_Found ~ SUSPECT_REPORTED_AGE, family = 'binomial', data = sq)
summary(m0)

Call:
glm(formula = Weapon_Found ~ SUSPECT_REPORTED_AGE, family = "binomial", 
    data = sq)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-0.4742  -0.4439  -0.4381  -0.4340   2.2019  

Coefficients:
                      Estimate Std. Error z value Pr(>|z|)    
(Intercept)          -2.364897   0.090012 -26.273   <2e-16 ***
SUSPECT_REPORTED_AGE  0.002777   0.002793   0.995     0.32    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6037.9  on 9788  degrees of freedom
Residual deviance: 6037.0  on 9787  degrees of freedom
AIC: 6041

Number of Fisher Scoring iterations: 5

From \(m_0\), the coefficient is positive,but very small.So we can say that as people get older, chances of weapon found slightly increase. From the \(Y-intercept\), I can say that when age is zero, the log odd of weapon been found is \(-2.365\). From the slope value, I can say that for every one-unit increase of age, the log odds of weopen found increases by \(0.002777\). Furthermore, from the \(Z\) \(value\) we can say that it less than one standard deviation way from zero therefore it is not statistically significant

Improving Model:

m1 <- glm(Weapon_Found ~  SUSPECT_RACE_DESCRIPTION + SUSPECT_SEX  + SUSPECT_REPORTED_AGE +SUSPECT_BODY_BUILD_TYPE,family = 'binomial', data = sq)
summary(m1)

Call:
glm(formula = Weapon_Found ~ SUSPECT_RACE_DESCRIPTION + SUSPECT_SEX + 
    SUSPECT_REPORTED_AGE + SUSPECT_BODY_BUILD_TYPE, family = "binomial", 
    data = sq)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-0.5079  -0.4657  -0.4572  -0.3726   2.7185  

Coefficients:
                                      Estimate Std. Error z value Pr(>|z|)    
(Intercept)                          -3.168466   0.189114 -16.754  < 2e-16 ***
SUSPECT_RACE_DESCRIPTIONLATINO/OTHER -0.013652   0.075153  -0.182 0.855851    
SUSPECT_RACE_DESCRIPTIONWHITE        -0.524010   0.144500  -3.626 0.000287 ***
SUSPECT_SEXMALE                       0.908596   0.171753   5.290 1.22e-07 ***
SUSPECT_REPORTED_AGE                  0.003876   0.002828   1.371 0.170492    
SUSPECT_BODY_BUILD_TYPESmall         -0.086086   0.073550  -1.170 0.241824    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6037.9  on 9788  degrees of freedom
Residual deviance: 5983.7  on 9783  degrees of freedom
AIC: 5995.7

Number of Fisher Scoring iterations: 5

We can see that log odds of finding weapon on Male significantly higher \(.9086\) and log odds of finding weapon on white people is \(-.524\) which is significantly lower then latino/Other, \(-.014\).

Keep Improving Model:

m2 <- glm(Weapon_Found ~ SUSPECT_SEX +SUSPECT_REPORTED_AGE + SUSPECT_RACE_DESCRIPTION+SUSPECT_BODY_BUILD_TYPE+  SUMMONS_ISSUED_FLAG + SEARCHED_FLAG, family = 'binomial', data = sq)
summary(m2)

Call:
glm(formula = Weapon_Found ~ SUSPECT_SEX + SUSPECT_REPORTED_AGE + 
    SUSPECT_RACE_DESCRIPTION + SUSPECT_BODY_BUILD_TYPE + SUMMONS_ISSUED_FLAG + 
    SEARCHED_FLAG, family = "binomial", data = sq)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-0.7797  -0.4955  -0.2515  -0.2415   3.1062  

Coefficients:
                                       Estimate Std. Error z value Pr(>|z|)    
(Intercept)                          -4.2682551  0.2058873 -20.731  < 2e-16 ***
SUSPECT_SEXMALE                       0.8715929  0.1763243   4.943 7.69e-07 ***
SUSPECT_REPORTED_AGE                 -0.0004927  0.0029936  -0.165 0.869267    
SUSPECT_RACE_DESCRIPTIONLATINO/OTHER -0.0768001  0.0790678  -0.971 0.331389    
SUSPECT_RACE_DESCRIPTIONWHITE        -0.5376049  0.1496365  -3.593 0.000327 ***
SUSPECT_BODY_BUILD_TYPESmall         -0.0332901  0.0773328  -0.430 0.666848    
SUMMONS_ISSUED_FLAGY                  0.1266151  0.1841361   0.688 0.491694    
SEARCHED_FLAGY                        2.2429199  0.0870336  25.771  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6037.9  on 9788  degrees of freedom
Residual deviance: 5113.1  on 9781  degrees of freedom
AIC: 5129.1

Number of Fisher Scoring iterations: 6

From our improve model, we can see that log odds of finding weapon significantly increase, \(2.268\) when people are been searched. Male, withe race remain significant as describe in last model.

Adding all Variable To Improving Model:

m3 <- glm(Weapon_Found ~ SUSPECT_SEX +SUSPECT_REPORTED_AGE +SUSPECT_RACE_DESCRIPTION +arrasted+Frisked+SUSPECT_HEIGHT+ SEARCHED_FLAG+SUMMONS_ISSUED_FLAG+SUSPECT_BODY_BUILD_TYPE, family = 'binomial', data = sq)
summary(m3)

Call:
glm(formula = Weapon_Found ~ SUSPECT_SEX + SUSPECT_REPORTED_AGE + 
    SUSPECT_RACE_DESCRIPTION + arrasted + Frisked + SUSPECT_HEIGHT + 
    SEARCHED_FLAG + SUMMONS_ISSUED_FLAG + SUSPECT_BODY_BUILD_TYPE, 
    family = "binomial", data = sq)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.3496  -0.4370  -0.2505  -0.1268   3.3136  

Coefficients:
                                      Estimate Std. Error z value Pr(>|z|)    
(Intercept)                          -6.099569   0.593934 -10.270  < 2e-16 ***
SUSPECT_SEXMALE                       0.669505   0.184605   3.627 0.000287 ***
SUSPECT_REPORTED_AGE                  0.004497   0.003180   1.414 0.157318    
SUSPECT_RACE_DESCRIPTIONLATINO/OTHER -0.067425   0.082905  -0.813 0.416058    
SUSPECT_RACE_DESCRIPTIONWHITE        -0.428232   0.156067  -2.744 0.006071 ** 
arrasted1                             1.697277   0.097607  17.389  < 2e-16 ***
Frisked1                              1.394994   0.102591  13.598  < 2e-16 ***
SUSPECT_HEIGHT                        0.093647   0.101533   0.922 0.356356    
SEARCHED_FLAGY                        1.204195   0.101597  11.853  < 2e-16 ***
SUMMONS_ISSUED_FLAGY                  0.775567   0.194737   3.983 6.82e-05 ***
SUSPECT_BODY_BUILD_TYPESmall         -0.021727   0.081055  -0.268 0.788658    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6037.9  on 9788  degrees of freedom
Residual deviance: 4613.0  on 9778  degrees of freedom
AIC: 4635

Number of Fisher Scoring iterations: 6

From this model, it is clear that log odd significant increase when they are been arrested and frisked (a police officer or other official pass the hands over)compare to those who are not arrested or frisked, \(1.698\) and \(1.394\) respectfully. Furthermore, after adding variable like arrested and frisked, summons issue became a significant coefficient with \(1.204\) positive log odds for finding weapon. Which is understandable since, if there is summon issue for an individual and he/she is arrested or frisked, it is most likely that individual was a criminal and criminal do carry weapon.

Adding Interaction To The Model:

m4 <- glm(Weapon_Found ~ SUSPECT_SEX +SUSPECT_REPORTED_AGE + Frisked+arrasted*SUSPECT_RACE_DESCRIPTION+OTHER_WEAPON_FLAG+SUMMONS_ISSUED_FLAG+ SEARCHED_FLAG+SUSPECT_BODY_BUILD_TYPE+SUSPECT_HEIGHT, family = 'binomial', data = sq)
summary(m4)

Call:
glm(formula = Weapon_Found ~ SUSPECT_SEX + SUSPECT_REPORTED_AGE + 
    Frisked + arrasted * SUSPECT_RACE_DESCRIPTION + OTHER_WEAPON_FLAG + 
    SUMMONS_ISSUED_FLAG + SEARCHED_FLAG + SUSPECT_BODY_BUILD_TYPE + 
    SUSPECT_HEIGHT, family = "binomial", data = sq)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.0035  -0.3811  -0.2218  -0.1171   3.1970  

Coefficients:
                                                Estimate Std. Error z value Pr(>|z|)    
(Intercept)                                    -6.651389   0.636264 -10.454  < 2e-16 ***
SUSPECT_SEXMALE                                 0.927612   0.210216   4.413 1.02e-05 ***
SUSPECT_REPORTED_AGE                            0.004382   0.003354   1.307   0.1914    
Frisked1                                        1.373826   0.107728  12.753  < 2e-16 ***
arrasted1                                       1.974126   0.131036  15.066  < 2e-16 ***
SUSPECT_RACE_DESCRIPTIONLATINO/OTHER            0.175152   0.161018   1.088   0.2767    
SUSPECT_RACE_DESCRIPTIONWHITE                   0.104885   0.278406   0.377   0.7064    
OTHER_WEAPON_FLAGY                              4.947763   0.325996  15.177  < 2e-16 ***
SUMMONS_ISSUED_FLAGY                            0.828262   0.204082   4.058 4.94e-05 ***
SEARCHED_FLAGY                                  1.179744   0.108300  10.893  < 2e-16 ***
SUSPECT_BODY_BUILD_TYPESmall                    0.001302   0.085548   0.015   0.9879    
SUSPECT_HEIGHT                                  0.092623   0.107211   0.864   0.3876    
arrasted1:SUSPECT_RACE_DESCRIPTIONLATINO/OTHER -0.356727   0.191294  -1.865   0.0622 .  
arrasted1:SUSPECT_RACE_DESCRIPTIONWHITE        -0.867756   0.345354  -2.513   0.0120 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6037.9  on 9788  degrees of freedom
Residual deviance: 4188.0  on 9775  degrees of freedom
AIC: 4216

Number of Fisher Scoring iterations: 6

Adding interaction between getting arrested and race, we can see that log odds of finding weapon when arrested still significantly lower amoung white compare to latino and other race,\(-0.866\) and \(-0.355\). Therefore,we can say that getting arrested donnot influeance the log odds of findinf weapon amoung different race.Furthermore, when other weapon beside firearms found, log odds of finding firearms (weapon) significantly increase by \(4.94\). Male, withe race,geting frisked,arrested, searched and summon issue remain significant as describe in other model.

Likelihood Ratio Test:

anova(m0, m1, m2,m3,m4, test = "Chisq")

Analysis of Deviance Table

Model 1: Weapon_Found ~ SUSPECT_REPORTED_AGE
Model 2: Weapon_Found ~ SUSPECT_RACE_DESCRIPTION + SUSPECT_SEX + SUSPECT_REPORTED_AGE + 
    SUSPECT_BODY_BUILD_TYPE
Model 3: Weapon_Found ~ SUSPECT_SEX + SUSPECT_REPORTED_AGE + SUSPECT_RACE_DESCRIPTION + 
    SUSPECT_BODY_BUILD_TYPE + SUMMONS_ISSUED_FLAG + SEARCHED_FLAG
Model 4: Weapon_Found ~ SUSPECT_SEX + SUSPECT_REPORTED_AGE + SUSPECT_RACE_DESCRIPTION + 
    arrasted + Frisked + SUSPECT_HEIGHT + SEARCHED_FLAG + SUMMONS_ISSUED_FLAG + 
    SUSPECT_BODY_BUILD_TYPE
Model 5: Weapon_Found ~ SUSPECT_SEX + SUSPECT_REPORTED_AGE + Frisked + 
    arrasted * SUSPECT_RACE_DESCRIPTION + OTHER_WEAPON_FLAG + 
    SUMMONS_ISSUED_FLAG + SEARCHED_FLAG + SUSPECT_BODY_BUILD_TYPE + 
    SUSPECT_HEIGHT
  Resid. Df Resid. Dev Df Deviance  Pr(>Chi)    
1      9787     6037.0                          
2      9783     5983.7  4    53.23 7.613e-11 ***
3      9781     5113.1  2   870.67 < 2.2e-16 ***
4      9778     4613.0  3   500.02 < 2.2e-16 ***
5      9775     4188.0  3   425.08 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Form this test, we can see that model 4 which is \(m_4\) has a significantly improved based on very small P-value.

Information Criteria:

Bayesian information criterion (BIC): \[BIC = -2L + k\times log(n)\]

Akaike information criterion (AIC): \[AIC = 2(L-k)\]

library(texreg)
#screenreg(list(m0, m1, m2,m3,m4), doctype = FALSE)
htmlreg(list(m0, m1, m2,m3,m4), doctype = FALSE)

Statistical models

	Model 1	Model 2	Model 3	Model 4	Model 5
(Intercept)	-2.36***	-3.17***	-4.27***	-6.10***	-6.65***
	(0.09)	(0.19)	(0.21)	(0.59)	(0.64)
SUSPECT_REPORTED_AGE	0.00	0.00	-0.00	0.00	0.00
	(0.00)	(0.00)	(0.00)	(0.00)	(0.00)
SUSPECT_RACE_DESCRIPTIONLATINO/OTHER		-0.01	-0.08	-0.07	0.18
		(0.08)	(0.08)	(0.08)	(0.16)
SUSPECT_RACE_DESCRIPTIONWHITE		-0.52***	-0.54***	-0.43**	0.10
		(0.14)	(0.15)	(0.16)	(0.28)
SUSPECT_SEXMALE		0.91***	0.87***	0.67***	0.93***
		(0.17)	(0.18)	(0.18)	(0.21)
SUSPECT_BODY_BUILD_TYPESmall		-0.09	-0.03	-0.02	0.00
		(0.07)	(0.08)	(0.08)	(0.09)
SUMMONS_ISSUED_FLAGY			0.13	0.78***	0.83***
			(0.18)	(0.19)	(0.20)
SEARCHED_FLAGY			2.24***	1.20***	1.18***
			(0.09)	(0.10)	(0.11)
arrasted1				1.70***	1.97***
				(0.10)	(0.13)
Frisked1				1.39***	1.37***
				(0.10)	(0.11)
SUSPECT_HEIGHT				0.09	0.09
				(0.10)	(0.11)
OTHER_WEAPON_FLAGY					4.95***
					(0.33)
arrasted1:SUSPECT_RACE_DESCRIPTIONLATINO/OTHER					-0.36
					(0.19)
arrasted1:SUSPECT_RACE_DESCRIPTIONWHITE					-0.87*
					(0.35)
AIC	6040.97	5995.73	5129.06	4635.04	4215.96
BIC	6055.35	6038.87	5186.58	4714.12	4316.61
Log Likelihood	-3018.48	-2991.87	-2556.53	-2306.52	-2093.98
Deviance	6036.97	5983.73	5113.06	4613.04	4187.96
Num. obs.	9789	9789	9789	9789	9789
p < 0.001, p < 0.01, p < 0.05

From both \(AIC\) and \(BIC\), we can see that models get better as their value decrease with more variable and complexity. The best performing model based on both of these metrics is Model 5 which is model \(m_4\)

Visualizations of Our Best Model:

library(visreg)
visreg(m4, "SUSPECT_REPORTED_AGE",scale="response",line=list(col="violetred2"),fill=list(col="midnightblue"),
       xlab="Suspect Age") +  theme_bw()

Conditions used in construction of plot
SUSPECT_SEX: MALE
Frisked: 1
arrasted: 0
SUSPECT_RACE_DESCRIPTION: BLACK
OTHER_WEAPON_FLAG: (null)
SUMMONS_ISSUED_FLAG: N
SEARCHED_FLAG: N
SUSPECT_BODY_BUILD_TYPE: BIG/ATHLETETIC
SUSPECT_HEIGHT: 5.7
NULL

We can see that, as age increase probability of finding weapon slightly increased as we saw in our model.

I will not use intersecting plot because my interection variables are factor( Race and arrested) not integer. Therefore, i will use visreg to check my interaction result.

visreg(m4, "SUSPECT_RACE_DESCRIPTION", by = "arrasted",scale ="response",line=list(col="darkgoldenrod1"),
                             fill=list(col="firebrick4"), xlab="Suspect Race")

From this graph, we can say that see that our interaction correctly mention that it is less likely that a weapon will be found in someone of white race even he/she is arrested compare to other race.

visreg(m4, "SUSPECT_SEX", by = "arrasted",scale ="response",line=list(col="brown2"),
                             fill=list(col="gray0"), xlab="Suspect Sex")

Male are more likely to carry weapon than female whether they were arrested or not.