Homework #5

Tidy Data

library(dplyr)
Rossi <- select(Rossi, arrest, race, mar, wexp, fin) #Subset Variables
Rossi <- rename(Rossi, Rearrested = "arrest", Race = "race", Marriage = "mar", Work.Experience = "wexp", Financial.Assistance = "fin") #Rename Variables

Structure of the Data

glimpse(Rossi)

## Rows: 432
## Columns: 5
## $ Rearrested           <int> 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1…
## $ Race                 <fct> black, black, other, black, other, black, black, …
## $ Marriage             <fct> not married, not married, not married, married, n…
## $ Work.Experience      <fct> no, no, yes, yes, yes, yes, yes, yes, no, yes, no…
## $ Financial.Assistance <fct> no, no, no, yes, no, no, no, yes, no, no, yes, no…

Rossi Data Table

DT::datatable(Rossi) 

Research Questions

• Does race influence the likelihood of being re-arrested?
  

• Does marriage status impact the likelihood of being re-arrested?
  

• Does having work experience reduce the likelihood of re-arrest?
  

• Does financial assistance reduce the likelihood of re-arrest?

Model <- glm(Rearrested ~ Race + Marriage + Work.Experience + Financial.Assistance, family = binomial, data = Rossi) 
summary(Model)

## 
## Call:
## glm(formula = Rearrested ~ Race + Marriage + Work.Experience + 
##     Financial.Assistance, family = binomial, data = Rossi)
## 
## Coefficients:
##                         Estimate Std. Error z value Pr(>|z|)  
## (Intercept)              -1.0114     0.4460  -2.268   0.0233 *
## Raceother                -0.2205     0.3547  -0.622   0.5341  
## Marriagenot married       0.5841     0.4140   1.411   0.1583  
## Work.Experienceyes       -0.5511     0.2280  -2.417   0.0156 *
## Financial.Assistanceyes  -0.4598     0.2239  -2.054   0.0400 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 498.60  on 431  degrees of freedom
## Residual deviance: 483.65  on 427  degrees of freedom
## AIC: 493.65
## 
## Number of Fisher Scoring iterations: 4

Interpretation

• There is no significant relationship between race and the likelihood of being rearrested.
• There is no significant relationship between marriage status and the likelihood of being rearrested.
• There is a significant relationship between work experience and the likelihood of being rearrested. As Work Experience increases, the likelihood of being rearrested decreases.
• There is a significant relationship between financial assistance and the likelihood of being rearrested. As Financial Assistance increases, the likelihood of being rearrested decreases.
  

Average Marginal Effects Description

• The average marginal effect is the average of the marginal effects across all observations in the sample.
• The marginal effect of a variable is the change in the expected value of the dependent variable for a one-unit change in the independent variable.

library(clarify) #Using clarify to interpret results

set.seed(123) #Set random seed to obtain repeatable results

sim_coefs <- sim(Model) #Simulate model parameters from the fitted model using sim() function

Use the sim_ame() function to calculate the average marginal effect of “Work.Experience” on the probability of being rearrested.

sim_est <- sim_ame(sim_coefs, var = "Work.Experience", 
                   contrast = "rd", verbose = F)
summary(sim_est)

##           Estimate  2.5 % 97.5 %
## E[Y(no)]     0.323  0.259  0.397
## E[Y(yes)]    0.217  0.173  0.275
## RD          -0.106 -0.190 -0.016

Interpretation

• Former convicts with no prior work experience have a 32% chance of being rearrested.
• Former convicts with prior work experience have a 22% chance of being rearrested.
• So it can said that having work experience reduces the probability of being rearrested by 10%.
  

Use the sim_ame() function to calculate the average marginal effects of “Financial Assistance” on the probability of being rearrested.

options(scipen=999) # To avoid scientific notation
sim_est1 <- sim_ame(sim_coefs, var = "Financial.Assistance", 
                   contrast = "rd", verbose = F)
summary(sim_est1)

##             Estimate      2.5 %     97.5 %
## E[Y(no)]   0.3073709  0.2548734  0.3754478
## E[Y(yes)]  0.2208248  0.1712448  0.2827665
## RD        -0.0865461 -0.1666826  0.0000329

Interpretation

• Former convicts who do not receive financial assistance have a 30% chance of being rearrested.
• Former convicts that do receive financial assistance have a 22% chance of being rearrested.
• So it can be said that receiving financial assistance reduces the probability of being rearrested by 8%.
  
  

Sim_Setx Function Description

• The sim_setx() function is used to compute predictions and first differences at set values.
  

Research Questions

• How does having work experience and receiving financial assistance influence the likelihood of rearrest?
• How does having no work experience and receiving no financial assistance influence the likelihood of rearrest?

est <- sim_setx(sim_coefs, x = list(Work.Experience = "yes", Financial.Assistance = "yes"),
                x1 = list(Work.Experience = "no", Financial.Assistance = "no"), verbose = FALSE)
summary(est)

##                                                       Estimate  2.5 % 97.5 %
## Work.Experience = "yes", Financial.Assistance = "yes"   0.1918 0.1371 0.2659
## Work.Experience = "no", Financial.Assistance = "no"     0.3947 0.3114 0.4928
## FD                                                      0.2029 0.0737 0.3256

Interpretation

• Ex convicts who have prior work experience and receive financial assistance have a 19% chance of being rearrested.
• Ex convicts who have no prior work experience and do not receive financial assistance have a 39% chance of being rearrested.
• The first difference depicts that convicts with no prior work experience and no financial assistance have a 20% higher probability of being rearrested compared to ex convicts with prior work experience and financial assistance.