Marijuana Arrests in Toronto: Racial Disparities

class: center, middle, inverse, title-slide

.title[
# Marijuana Arrests in Toronto: Racial Disparities
]
.author[
### Fernando José Álvarez Petro & Diego Andrés Moreno López
]
.date[
### 2023-05-26
]

---

### Marijuana Arrests in Toronto: Racial Disparities

* Base de datos recopilada como parte de un estudio sobre disparidades raciales en los arrestos por posesión de marihuana en Toronto.

* Contiene 5226 observaciones y 8 variables.

* Propósito: examinar el tratamiento policial de individuos arrestados por posesión simple de marihuana en la ciudad.

---
### Descripción de variables

1. released: Indica si la persona arrestada fue liberada con una citación. Categorías: "No" y "Yes".

2. colour: Representa la raza del individuo arrestado. Categorías: "Black" (negro) y "White" (blanco).

3. year: Indica el año del arresto. Rango: 1997-2002.

4. age: Edad de la persona arrestada en años. Variable numérica continua.

5. sex: Género de la persona arrestada. Categorías: "Female" (mujer) y "Male" (hombre).

6. employed: Indica si la persona arrestada está empleada. Categorías: "No" y "Yes".

7. citizen: Indica si la persona arrestada es ciudadana. Categorías: "No" y "Yes".

8. checks: Número de bases de datos policiales en las que aparece el nombre del arrestado. Variable numérica continua.

---
### Paquetes

```r
library(tidyverse)
library(plotly)
library(leaps) 
library(MASS)
```

### Exportar archivo

```r
#file.choose()

datos <- read.csv("C:\\Users\\ferna\\OneDrive - UPB\\Documents\\Upb\\Semestre 9\\Ciencia de datos\\FINAL PROJECT\\Arrests.csv")
```

---

### Acercamiento a la base de datos

```r
head(datos)
```

```
##   X released colour year age    sex employed citizen checks
## 1 1      Yes  White 2002  21   Male      Yes     Yes      3
## 2 2       No  Black 1999  17   Male      Yes     Yes      3
## 3 3      Yes  White 2000  24   Male      Yes     Yes      3
## 4 4       No  Black 2000  46   Male      Yes     Yes      1
## 5 5      Yes  Black 1999  27 Female      Yes     Yes      1
## 6 6      Yes  Black 1998  16 Female      Yes     Yes      0
```

```r
datos <- datos %>% rename(
 observación = X,
 detenido = released,
 color_piel = colour,
 año = year,
 edad = age,
 sexo = sex,
 empleado = employed,
 ciudadano = citizen,
 n_arrestos = checks
 )
```

---
### Transformación de datos

```r
datos <- datos %>% mutate(
 capturas = ifelse(n_arrestos >= 3 & detenido == "No", "Investigar", "No investigar")
 )
```

---

### EDA

Se realiza un analisis exploratorio a los datos con el fin de explorar el comportamiento individual y en conjunto de algunas varible.

```r
g1 <- ggplot(datos, aes(x = color_piel, fill = detenido)) + 
 geom_bar(position = "dodge") +
 labs(x = "Color de piel", y = "Número de observaciones", fill = "Detenido", title = "Personas detenidas vs Raza")
ggplotly(g1)
```

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---

```r
g2 <- ggplot(datos, aes(x = edad)) + 
 geom_bar(position = "dodge") +
 labs(x = "Edad", y = "Número de observaciones", title = "Edad de las personas que portaban droga")
ggplotly(g2)
```

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---

```r
g3 <- ggplot(datos, aes(x = capturas)) + 
 geom_bar(position = "dodge", fill = "red") +
 labs(x = "Capturas", y = "Número de observaciones", title = "Relación entre el número de arrestos y las personas detenidas")
ggplotly(g3)
```

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---

```r
g4 <- ggplot(data = datos, aes(x = año, y = edad)) + 
 geom_point(col = "blue") +
 labs(x = "Año", y = "Edad", title = "Relación entre la edad de la persona vs año en que se presento")
ggplotly(g4)
```

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```r
#cor.test(año, edad)
```

---

```r
g5 <- ggplot(datos, aes(x = n_arrestos)) + 
 geom_density(aes(colour = detenido)) +
 labs(x = "Número de arrestos", y = "Número de observaciones", title = "Historial arrestos vs ultima detención")
ggplotly(g5)
```

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---

```r
g6 <- ggplot(datos, aes(x = edad, fill = as.character(datos$n_arrestos))) + 
 geom_bar(position = "dodge") +
 labs(x = "Edad", y = "Número de observaciones", fill = "Número de arrestos", title = "Relación del número de arrestos vs edad de la persona")
ggplotly(g6)
```

```
## Warning: Use of `datos$n_arrestos` is discouraged.
## ℹ Use `n_arrestos` instead.
```

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---

```r
g7 <- ggplot(data = datos, aes(x = edad, y = n_arrestos)) + 
 geom_point(col = "blue") +
 labs(x = "Edad", y = "Número de arrestos", title = "Relación del número de arrestos vs edad de la persona")
ggplotly(g7)
```

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de arrestos","font":{"color":"rgba(0,0,0,1)","family":"","size":14.6118721461187}},"hoverformat":".2f"},"shapes":[{"type":"rect","fillcolor":null,"line":{"color":null,"width":0,"linetype":[]},"yref":"paper","xref":"paper","x0":0,"x1":1,"y0":0,"y1":1}],"showlegend":false,"legend":{"bgcolor":"rgba(255,255,255,1)","bordercolor":"transparent","borderwidth":1.88976377952756,"font":{"color":"rgba(0,0,0,1)","family":"","size":11.689497716895}},"hovermode":"closest","barmode":"relative"},"config":{"doubleClick":"reset","modeBarButtonsToAdd":["hoverclosest","hovercompare"],"showSendToCloud":false},"source":"A","attrs":{"2f4c7dd75fe2":{"x":{},"y":{},"type":"scatter"}},"cur_data":"2f4c7dd75fe2","visdat":{"2f4c7dd75fe2":["function (y) ","x"]},"highlight":{"on":"plotly_click","persistent":false,"dynamic":false,"selectize":false,"opacityDim":0.2,"selected":{"opacity":1},"debounce":0},"shinyEvents":["plotly_hover","plotly_click","plotly_selected","plotly_relayout","plotly_brushed","plotly_brushing","plotly_clickannotation","plotly_doubleclick","plotly_deselect","plotly_afterplot","plotly_sunburstclick"],"base_url":"https://plot.ly"},"evals":[],"jsHooks":[]}</script>

```r
#cor.test(edad, n_arrestos)
```

---

```r
g8 <- ggplot(data = datos, aes(x = año, y = n_arrestos)) + 
 geom_point(col = "blue") +
 labs(x = "Año", y = "Número de arrestos", title = "Relación del número de arrestos vs año en que se presento")
ggplotly(g8)
```

<div class="plotly html-widget html-fill-item-overflow-hidden html-fill-item" id="htmlwidget-cbc6601f20405e5cbad9" style="width:720px;height:360px;"></div>
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```r
#cor.test(año, n_arrestos)
```

---

```r
g9 <- ggplot(data = datos, aes(x = año, y = edad)) + 
 geom_point(col = "blue") +
 labs(x = "Año", y = "Edad", title = "Relación entre la edad de la persona vs año en que se presento")
ggplotly(g9)
```

<div class="plotly html-widget html-fill-item-overflow-hidden html-fill-item" id="htmlwidget-4d3b834ea16f09981f02" style="width:720px;height:360px;"></div>
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```r
#cor.test(año, edad)
```
---
## Transformación de variables

```r
datos <- datos %>%
 mutate(across(c(detenido, color_piel, sexo, empleado, ciudadano, capturas), ~as.factor(.))) %>%
 mutate(across(c(detenido, color_piel, sexo, empleado, ciudadano, capturas), ~as.integer(.)))
```

---
### Regresión

### Metodo de selección de variable

```r
resultados <- numeric(9)

for (i in 1:9) {
mod_select <- regsubsets(x = n_arrestos ~ . ,
 data = datos, nvmax = i,
 nbest = 1, method = "exhaustive") #Ajuste la variable salario con la restante que se encuentra en la base de datos
Resumen <- summary(mod_select)$adjr2
resultados[i] <- Resumen[i]
}
mejor_i <- which.max(resultados)

print(resultados)
```

```
## [1] 0.1854154 0.2122695 0.2241012 0.2370082 0.2456348 0.2533186 0.2545948
## [8] 0.2553478 0.2553347
```

```r
print(mejor_i)
```

```
## [1] 8
```

```r
mod_select1 <- regsubsets(x = n_arrestos ~ . ,
 data = datos, nvmax = mejor_i,
 nbest = 1, method = "exhaustive") #Ajuste la variable salario con la restante que se encuentra en la base de datos
Resumen1 <- summary(mod_select)$adjr2
plot(mod_select1, scale = "adjr2")
```

![](rmarkdown-slides_files/figure-html/unnamed-chunk-16-1.png)

---

### Método forward

```r
resultados2 <- numeric(8)

for (i in 1:8) {
mod_select2 <- regsubsets(x = n_arrestos ~ .,
 data = datos,
 nvmax = i,
 nbest = 1,
 method = "forward")
res2 <- summary(mod_select2)
}

tb1 <- tibble(nvar = 1:8, r2adj1 = res2$adjr2, r21 = res2$rsq, cp1 = res2$cp, bic1 = res2$bic)
res2$which
```

```
##   (Intercept) observación detenido color_piel   año  edad  sexo empleado
## 1        TRUE       FALSE    FALSE      FALSE FALSE FALSE FALSE    FALSE
## 2        TRUE       FALSE    FALSE      FALSE FALSE FALSE FALSE     TRUE
## 3        TRUE       FALSE     TRUE      FALSE FALSE FALSE FALSE     TRUE
## 4        TRUE       FALSE     TRUE       TRUE FALSE FALSE FALSE     TRUE
## 5        TRUE       FALSE     TRUE       TRUE FALSE  TRUE FALSE     TRUE
## 6        TRUE       FALSE     TRUE       TRUE FALSE  TRUE  TRUE     TRUE
## 7        TRUE       FALSE     TRUE       TRUE  TRUE  TRUE  TRUE     TRUE
## 8        TRUE       FALSE     TRUE       TRUE  TRUE  TRUE  TRUE     TRUE
##   ciudadano capturas
## 1     FALSE     TRUE
## 2     FALSE     TRUE
## 3     FALSE     TRUE
## 4     FALSE     TRUE
## 5     FALSE     TRUE
## 6     FALSE     TRUE
## 7     FALSE     TRUE
## 8      TRUE     TRUE
```

```r
Point <- tb1 %>% filter(r2adj1 == max(tb1$r2adj1))
```

---

### Método back

```r
resultados2 <- numeric(8)

for (i in 1:8) {
 mod_select4 <- regsubsets(x = n_arrestos ~ .,
 data = datos,
 nvmax = i,
 nbest = 1,
 method = "back")
 res4 <- summary(mod_select4)
}

tb4 <- tibble(nvar = 1:8, r2adj4 = res4$adjr2, r24 = res4$rsq, cp4 = res4$cp, bic4 = res4$bic)
res4$which
```

```r
Point <- tb4 %>% filter(r2adj4 == max(tb4$r2adj4))
```

---

### Estimación del mejor modelo

```r
mod1 <- lm(formula = n_arrestos ~ ., data = datos)
summary(mod1)
```

```
## 
## Call:
## lm(formula = n_arrestos ~ ., data = datos)
## 
## Residuals:
## Min 1Q Median 3Q Max 
## -2.7644 -1.1847 -0.2342 0.8594 4.4843 
## 
## Coefficients:
## Estimate Std. Error t value Pr(>|t|) 
## (Intercept) 1.078e+02 2.745e+01 3.926 8.75e-05 ***
## observación -1.161e-05 1.219e-05 -0.953 0.340742 
## detenido 6.868e-01 7.222e-02 9.509 < 2e-16 ***
## color_piel -4.016e-01 4.434e-02 -9.057 < 2e-16 ***
## año -5.116e-02 1.374e-02 -3.722 0.000199 ***
## edad 1.758e-02 2.232e-03 7.874 4.14e-15 ***
## sexo 5.048e-01 6.636e-02 7.607 3.31e-14 ***
## empleado -6.089e-01 4.639e-02 -13.127 < 2e-16 ***
## ciudadano 1.394e-01 5.568e-02 2.504 0.012317 * 
## capturas -2.591e+00 9.061e-02 -28.597 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.328 on 5216 degrees of freedom
## Multiple R-squared: 0.2566, Adjusted R-squared: 0.2553 
## F-statistic: 200.1 on 9 and 5216 DF, p-value: < 2.2e-16
```

---

### Estimación de los parametros

Se busca predecir los cambios en el número de arrestos a lo largo del tiempo.

```r
mod1$coefficients
```

```
##   (Intercept)   observación      detenido    color_piel           año 
##  1.077702e+02 -1.160997e-05  6.867598e-01 -4.016072e-01 -5.115508e-02 
##          edad          sexo      empleado     ciudadano      capturas 
##  1.757521e-02  5.047902e-01 -6.089160e-01  1.394233e-01 -2.591278e+00
```

Se podría identificar patrones temporales, de  aumentos o disminuciones en la actividad delictiva a lo largo de este año.

---

### Modelos de clasificación

### Ajustar el modelo LDA con variables codificadas

```r
#modelo_lda <- lda(detenido ~ ., data = datos)
```
---

### Hacer predicciones y evaluar el rendimiento del modelo

```r
#predicciones <- predict(modelo_lda, newdata = datos)
#clases_predichas <- predicciones$class
#tabla_confusion <- table(clases_predichas, datos$detenido)
#accuracy <- sum(diag(tabla_confusion)) / sum(tabla_confusion)
```

---

### Conclusión