Classwork 5

Logistic Regression II - Quasi-Separation & Regularization

0.1 Packages

library(tidyverse)
library(broom)
library(stargazer)
library(margins)
library(yardstick)
library(WVPlots)
library(pROC)
library(glmnet)
library(gamlr)

0.2 Data

df <- read_csv('https://bcdanl.github.io/data/car-data.csv')

df |> 
  rmarkdown::paged_table()

0.3 Variable description

Variable	Description
buying	Buying price of the car (vhigh, high, med, low)
maint	Maintenance cost (vhigh, high, med, low)
doors	Number of doors (2, 3, 4, 5more)
persons	Capacity in terms of persons to carry (2, 4, more)
lug_boot	Size of luggage boot (small, med, big)
safety	Estimated safety of the car (low, med, high)
rating	Car acceptability (unacc, acc, good, vgood)
fail	TRUE if the car is unacceptable (unacc), otherwise FALSE

1 Question 1

• Divide the df DataFrame into training and test DataFrames.
  • Use dtrain and dtest for training and test DataFrames, respectively.
  • 70% of observations in the df are assigned to dtrain; the rest is assigned to dtest.

2 Question 2

Fit the following regression model:

\[ \begin{align} &\quad\;\; \text{Prob}(\text{fail}_{i} = 1) \\ &= G\Big(\beta_{0} \\ &\qquad\quad\;\;\; \,+\, \beta_{4} \text{buying\_med}_{i} \,+\, \beta_{4} \text{buying\_high}_{i} \,+\, \beta_{4} \text{buying\_vhigh}_{i} \\ &\qquad\quad\;\;\; \,+\, \beta_{4} \text{maint\_med}_{i} \,+\, \beta_{4} \text{maint\_high}_{i} \,+\, \beta_{4} \text{maint\_vhigh}_{i} \\ &\qquad\quad\;\;\; \,+\, \beta_{7} \text{persons\_4}_{i} \,+\, \beta_{8} \text{persons\_more}_{i} \\ &\qquad\quad\;\;\; \,+\, \beta_{10} \text{lug\_boot\_med}_{i}\,+\, \beta_{10} \text{lug\_boot\_big}_{i} \\ &\qquad\quad\;\;\; \,+\, \beta_{11} \text{safety\_med}_{i}\,+\, \beta_{11} \text{safety\_high}_{i} \Big), \end{align} \]

where \(G(\,\cdot\,)\) is

\[ G(\,\cdot\,) = \frac{\exp(\,\cdot\,)}{1 + \exp(\,\cdot\,)}. \]

Provide the summary of the regression result.

• Set the reference levels accordingly.

3 Question 3

• How are coefficient estimates?

4 Question 4

• Calculate the followings:
  • Confusion matrix with the appropriate threshold level.
  • Accuracy
  • Precision
  • Recall
  • Specificity
  • Average rate of at-risk babies
  • Enrichment

5 Question 5

Visualize the variation in recall and enrichment across different threshold levels.

6 Question 6

• Draw the receiver operating characteristic (ROC) curve.
• Calculate the area under the curve (AUC).

7 Question 7

• Use glmnet to fit a Lasso logistic regression.
  • Repeat Questions 2-6.

8 Question 8

• Use glmnet to fit a Ridge logistic regression.
  • Repeat Questions 2-6.

9 Question 9

• Use glmnet to fit a Elastic Net logistic regression.
  • Repeat Questions 2-6.

10 Discussion

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