AE 20: Assessing Logistic Regression Models

Important

  • Open RStudio and create a subfolder in your AE folder called “AE-20”.

  • Go to the Canvas and locate your AE-20 assignment to get started.

  • Upload the ae-20.qmd and framingham.csv files into the folder you just created. The .qmd and PDF responses are due in Canvas. You can check the due date on the Canvas assignment.

Packages

library(tidyverse)
library(broom)
library(ggformula)
library(mosaic)
library(knitr)

heart_disease <- read_csv("framingham.csv") |>
  select(totChol, TenYearCHD, age, BMI, cigsPerDay, heartRate, sysBP, diabetes) |>
  drop_na()

Data: Framingham study

This data set is from an ongoing cardiovascular study on residents of the town of Framingham, Massachusetts. We want to predict if a randomly selected adult is high risk for heart disease in the next 10 years.

Response variable

  • TenYearCHD:
    • 1: Patient developed heart disease within 10 years of exam
    • 0: Patient did not develop heart disease within 10 years of exam

What’s my predictor variable?

Based on your group, use the following as your predictor variable.

  • Group 1 - totChol: total cholesterol (mg/dL)
  • Group 2 -BMI: patient’s body mass index
  • Group 3 -cigsPerDay: number of cigarettes patient smokes per day
  • Group 4 -heartRate: Heart rate (beats per minute)

Additional Variables

  • sysbp - the patients systolic blood pressure at the time of examination

  • diabetes - 1 if the patient had diabetes and 0 if the patient didn’t have diabetes at the time of examination

Exercise 0

Fit a logistic regression model predicting TenYearCHD from your group’s predictor variable. Note that we won’t return to this model until Exercise 3.

Exercise 1

Before you work on your own model, lets consider the variable sysBP which represents the patients systolic blood pressure (the top number). You have 120 seconds, find the \(\beta\)’s that result in the largest log-likelihood for a logistic regression model predicting the risk of coronary heart disease from sysBP:

# Change these
beta0 <- 1
beta1 <- 1


# Don't change anything below this line
predicted_probabilities <- exp(beta0 + beta1*heart_disease$sysBP)/(1+exp(beta0 + beta1*heart_disease$sysBP))
log_likelihoods <- heart_disease$TenYearCHD*log(predicted_probabilities) +
                        (1-heart_disease$TenYearCHD)*log(1-predicted_probabilities)

# Final log likelihood
sum(log_likelihoods)
[1] NaN

Exercise 2

Compute the empirical logit for each level of diabetes:

  1. Use the function tally to compute the count the number of successes and failures for each level of diabetes.
  2. Compute the empirical odds.
  3. Compute the log of these odds.

Exercise 3

Is linearity satisfied for the model you fit in Exercise 0?

Exercise 4 (Time Permitting)

On a whiteboard, design a simulation-based hypothesis test for determining whether the coefficient of your explanatory variable is a statistically significant predictor for the risk of TenYearCHD.

Submission

Important

To submit the AE:

  • Render the document to produce the PDF with all of your work from today’s class.
  • Upload your QMD and PDF files to the Canvas assignment.