AE 11: Multinomial logistic regression

Sesame Street

Author

Insert your name

Published

April 14, 2025

Important

Render, commit, and push your responses to GitHub by the end of class.

Introduction

library(tidyverse)
library(knitr)
library(broom)
library(nnet) # for multinomial logistic regression

Today’s data comes from an experiment by the Educational Testing Service to test the effectiveness of the children’s program Sesame Street. Sesame Street is an educational program designed to teach young children basic educational skills such as counting and the alphabet

As part of the experiment, children were assigned to one of two groups: those who were encouraged to watch the program and those who were not.

The show is only effective if children watch it, so we want to understand what effect the encouragement had on the frequency children watched the program.

Response:

  • viewcat
    • 1: rarely watched show
    • 2: watched once or twice a week
    • 3: watched three to five times a week
    • 4: watched show on average more than five times a week

Predictors:

  • age: child’s age in months
  • prenumb: score on numbers pretest (0 to 54)
  • prelet: score on letters pretest (0 to 58)
  • viewenc: 1: encouraged to watch, 0: not encouraged
  • site:
    • 1: three to five year old from urban area
    • 2: four year old from suburban area
    • 3: from rural area with high socioeconomic status
    • 4: from rural area with low socioeconomic status
    • 5: from Spanish speaking home
# read in dataset
sesame <- read_csv("https://bit.ly/sesame-street-data")

# mean-center relevant continuous variables, make categorical variables factors
sesame <- sesame |> 
  mutate(viewcat = factor(viewcat), 
         site = factor(site), 
         prenumbCent = prenumb - mean(prenumb), 
         preletCent = prelet - mean(prelet), 
         ageCent = age - mean(age),
         viewenc = factor(if_else(viewenc == 1, "1", "0"))
  )

Exercises

Exercise 1

Create a plot to visualize the relationship between the response, viewcat and the primary variable of interest in this analysis, viewenc. What do you observe from the plot?

Exercise 2

Create a plot to visualize the relationship between the response, viewcat and age. What do you observe from the plot?

Exercise 3

Fit a model using the ageCent and viewenc to understand the odds a child is in a given category of viewcat. Display the model including 95% confidence intervals for the coefficients.

Exercise 4

  • What is the baseline category for viewcat? What is the baseline category for viewenc?

  • Interpret the intercept associated with the odds of a child being in the category viewcat == 2 versus the baseline.

  • Interpret the effect of age in terms of the odds of a child being in the category viewcat == 2 versus the baseline. Based on the confidence interval for the coefficient, is the numeric predictor a statistically significant predictor of viewership?

Exercise 5

Should the interaction between ageCent and viewenc be included in the model? Show any analysis used to make your conclusion.

Exercise 6

The primary objective of the experiment was to understand the effect of encouragement on viewership. Does encouragement have a significant effect on viewership after adjusting for age? If so, describe the effect. Otherwise, explain why not.

Exercise 7

  • Use the model selected in Exercise 5 to compute the predicted probabilities and predicted classes for viewcat.

  • Make a confusion matrix.

  • What percentage of observations were correctly classified?

Exercise 8

  • Assess the overall model performance.

  • Were there particular categories in which the model has a harder time differentiating?

Submission

Important

To submit the AE:

  • Render the document to produce the PDF with all of your work from today’s class.

  • Push all your work to your AE repo on GitHub. You’re done! 🎉