Inference for Logistic Regression in R

Pairs Today

Please pair up (your choice).
- At least one person in each pair needs to have a device that can use RStudio (installed or using rstudio.cloud). This person is the Operator.
- Ideally, everyone has an RStudio-enabled device. If you don’t, you can still take notes by keeping track of the code and trying it on your own later.

NBA Rookie Data

Observational Units: 2621 NBA Rookies.
Response (Outcome) Variable: Are they still in the NBA after 5 years? (TRUE/FALSE)
Several possible explanatory variables: games played, minutes per game, points per game, rebounds, assists, etc.
Can we predict which types of players will remain in the NBA?
- Which predictors are important?
- Which predictors are correlated?

Data Carpentry

Group Exercises

Do all the challenges.

library(tidyverse)
library(caret)

## Load and inspect the data
nba <- read_csv("https://math.westmont.edu/data/nba.csv")
view(nba)

ggplot(nba, aes(x = PTS)) + geom_histogram()
ggplot(nba, aes(x = PTS, y = TARGET_5Yrs)) + geom_point()
ggplot(nba, aes(x = PTS, y = TARGET_5Yrs)) + geom_boxplot()

## Logistic regression models
bbmod1 <- glm(TARGET_5Yrs ~ PTS, family = "binomial", data = nba)
summary(bbmod1)

bbmod2 <- glm(TARGET_5Yrs ~ 3P%, family = "binomial", data = nba) # error

glimpse(nba)
bbmod2 <- glm(TARGET_5Yrs ~ `3P%`, family = "binomial", data = nba)
summary(bbmod2)

# Challenge: Improve bbmod2 by controlling for 3 point attempts (3PA). Do
# the p-values change? Can you explain why?

## Correlated predictors?
cor(nba[,7:31])
round(cor(nba[,7:31]), 1)

## Challenge: Why are some of the correlations NA? 

## Cross Validation

tc <- trainControl(method = "cv", number = 10)
train(TARGET_5Yrs ~ PTS,  data = nba, 
      method = "glm", family = "binomial", trControl = tc)
nba <- nba %>%
  mutate(T5Y = factor(ifelse(TARGET_5Yrs, "Yes", "No")))
train(T5Y ~ PTS,  data = nba, 
      method = "glm", family = "binomial", trControl = tc)
bbcv1 <- train(T5Y ~ PTS, 
               data = nba, method = "glm", family = "binomial", trControl = tc)
confusionMatrix(bbcv1)

bbcv2 <- train(T5Y ~ `3P%` + `3PA`, 
               data = nba, method = "glm", family = "binomial", trControl = tc)
bbcv2 <- train(T5Y ~ `3P` + `3PA`, 
               data = nba, method = "glm", family = "binomial", trControl = tc)
confusionMatrix(bbcv2)
bbcv2

## Challenge: Find a model with a better prediction accuracy.
## For the best model you find, generate a logistic regression 
## table. Which predictors are most important? 

## Search for best model?
nba_complete <- nba %>%
  select(-TARGET_5Yrs, -PlayerID, -Player, -Pos, -Age, -Tm, -Year, -`FG%`, -`3P%`, -`2P%`, -`eFG%`, -`FT%`, -GS)
fullmod <- glm(T5Y ~ ., family = "binomial", data = nba_complete)
summary(fullmod)
step(fullmod)

## Challenge: Use the results of step, make a regression model using glm
## and test its accuracy using train. Does it beat the other models we found?