model-selection.md

Model selection

Let's use the baseball data set from class, where we'll predict AVG (batting average):

baseball <- read.csv("https://raw.githubusercontent.com/brianlukoff/sta371g/master/data/baseball.csv")

Stepwise regression

We can do both forward and backward stepwise regression using the step function. First we define a "null" model with no predictor variables, as a base for R to build on (or fall back on, if it turns out that none of the predictor variables are worth keeping!), and a "full" model that contains all of the predictors we want to consider:

null <- lm(AVG ~ 1, data=baseball)
full <- lm(AVG ~ OBP + SLG + EXP + PAYR + MLAVG + MLOBP + MLSLG + AVGcumLag1 + OBPcumLag1 + SLGcumLag1 + G + YRINDEX, data=baseball)

Now we can do forward stepwise regression, starting at null:

step(null, scope=list(lower=null, upper=full), direction="forward")

Or backward stepwise regression, starting at full:

step(full, scope=list(lower=null, upper=full), direction="backward")

Best-subsets regression

The regsubsets command runs best subsets regression; the syntax is similar to lm. However, we first have to load the leaps library (if you get an error when you try to run the library command below, first run install.packages("leaps") and then re-run it; you'll only have to do that once).

library(leaps)
results <- regsubsets(AVG ~ OBP + SLG + EXP + PAYR + MLAVG + MLOBP + MLSLG + AVGcumLag1 + OBPcumLag1 + SLGcumLag1 + G + YRINDEX, data=baseball)

The results can be plotted against a number of different selection metrics:

plot(results, scale="adjr2")
plot(results, scale="bic")