Fitting the model

• In lme4 (and others) this is expressed as:

library(lme4)
fit <- glmer(
  HR ~ (1 | pitcher) + (1 | batter),
  data = sc_2023,
  family = binomial
)
VarCorr(fit)  # get sigma_p and sigma_b

##  Groups  Name        Std.Dev.
##  pitcher (Intercept) 0.188   
##  batter  (Intercept) 0.523

• Results suggest more of the variation in home runs is due to batter effects then pitcher effects.