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In multilevel models, it is possible to predict (not estimate) the random effects by Empirical Bayes after the model parameters have been estimated.

I know how to use the ranef() command to do that. However, I am interested in understanding the procedure.

Can someone provide an explanation/example how I can derive the Empirical Bayes predictions for the random effects “manually” for the example below?

# Load R package
library(lme4)

# Load data
data(sleepstudy)

# Estimate model
fit <- lmer(Reaction ~ Days + (Days | Subject), data=sleepstudy)

# Get model results
summary(fit)

# Get random effects with conditional variances
ranef(fit, condVar=TRUE)
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