An introduction to repeated measures

Hierarchical and Mixed Effects Models in R

Richard Erickson

Data Scientist

Repeated measures

• Follow same unit of study through time
• e.g., cohort of students, individuals
• More powerful because of individual-level variability observed

Paired t-test

• Special case of a t-test
• Example of change in test scores pre- and post-intervention
• Nice conceptual introduction to repeated measures

Paired t-test in R

t.test(x1, x2, paired = TRUE)

Repeated measures ANOVA

• Conceptual extension of paired t-test
• Tests if means are constant across time
• Example of change in student test-scores with >2 tests

Repeated measures in R

library(lmerTest)

anova(lmer(y ~ time + (1 | individual))

Extension to lmer and glmer

• Repeated measures a special type of mixed-effect
• Can be applied to glmer as well
• Powerful additional use of tool
• Degrees of freedom is an open research method

Let's practice!

Hierarchical and Mixed Effects Models in R