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Mixed Effects Models Exercises in R: 15 Practice Problems

Fifteen practice problems on mixed-effects models in R: lme4, random intercepts and slopes, nested groups, REML, model comparison. Hidden solutions.

By Selva Prabhakaran  ·  Published May 11, 2026  ·  Last updated May 11, 2026
RRun this once before any exercise
library(lme4) library(lmerTest) library(dplyr) library(performance)

  

  





Exercise 1: Random intercept



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

    
data(sleepstudy)
lmer(Reaction ~ Days + (1 | Subject), data = sleepstudy)

    

      
      
    

    

  

  








Exercise 2: Random slope



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
data(sleepstudy)
lmer(Reaction ~ Days + (Days | Subject), data = sleepstudy)

    

      
      
    

    

  

  








Exercise 3: Uncorrelated random slope



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
data(sleepstudy)
lmer(Reaction ~ Days + (Days || Subject), data = sleepstudy)

    

      
      
    

    

  

  








Exercise 4: Summary with p-values



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

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

    

      
      
    

    

  

  








Exercise 5: Random effects estimates



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

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

    

      
      
    

    

  

  








Exercise 6: Fixed effects



Difficulty: Beginner.



Show solution



  

    
RInteractive R

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

    

      
      
    

    

  

  








Exercise 7: Confidence intervals via profile



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
data(sleepstudy)
fit <- lmer(Reaction ~ Days + (1 | Subject), data = sleepstudy)
confint(fit)

    

      
      
    

    

  

  








Exercise 8: ICC (intraclass correlation)



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
data(sleepstudy)
fit <- lmer(Reaction ~ 1 + (1 | Subject), data = sleepstudy)
performance::icc(fit)

    

      
      
    

    

  

  








Exercise 9: Nested random effect



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
df <- tibble(school = rep(1:3, each = 20), student = rep(1:10, 6),
             score = rnorm(60))
lmer(score ~ 1 + (1 | school/student), data = df)

    

      
      
    

    

  

  








Exercise 10: Crossed random effects



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
df <- tibble(rater = sample(1:5, 100, replace = TRUE),
             subject = sample(1:20, 100, replace = TRUE),
             y = rnorm(100))
lmer(y ~ 1 + (1 | rater) + (1 | subject), data = df)

    

      
      
    

    

  

  








Exercise 11: Compare nested models



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
data(sleepstudy)
f1 <- lmer(Reaction ~ Days + (1 | Subject), data = sleepstudy, REML = FALSE)
f2 <- lmer(Reaction ~ Days + (Days | Subject), data = sleepstudy, REML = FALSE)
anova(f1, f2)

    

      
      
    

    

  

  








Exercise 12: glmer (logistic mixed)



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
df <- tibble(group = rep(1:5, each = 20),
             x = rnorm(100),
             y = rbinom(100, 1, 0.3))
glmer(y ~ x + (1 | group), data = df, family = binomial)

    

      
      
    

    

  

  








Exercise 13: Predict random effects



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
data(sleepstudy)
fit <- lmer(Reaction ~ Days + (Days | Subject), data = sleepstudy)
predict(fit, newdata = sleepstudy[1:5, ])

    

      
      
    

    

  

  








Exercise 14: Marginal vs conditional predictions



Difficulty: Advanced.



Show solution



  

    
RInteractive R

    
data(sleepstudy)
fit <- lmer(Reaction ~ Days + (Days | Subject), data = sleepstudy)
# Marginal (population): re.form = NA
predict(fit, newdata = sleepstudy[1:3, ], re.form = NA)

    

      
      
    

    

  

  








Exercise 15: Diagnostic plot



Difficulty: Intermediate.



Show solution



  

    
RInteractive R

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

    

      
      
    

    

  

  








What to do next



    


  • Linear-Regression-Exercises (shipped), fixed-effects baseline.
    • 


  • Bayesian-Statistics-Exercises (shipped), Bayesian alternative.
    • 






          
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© 2016-2026 Selva Prabhakaran.
          This work is licensed under the Creative Commons License.
        

        

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