Repeated measures ANOVA

In the previous exercise, you saw how a paired t-test is more powerful than a regular t-test. During this exercise, you will see how statistical methods generalize. First, you will see how a paired t-test is a special case of a repeated measures ANOVA. In the process, you will see how a repeated measures ANOVA is a special case of a mixed-effects model by using lmer() in R.

The first part of this exercise will consist of transforming the simulated data from two vectors into a data.frame(). The second part will have you examine the model results to see how they are different. The third part will have you examine the outputs of the models and compare the results.

This exercise is part of the course

Hierarchical and Mixed Effects Models in R

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Create the data.frame, using the variables from the previous exercise. 
# y is the joined vectors before and after.
# trial is the repeated names before and after, each one repeated n_ind
# ind is the letter of the individual, repeated 2 times (because there were two observations)
dat <- data.frame(y = c(___, ___), 
                  trial = rep(c("before", "after"), each = ___),
                  ind = rep(letters[1:n_ind], times = ___))

Edit and Run Code

This exercise is part of the course

Hierarchical and Mixed Effects Models in R

AdvancedSkill Level

4.6+

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The first chapter provides an example of when to use a mixed-effect and also describes the parts of a regression. The chapter also examines a student test-score dataset with a nested structure to demonstrate mixed-effects.

Exercise 1: What is a hierarchical model?Exercise 2: Examples of hierarchical datasets Exercise 3: Multi-level student data Exercise 4: Exploring multiple-levels: Classrooms and schools Exercise 5: Parts of a regression Exercise 6: Intercepts Exercise 7: Slopes and multiple regression Exercise 8: Random-effects in regressions with school data Exercise 9: Random-effect intercepts Exercise 10: Random-effect slopes Exercise 11: Building the school model Exercise 12: Interpreting the school model

This chapter providers an introduction to linear mixed-effects models. It covers different types of random-effects, describes how to understand the results for linear mixed-effects models, and goes over different methods for statistical inference with mixed-effects models using crime data from Maryland.

Exercise 1: Linear mixed effect model- Birth rates data Exercise 2: Building a lmer model with random effects Exercise 3: Including a fixed effect Exercise 4: Random-effect slopes Exercise 5: Uncorrelated random-effect slope Exercise 6: Fixed- and random-effect predictor Exercise 7: Understanding and reporting the outputs of a lmer Exercise 8: Comparing print and summary output Exercise 9: Extracting coefficients Exercise 10: Displaying the results from a lmer model Exercise 11: Statistical inference with Maryland crime data Exercise 12: Visualizing Maryland crime data Exercise 13: Rescaling slopes Exercise 14: Null hypothesis testing Exercise 15: Controversies around P-values Exercise 16: Model comparison with ANOVA

This chapter extends linear mixed-effects models to include non-normal error terms using generalized linear mixed-effects models. By altering the model to include a non-normal error term, you are able to model more kinds of data with non-linear responses. After reviewing generalized linear models, the chapter examines binomial data and count data in the context of mixed-effects models.

Exercise 1: Crash course on GLMs Exercise 2: Logistic regression Exercise 3: Poisson Regression Exercise 4: Plotting GLMs Exercise 5: Binomial data Exercise 6: Toxicology data Exercise 7: Marketing example Exercise 8: Calculating odds-ratios Exercise 9: Count data Exercise 10: Internet click-throughs Exercise 11: Chlamydia by age-group and county Exercise 12: Displaying chlamydia results

This chapter shows how repeated-measures analysis is a special case of mixed-effect modeling. The chapter begins by reviewing paired t-tests and repeated measures ANOVA. Next, the chapter uses a linear mixed-effect model to examine sleep study data. Lastly, the chapter uses a generalized linear mixed-effect model to examine hate crime data from New York state through time.

Exercise 1: An introduction to repeated measures Exercise 2: Paired t-test Exercise 3: Repeated measures ANOVA

Current Exercise

Exercise 4: Sleep study Exercise 5: Exploring the data Exercise 6: Building models Exercise 7: Comparing regressions and ANOVAs Exercise 8: Plotting results Exercise 9: Hate in NY state?Exercise 10: Exploring NY hate data Exercise 11: Building the model Exercise 12: Interpreting model results Exercise 13: Displaying the results Exercise 14: Hierarchical models in R review Exercise 15: Conclusion