Chapter 4 Random and Mixed Effect Models

If your experiment needs statistics, you ought to have done a better experiment. — Ernest Rutherford

4.1 Nested design

• Motivations for a nested design
• Nested design with fixed factors
  • Sampling scheme
  • Hypothesis testing
  • Causal interpretation
• Nested design with random factors
• Nested design with mixed factors
  • Repeated measures design

4.2 Random effects model

• One-way ANOVA model with random effects
• Estimation
  • Decomposition of variances
• Hypothesis testing and confidence intervals
• Mixed effects model
• Unbalanced mixed and random effect models
  • REML (see among others, this note)

For more discussion, see Chapter 7 here.

4.3 Learning Objectives

• Students are able to write down the two-way ANOVA model with random effects.
• Students can properly decide whether to model a factor using fixed or random effects.
• Students recognize the key assumptions associated with the random effects model.
• Students can implement the aforemened tasks in R.
• Students can explore extension of random effect model on the Internet.