Introduction to Mixed Models (Self-Guided)

This course is best taken on Canvas, where you can post discussion questions, take quizzes, and practice in R. The first lesson contains instructions on accessing canvas and the passkey for doing so.

Mixed Models Introduction

• The assumption of independence and "duplicating" your dataset
• Consequences of violating independence
• HLM vs mixed models, vs multilevel models
• What mixed models are doing geometrically
• Fixed vs. random effects
• Visual representation of
  • random slope/intercept models
  • random slopes models
  • random intercepts models
• Three ways to tell if an effect is fixed or random
  • They must vary within cluster
  • Use theory to guide you
  • Use model comparisons
• Three ways to identify what your cluster variable is

Your First Mixed Model

• lme4
• Going from wide to long format
• Four elements of mixed model syntax
• Syntax for a simple model
• Every time you have a random effect you also have to have a fixed effect
• What "1" means in R syntax
• Syntax for
  • A model with no random slopes
  • A model with no predictors (and what it means)
  • A model with a fixed slope
• Interpreting fixed effects as regression coefficients
• Syntax for visualizing mixed models

Visualizing Mixed Models

• Why IDs should be factors
• What happens when we plot all IDs as colors/lines/symbols
  • (you can see how parallel the slopes are, but you can’t see how well the model fits)
• Limitation with viewing the cluster variable in panels
• Why we should not use the flexplot function for mixed models
• What should we use instead?
• How to increase the number of clusters sampled
• How to customize the plot with visualize
• Pros/cons of plotting the cluster as line/color/symbol versus panels
• Why we should plot multiple plots

Mixed Model Notation

• Subscript notation for regression
• The i index
• The j index
• Notation for fixed/random intercepts and fixed/random slopes
• Level 2 models
• The meaning of gammas
• The meaning of the "U" parameter
• What the first versus second subscript represent for parameters
• Be able to match R code to notation to images

• Three ways we evaluate models
• How to interpret fixed effects
• How to interpret random effects
• How to interpret residuals in mixed models
• Know what variance explained means
• Why variance explained is more complicated for mixed models
• Know what ICC tells you
• Know what the design effect tells you
• Rule of thumb for design effects
• Why R squared is more complicated with mixed models
• Two methods of comparing models
• How to perform model comparisons in R

• What is an optimization algorithm
• What is a loss function
• Starting parameters
• What is a convergence failure?
• Why talk about convergence?
• Two types of warnings
• Reasons we have singularity or convergence failures
• How to correct singularity or convergence failures