Introduction to Mixed Models (Live) – August 2024

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