Models

Regression models

Regression estimates how an outcome changes with predictors.

A simple treatment effect — one predictor (condition) recovers the contrast Estimation describes.
Adding predictors — control for covariates or test multiple factors at once.
Interactions — when the effect of one factor depends on another (e.g., a manipulation works for one group but not another).
When does linear regression work? When relationships are approximately linear and errors well-behaved; otherwise transform or use a different model.

Generalized linear models (GLM)

When the outcome isn't continuous (binary choice, count, reaction-time-in-seconds), a GLM pairs linear prediction with an appropriate link and error family—logistic regression for yes/no, Poisson for counts.

Linear mixed-effects models (LMM)

Experiments cluster data: participants do many trials; items are seen by many participants.

Modeling random variation in clusters — random intercepts let each participant or item deviate from the mean.
Random slopes — let the effect size vary by participant/item. Powerful but harder to estimate; requires enough data per cluster.

How do you use models to analyze data?

When to include covariates — adjust for variables correlated with the outcome to reduce noise and bias, but don't fish for the specification that "works."
Robustness checks and the multiverse — show the conclusion holds across reasonable model choices. A "multiverse analysis" displays results across many defensible analytic paths, exposing how fragile a finding is.

Key terms

Fixed effect — a population-level parameter you estimate.
Random effect — variation across clusters (participants/items) treated as a distribution.
Multiverse analysis — reporting results across many reasonable analytic specifications.