Generalized Linear Mixed Models

TL;DR

• Regression models that include both individual-level (fixed) and group-level (random) factors.
• Let researchers account for influences at different levels (e.g., person and group) on an outcome.
• Provide a more nuanced understanding of predictor–outcome relationships when both types of factors are present.

Definition

Generalized linear mixed models (GLMMs) are a type of regression analysis that allows for the modeling of both fixed and random effects.

Explanation

GLMMs combine fixed effects, which represent individual-level factors, with random effects, which represent group-level factors. Including both types of effects lets researchers account for the potential influence of individual and group characteristics on the outcome of interest, producing a more nuanced understanding of the relationship between predictors and the outcome.

Examples

Income and happiness

A study of the relationship between income and happiness could include individual-level factors such as age and education as fixed effects, and group-level factors such as state and region as random effects. This setup accounts for potential influences of both individual and group-level factors on happiness.

Medical treatment and blood pressure

A study examining the effect of a medical treatment on blood pressure could include individual-level factors such as age and gender as fixed effects, and group-level factors such as clinic location and doctor as random effects. This setup accounts for potential influences of both individual and group-level factors on blood pressure.

Use cases

• Useful in many research settings where both individual-level and group-level factors may impact an outcome.
• Applied when researchers want to include and account for both fixed and random effects in analysis to obtain more accurate and comprehensive results.

Related terms

• Fixed effects
• Random effects