Module mixed 

Mixed effects models for StatOxide

This module implements linear mixed models (LMM) and generalized linear mixed models (GLMM) for hierarchical or clustered data.

Model Specification

Linear Mixed Model: y = Xβ + Zb + ε where:

• y: response vector
• X: fixed effects design matrix
• β: fixed effects coefficients
• Z: random effects design matrix
• b: random effects coefficients ~ N(0, G)
• ε: residuals ~ N(0, R)

Generalized Linear Mixed Model extends LMM to non-Gaussian responses using link functions.

Estimation Methods

1. REML: Restricted Maximum Likelihood (preferred for variance components)
2. ML: Maximum Likelihood
3. PQL: Penalized Quasi-Likelihood (for GLMM)
4. Laplace Approximation: For non-Gaussian GLMM

Structs

GLMMBuilder

Generalized Linear Mixed Model builder

GLMMResults

Generalized Linear Mixed Model (GLMM) results

LMMResults

Linear Mixed Model (LMM) results

LinearMixedModelBuilder

Linear Mixed Model builder

RandomEffect

Random effects structure specification

Enums

EstimationMethod

Estimation method for mixed models

GLMMEstimationMethod

Estimation method for GLMM

RandomCovariance

Covariance structure for random effects