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Mixed Effects

Linear mixed-effects models

A linear mixed-effects model includes both fixed and random effects in modeling a response variable. This type of model can account for global and local trends in a data set by including the random effects of a clustering variable. You can fit a linear mixed-effects model using fitlme if your data is in a table. Alternatively, if your model is not easily described using a formula, you can create matrices to define the fixed and random effects, and then fit the model using fitlmematrix.

Functions

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Create `LinearMixedModel` Object

`fitlme`	Fit linear mixed-effects model
`fitlmematrix`	Fit linear mixed-effects model

Estimate Responses and Effects

`predict`	Predict response of linear mixed-effects model
`random`	Generate random responses from fitted linear mixed-effects model
`fixedEffects`	Estimates of fixed effects and related statistics
`randomEffects`	Estimates of random effects and related statistics
`fitted`	Fitted responses from a linear mixed-effects model

Evaluate Linear Mixed-Effects Model

`anova`	Analysis of variance for linear mixed-effects model
`coefCI`	Confidence intervals for coefficients of linear mixed-effects model
`coefTest`	Hypothesis test on fixed and random effects of linear mixed-effects model
`compare`	Compare linear mixed-effects models
`designMatrix`	Fixed- and random-effects design matrices
`covarianceParameters`	Extract covariance parameters of linear mixed-effects model
`partialDependence`	Compute partial dependence (Since R2020b)
`residuals`	Residuals of fitted linear mixed-effects model
`response`	Response vector of the linear mixed-effects model

Visualize Linear Mixed-Effects Model and Summary Statistics

`plotPartialDependence`	Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots
`plotResiduals`	Plot residuals of linear mixed-effects model

Objects

LinearMixedModel Linear mixed-effects model

Topics

Prepare Data for Linear Mixed-Effects Models
Store data in the correct form for fitting a linear mixed-effects model.
Relationship Between Formula and Design Matrices
Understand the relationship between a model formula and the design matrices in linear mixed-effects models.
Linear Mixed-Effects Model Workflow
This example shows how to fit and analyze a linear mixed-effects model (LME).
Fit Mixed-Effects Spline Regression
This example shows how to fit a mixed-effects linear spline model.
Linear Mixed-Effects Models
Linear mixed-effects models are extensions of linear regression models for data that are collected and summarized in groups.
Estimating Parameters in Linear Mixed-Effects Models
The two most commonly used approaches to parameter estimation in linear mixed-effects models are maximum likelihood and restricted maximum likelihood methods.
Wilkinson Notation
Wilkinson notation provides a way to describe regression and repeated measures models without specifying coefficient values.