# 18 Mixed Effects Models

## Overview

In this chapter, we’ll make a quick non-technical overview of fitting mixed effects models, focusing on the use of the function `lme()`

.

Objectives

Upon completion of this lesson, you should be able to:

- Recognize when a mixed effects model might be appropriate
- Be able to fit simple repeated measures models with
`lme()`

- Be able to fit simple split-plot models with
`lme()`

## Data and R Code Files

The R code file and data files for this lesson can be found on the Essential R - Notes on learning R page.

## 18.1 What is a Mixed Effects Model?

Here we’ll introduce the idea behind the mixed-effects model.

## 18.2 Repeated Measures Done the Wrong Way

Now we’ll begin a demonstration of the *wrong* way to analyze data that includes repeated measures, using the “machines” data included in the package `nlme`

.

## 18.3 Repeated Measures Using Mixed Effects I

Here we’ll demonstrate the use of `lme()`

to fit a mixed effects model - in this case a separate intercept for each worker.

## 18.4 Repeated Measures Using Mixed Effects II

Now we’ll try a different model, with the machine * worker interaction as a random effect. The substantial reducion in AIC and the more reduced patterning in the residuals suggests that this ia a superior model.

## 18.5 Split-plot Using Mixed Effects

Here we’ll revisit the split-plot experiment we analyzed using `aov()`

in **Lesson 13**, this time with `lme()`

.

## 18.6 Using `anova()`

to Compare Models

Here we’ll demonstrate the use of `anova()`

to compare two models fit by `lme()`

- note that the models must be nested and both must be fit by ML rather than REML.