Mixed Models: Introduction

Mixed Models are regression models which contain random and fixed effects. These models are widely used by researchers to account for sources of variation in their studies.

The examples in this article series are done using the R language. Just enough R is covered to allow one to follow the examples and to do the exercises. The R results from the exercises contains similar information to the results produced by other statistical software languages, such as Stata and SAS. Thus, this article series will be useful to anyone who is learning how to include mixed models in their research.

About This Series

The goal of the Mixed Model article series is to provide you with an introduction to the theory of mixed models. The focus of the included theory is to provide an understanding of how mixed models differ from fixed effect models and how these differences change diagnostics and inferences.

The Mixed Models article series includes the following articles:

  1. Introduction
  2. Models
  3. Testing Significance of Effects
  4. Diagnostics and Other Inferences
  5. Multiple Random Parameters

The Models article provides a brief overview of mixed models theory and the terminology which will be used throughout this article series. The Models article also explains how random model parameters are specified and how to construct mixed models using lmer() and glmer() from the lme4 package in R.

The Testing Significance of Effects article provides an overview of testing significance in mixed models. Mixed models in many cases do not have asymptotic theory to rely on for tests of significance. This article provides some background on a few of the common tests which are available to test for significance.

The Diagnostics and Other Inferences article describes some of the available diagnostic tools for mixed models. Some additional inferences which can be made from mixed models are also covered.

The Multiple Random Parameters article cover models which contain both random intercepts and random slopes. Nested and crossed effects are also covered.

Materials for these articles

The instruction for loading the data sets and R packages needed to work the examples and exercises in these articles is included in the Models article.

Most of the models in the examples are constructed using the lme4 package in R. If you have any difficulties following the R code in the examples, the R For Researchers article series provides an introduction to R.

Next: Models

Last Revised: 9/28/2016