# Chapter 1 Introduction

## 1.1 Overview

These materials focus on conceptual foundations of multilevel models (MLMs), specifiying them, and interpreting the results. Topics include multilevel data and approaches to dependence, specifying and interpreting fixed and random effects, model estimation, centering, repeated measures and longitudinal models, assumptions testing, and effect sizes in MLMs.

## 1.2 Goals

These materials are intended for students and instructors.

By the end of this course, students will be able to:

1. Estimate variance components and interpret the intraclass correlation coefficient;
2. Decide if and when a multilevel model is needed;
3. Specify and build multilevel models with covariates at level 1 and 2 with both cross-sectional and repeated measures designs;
4. Interpret regression coefficients and variance components from multilevel models;
5. Assess the assumptions of multilevel models;
6. Calculate effect sizes for multilevel models.

## 1.3 Prerequisites

Readers should be comfortable with multiple linear regression, including building regression models, interpreting regression output, and testing for and interpreting regression coefficients including interactions. The first module reviews multiple regression and can be used to gauge your preparedness for continuing. For those wishing to brush up their regression skills before working through these materials, we recommend UCLA’s Statistical Methods and Data Analytics resources and online seminars: https://stats.oarc.ucla.edu/other/mult-pkg/seminars/

The worked examples will be conducted using lme4 in R. The lme4 documentation provides details of the workings of lme4, for interested readers.

## 1.4 Materials

All materials are available for download in the appendix. The following are available for download:

• Data: the data used in each chapter
• R Script: an R script of the code used in each chapter
• Worksheet: a worksheet with questions that follows a similar structure to each chapter, but without answers provided

We recommend that people self-studying download the data and R script and following along with the code and output interpretations in each chapter. Instructors can benefit from downloading the data, code, and worksheets for use in a lab portion in their classes.