Multilevel Modeling Using Mplus

Holmes Finch, Jocelyn Bolin

• Publisher: Chapman and Hall/CRC
• Year: 2017
• Print ISBN:
  9780367833299
• eBook ISBN:
  9781351678407
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

This book is designed primarily for upper level undergraduate and graduate level students taking a course in multilevel modelling and/or statistical modelling with a large multilevel modelling component. The focus is on presenting the theory and practice of major multilevel modelling techniques in a variety of contexts, using Mplus as the software tool, and demonstrating the various functions available for these analyses in Mplus, which is widely used by researchers in various fields, including most of the social sciences. In particular, Mplus offers users a wide array of tools for latent variable modelling, including for multilevel data.

1

Linear Models

Statistical models provide powerful tools to researchers in a wide array of disciplines. Such models allow for the examination of relationships among multiple variables, which in turn can lead to a better understanding of the world. For example, sociologists use linear regression to gain insights into how factors such as ethnicity, gender, and level of education are related to an individual’s income. Biologists can use the same type of model to understand the interplay between sunlight, rainfall, industrial runoff, and biodiversity in a rain forest. In addition, using linear regression, educational researchers can develop powerful tools for understanding the role that different instructional strategies have on student achievement. Apart from providing a path by which various phenomena can be better understood, statistical models can also be used as predictive tools. For example, econometricians might develop models to predict labor market participation given a set of economic inputs, whereas higher education administrators may use similar types of models to predict grade point average (GPA) for prospective incoming freshmen in order to identify those who might need academic assistance during their first year of college.

As can be seen from these few examples, statistical modeling is very important across a wide range of fields, providing researchers with tools for both explanation and prediction. Certainly, the most popular of such models over the past 100 years of statistical practice has been the general linear model (GLM). The GLM links a dependent, or outcome, variable to one or more independent variables and can take the form of such popular tools as analysis of variance (ANOVA) and regression. Given its popularity and utility, and the fact that it serves as the foundation for many other models, including the multilevel models featured in this book, we will start with a brief review of the linear model, particularly focusing on regression. This chapter will include a short technical discussion of linear regression models, followed by a description of how they can be estimated using Mplus. The technical aspects of this discussion are purposefully not highly detailed, as we focus on the model from a conceptual perspective. However, sufficient detail is presented so that the reader having only limited familiarity with the linear regression model will be provided with a basis for moving forward to multilevel models, and so that particular features of these more complex models that are shared with the linear model can be explicated. Readers particularly familiar with linear regression and with using R to conduct such analyses may elect to skip this chapter with no loss of understanding in future chapters.

Simple Linear Regression

As noted previously, the GLM framework serves as the basis for the multilevel models that we describe in subsequent chapters. Thus, in order to provide the foundation for the rest of the book, we will focus in this chapter on the linear regression model, although its form and function can easily be translated to ANOVA as well. The simple linear regression model in population form is

$y_i={\text{β}}_0+{\text{β}}_1{x}_i+{\epsilon }_i$

(1.1)

where:

y_i is the...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Authors
• 1. Linear Models
• 2. An Introduction to Multilevel Data Structure
• 3. Fitting Two-Level Models in Mplus
• 4. Additional Issues in Fitting Two-Level Models
• 5. Fitting Three-Level Models in Mplus
• 6. Longitudinal Data Analysis Using Multilevel Models
• 7. Brief Introduction to Generalized Linear Models
• 8. Multilevel Generalized Linear Models (MGLMs) and Multilevel Survival Models
• 9. Brief Review of Latent Variable Modeling in Mplus
• 10. Multilevel Latent Variable Models in Mplus
• 11. Bayesian Multilevel Modeling
• Appendix: A Brief Introduction to Mplus
• References
• Index