Multilevel Modeling Using R

W. Holmes Finch, Jocelyn E. Bolin, Ken Kelley

• Éditeur: Chapman and Hall/CRC
• Année: 2019
• ISBN:
  9781351062244
• Édition: 2
• Sujet: Mathématiques
• Sous-sujet: Probabilités et statistiques

Like its bestselling predecessor, Multilevel Modeling Using R, Second Edition provides the reader with a helpful guide to conducting multilevel data modeling using the R software environment.

After reviewing standard linear models, the authors present the basics of multilevel models and explain how to fit these models using R. They then show how to employ multilevel modeling with longitudinal data and demonstrate the valuable graphical options in R. The book also describes models for categorical dependent variables in both single level and multilevel data.

New in the Second Edition:

• 
  
  

• Features the use of lmer (instead of lme ) and including the most up to date approaches for obtaining confidence intervals for the model parameters.

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• Discusses measures of R2 (the squared multiple correlation coefficient) and overall model fit.

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• Adds a chapter on nonparametric and robust approaches to estimating multilevel models, including rank based, heavy tailed distributions, and the multilevel lasso.

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• Includes a new chapter on multivariate multilevel models.

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• Presents new sections on micro-macro models and multilevel generalized additive models.

This thoroughly updated revision gives the reader state-of-the-art tools to launch their own investigations in multilevel modeling and gain insight into their research.

About the Authors:

W. Holmes Finch

is the George and Frances Ball Distinguished Professor of Educational Psychology at Ball State University.

Jocelyn E. Bolin

is a Professor in the Department of Educational Psychology at Ball State University.

Ken Kelley

is the Edward F. Sorin Society Professor of IT, Analytics and Operations and the Associate Dean for Faculty and Research for the Mendoza College of Business at the University of Notre Dame.

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. And using linear regression, educational researchers can develop powerful tools for understanding the role that different instructional strategies have on student achievement. In addition to 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 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 last 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 review will include a short technical discussion of linear regression models, followed by a description of how they can be estimated using the R language and environment (R Development Core Team, 2012). 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 above, 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

$$y_i={\beta }_0+{\beta }_1{x}_i+{\epsilon }_i,$$

(1.1)

where y _i is the dependent variable for indiv...