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Multiple Regression and Beyond: An Introduction to Multiple Regression and Structural Equation Modeling PDF

605 Pages·2015·4.06 MB·English
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Multiple Regression and Beyond Multiple Regression and Beyond offers a conceptually oriented introduction to multiple regression (MR) analysis and structural equation modeling (SEM), along with analyses that fl ow naturally from those methods. By focusing on the concepts and purposes of MR and related methods, rather than the derivation and calculation of formulae, this book introduces material to students more clearly, and in a less threatening way. In addition to illuminating content necessary for coursework, the accessibility of this approach means students are more likely to be able to conduct research using MR or SEM—and more likely to use the methods wisely. • Covers both MR and SEM, while explaining their relevance to one another • Also includes path analysis, confirmatory factor analysis, and latent growth modeling • Figures and tables throughout provide examples and illustrate key concepts and techniques Timothy Z. Keith is Professor and Program Director of School Psychology at University of Texas, Austin. This page intentionally left blank Multiple Regression and Beyond An Introduction to Multiple Regression and Structural Equation Modeling 2nd Edition Timothy Z. Keith Second edition published 2015 by Routledge 711 Third Avenue, New York, NY 10017 and by Routledge 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business © 2015 Taylor & Francis The right of Timothy Z. Keith to be identified as author of this work has been asserted by him in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. First edition published by Pearson Education, Inc. 2006 Library of Congress Cataloging-in-Publication Data Library of Congress Control Number: 2014956124 ISBN: 978-1-138-81194-2 (hbk) ISBN: 978-1-138-81195-9 (pbk) ISBN: 978-1-315-74909-9 (ebk) Typeset in Minion by Apex CoVantage, LLC Contents Preface vii Acknowledgments xi Part I Multiple Regression 1 1 Introduction: Simple (Bivariate) Regression 3 2 Multiple Regression: Introduction 26 3 Multiple Regression: More Detail 44 4 Three and More Independent Variables and Related Issues 57 5 Three Types of Multiple Regression 77 6 Analysis of Categorical Variables 108 7 Categorical and Continuous Variables 129 8 Continuous Variables: Interactions and Curves 161 9 Multiple Regression: Summary, Assumptions, Diagnostics, Power, and Problems 182 10 Related Methods: Logistic Regression and Multilevel Modeling 213 Part II Beyond Multiple Regression: Structural Equation Modeling 241 11 Path Modeling: Structural Equation Modeling With Measured Variables 243 v vi (cid:129) CONTENTS 12 Path Analysis: Dangers and Assumptions 267 13 Analyzing Path Models Using SEM Programs 282 14 Error: The Scourge of Research 318 15 Confirmatory Factor Analysis I 332 16 Putting It All Together: Introduction to Latent Variable SEM 371 17 Latent Variable Models: More Advanced Topics 391 18 Latent Means in SEM 424 19 Confirmatory Factor Analysis II: Invariance and Latent Means 455 20 Latent Growth Models 493 21 Summary: Path Analysis, CFA, SEM, and Latent Growth Models 514 Appendices Appendix A: Data Files 537 Appendix B: Review of Basic Statistics Concepts 539 Appendix C: Partial and Semipartial Correlation 557 Appendix D: Symbols Used in This Book 565 Appendix E: Useful Formulae 567 References 569 Author Index 579 Subject Index 583 Preface Multiple Regression and Beyond is designed to provide a conceptually oriented introduction to multiple regression along with more complex methods that fl ow naturally from multiple regres- sion: path analysis, confi rmatory factor analysis, and structural equation modeling. Multiple regression (MR) and related methods have become indispensable tools for modern social science researchers. MR closely implements the general linear model and thus subsumes methods, such as analysis of variance (ANOVA), that have traditionally been more commonplace in psycho- logical and educational research. Regression is especially appropriate for the analysis of nonex- perimental research, and with the use of dummy variables and modern computer packages, it is often more appropriate or easier to use MR to analyze the results of complex quasi-experimental or even experimental research. Extensions of multiple regression—particularly structural equa- tion modeling (SEM)—partially obviate threats due to the unreliability of the variables used in research and allow the modeling of complex relations among variables. A quick perusal of the full range of social science journals demonstrates the wide applicability of the methods. Despite its importance, MR-based analyses are too often poorly conducted and poorly reported. I believe one reason for this incongruity is inconsistency between how material is presented and how most students best learn. Anyone who teaches (or has ever taken) courses in statistics and research methodology knows that many students, even those who may become gifted researchers, do not always gain conceptual understanding through numerical presentation. Although many who teach statistics understand the processes underlying a sequence of formulas and gain conceptual understanding through these formulas, many students do not. Instead, such students often need a thorough conceptual explanation to gain such understanding, after which a numeri- cal presentation may make more sense. Unfortunately, many multiple regression textbooks assume that students will understand multiple regression best by learning matrix algebra, wading through formulas, and focusing on details. At the same time, methods such as structural equation modeling (SEM) and confirma- tory factor analysis (CFA) are easily taught as extensions of multiple regression. If structured properly, multiple regression flows naturally into these more complex topics, with nearly complete carry-over of concepts. Path models (simple SEMs) illustrate and help deal with some of the problems of MR, CFA does the same for path analysis, and latent variable SEM combines all the previous topics into a powerful, flexible methodology. I have taught courses including these topics at four universities (the University of Iowa, Virginia Polytechnic Institute & State University, Alfred University, and the University of vii viii (cid:129) PREFACE Texas). These courses included faculty and students in architecture, engineering, educational psychology, educational research and statistics, kinesiology, management, political science, psychology, social work, and sociology, among others. This experience leads me to believe that it is possible to teach these methods by focusing on the concepts and purposes of MR and related methods, rather than the derivation and calculation of formulas (what my wife calls the “plug and chug” method of learning statistics). Students generally find such an approach clearer, more conceptual, and less threatening than other approaches. As a result of this conceptual approach, students become interested in conducting research using MR, CFA, or SEM and are more likely to use the methods wisely. THE ORIENTATION OF THIS BOOK My overriding bias in this book is that these complex methods can be presented and learned in a conceptual, yet rigorous, manner. I recognize that not all topics are covered in the depth or detail presented in other texts, but I will direct you to other sources for topics for which you may want additional detail. My style is also fairly informal; I’ve written this book as if I were teaching a class. Data I also believe that one learns these methods best by doing, and the more interesting and rel- evant that “doing,” the better. For this reason, there are numerous example analyses through- out this book that I encourage you to reproduce as you read. To make this task easier, the Web site that accompanies the book (www.tzkeith.com) includes the data in a form that can be used in common statistical analysis programs. Many of the examples are taken from actual research in the social sciences, and I’ve tried to sample from research from a variety of areas. In most cases simulated data are provided that mimic the actual data used in the research. You can reproduce the analyses of the original researchers and, perhaps, improve on them. And the data feast doesn’t end there! The Web site also includes data from a major federal data set: 1000 cases from the National Education Longitudinal Study (NELS) from the National Center for Education Statistics. NELS was a nationally representative sample of 8th-grade stu- dents first surveyed in 1988 and resurveyed in 10th and 12th grades and then twice after leav- ing high school. The students’ parents, teachers, and school administrators were also surveyed. The Web site includes student and parent data from the base year (8th grade) and student data from the first follow-up (10th grade). Don’t be led astray by the word Education in NELS; the students were asked an incredible variety of questions, from drug use to psychological well- being to plans for the future. Anyone with an interest in youth will find something interesting in these data. Appendix A includes more information about the data at www.tzkeith.com. Computer Analysis Finally, I fi rmly believe that any book on statistics or research methods should be closely related to statistical analysis software. Why plug and chug—plug numbers into formulas and chug out the answers on a calculator—when a statistical program can do the calculations more quickly and accurately with, for most people, no loss of understanding? Freed from the drudgery of hand calculations, you can then concentrate on asking and answering important research ques- tions, rather than on the intricacies of calculating statistics. This bias toward computer calcu- lations is especially important for the methods covered in this book, which quickly become unmanageable by hand. Use a statistical analysis program as you read this book; do the exam- ples with me and the problems at the end of the chapters, using that program. Which program? I use SPSS as my general statistical analysis program, and you can get the program for a reasonable price as a student in a university (approximately $100–$125 PREFACE (cid:129) ix per year for the “Grad Pack” as this is written). But you need not use SPSS; any of the com- mon packages will do (e.g., SAS or SYSTAT). The output in the text has a generic look to it, which should be easily translatable to any major statistical package output. In addition, the website (www.tzkeith.com) includes sample multiple regression and SEM output from vari- ous statistical packages. For the second half of the book, you will need access to a structural equation modeling program. Fortunately, student or tryout versions of many such programs are available online. Student pricing for the program used extensively in this book, Amos, is available, at this writ- ing, for approximately $50 per year as an SPSS add-on. Although programs (and pricing) change, one current limitation of Amos is that there is no Mac OS version of Amos. If you want to use Amos, you need to be able to run Windows. Amos is, in my opinion, the easiest SEM program to use (and it produces really nifty pictures). The other SEM program that I will frequently reference is Mplus. We’ll talk more about SEM in Part 2 of this book. The website for this text has many examples of SEM input and output using Amos and Mplus. Overview of the Book This book is divided into two parts. Part 1 focuses on multiple regression analysis. We begin by focusing on simple, bivariate regression and then expand that focus into multiple regres- sion with two, three, and four independent variables. We will concentrate on the analysis and interpretation of multiple regression as a way of answering interesting and important research questions. Along the way, we will also deal with the analytic details of multiple regression so that you understand what is going on when we do a multiple regression analysis. We will focus on three different types, or fl avors, of multiple regression that you will encoun- ter in the research literature, their strengths and weaknesses, and their proper interpretation. Our next step will be to add categorical independent variables to our multiple regression analyses, at which point the relation of multiple regression and ANOVA will become clearer. We will learn how to test for interactions and curves in the regression line and to apply these methods to interesting research questions. The penultimate chapter for Part 1 is a review chapter that summarizes and integrates what we have learned about multiple regression. Besides serving as a review for those who have gone through Part 1, it also serves as a useful introduction for those who are interested primarily in the material in Part 2. In addition, this chapter introduces several important topics not covered completely in previous chapters. The final chapter in Part 1 presents two related methods, logistic regression and multilevel modeling, in a conceptual fashion using what we have learned about multiple regression. Part 2 focuses on structural equation modeling—the “Beyond” portion of the book’s title. We begin by discussing path analysis, or structural equation modeling with measured variables. Simple path analyses are easily estimated via multiple regression analysis, and many of our questions about the proper use and interpretation of multiple regression will be answered with this heuristic aid. We will deal in some depth with the problem of valid versus invalid inferences of causality in these chapters. The problem of error (“the scourge of research”) serves as our jumping off place for the transition from path analysis to methods that incorporate latent variables (confirmatory factor analysis and latent variable structural equation modeling). Confirmatory factor analysis (CFA) approaches more closely the con- structs of primary interest in our research by separating measurement error from variation due to these constructs. Latent variable structural equation modeling (SEM) incorporates the advantages of path analysis with those of confirmatory factor analysis into a powerful and flexible analytic system that partially obviates many of the problems we discuss as the book progresses. As we progress to more advanced SEM topics we will learn how to test for

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