Confirmatory factor analysis for applied research

1 Confirmatory factor analysis for applied ResearchMethodology in the Social SciencesDavid A. Kenny, Series EditorSPECTRAL analysis OF TIME-SERIES DATAR ebecca M. WarnerA PRIMER ON REGRESSION ARTIFACTSD onald T. Campbell and David A. KennyREGRESSION analysis FOR CATEGORICAL MODERATORSH erman AguinisHOW TO CONDUCT BEHAVIORAL research OVER THE INTERNET:A BEGINNER S GUIDE TO HTML AND CGI/PERLR. Chris FraleyPRINCIPLES AND PRACTICE OF STRUCTURAL EQUATION MODELINGS econd EditionRex B. KlineCONFIRMATORY factor analysis FOR applied RESEARCHT imothy A. BrownConfirmatory FactorAnalysis forApplied ResearchTimothy A. BrownSERIES EDITOR S NOTE byDavid A. KennyTHE GUILFORD PRESSNew York London 2006 The Guilford PressA Division of Guilford Publications, Spring Street, New York, NY rights reservedNo part of this book may be reproduced, translated, stored in aretrieval system, or transmitted, in any form or by any means,electronic, mechanical, photocopying, microfilming, recording,or otherwise, without written permission from the in the United States of AmericaThis book is printed on acid-free digit is print number:987654321 Library of Congress Cataloging-in-Publication DataBrown, Timothy factor analysis for applied research /Timothy A.

2 Cm. (Methodology in the social sciences)Includes bibliographical references and : 978-1-59385-274-0 (pbk.)ISBN-10: 1-59385-274-6 (pbk.)ISBN-13: 978-1-59385-275-7 (hardcover)ISBN-10: 1-59385-275-4 (hardcover)1. factor analysis . I. Title. II. 5195354 dc222006001103 For my father, Kaye,and Nick and GregAbout the AuthorTimothy A. Brown, PsyD,is a professor in the Department of Psychologyat Boston University, and Director of research at Boston University sCenter for Anxiety and Related Disorders. He has published extensively inthe areas of the classification of anxiety and mood disorders, vulnerabilityto emotional disorders, psychometrics, and methodological advances insocial sciences research . In addition to conducting his own grant-sup-ported research , Dr.

3 Brown serves as a statistical investigator or consultanton numerous federally funded research projects. He has been on the edito-rial boards of several scientific journals, including recent appointments asAssociate Editor of theJournal of Abnormal Editor s NoteSeries Editor s NoteSeries Editor s NoteFor some reason, the topic of Confirmatory factor analysis (CFA) has notreceived the attention that it deserves. Two closely related topics, explor-atory factor analysis (EFA) and structural equation modeling (SEM), havedozens of textbooks written about them. Book-length treatments of CFAare rare and that is what makes this book might think that there are so few books on CFA because it is sorarely used. However, this is not the case. Very often, those who conductEFA follow up the analysis with CFA.

4 Additionally, SEM always involves ameasurement model and very often the best way to test that model is withCFA. Poor-fitting structural equation models are almost always due to CFAproblems. Thus, to be proficient at SEM, the analyst must know CFA. Thisbook very nicely explains the links between CFA and these two differentmethods, in particular the natural process of beginning with EFA, proceed-ing to CFA, and then think it is ironic that SEM has received so much more attention thanCFA, because the social and behavioral sciences have learned much morefrom CFA than from SEM. In particular, through CFA we are able tounderstand the construct validity of attitudes and personality, and CFAprovides important information about the relative stability of individualdifferences throughout the most books on factor analysis , this one spares us all the matri-ces with their transposes, Kronecker products, and inverses.

5 Certainlymatrix algebra is critical in the theory, proofs, and estimation of CFA, butfor day-to-day practitioners, it just gets in the way. This is not to say thatthe author, Timothy A. Brown, doesn t discuss technical issues where nec-essary. The text is complicated where example of one such complicated topic is the multitrait multimethod matrix, first proposed by Donald Campbell and DonaldFiske. I am pleased that Brown decided to devote a full chapter to thetopic. Interestingly, a generation of researchers tried to find EFA modelsfor the matrix and never developed a completely satisfactory generation of researchers worked on several CFA models for thematrix, and Brown very nicely summarizes the models they useful feature of this book is that it contains an entire chapterdevoted to issues of statistical power and sample sizes.

6 Investigators needto make decisions, costly both in terms of time and money, about samplesize. Very often they make those decisions using rather arbitrary proce-dures. The book outlines a formal and practical approach to that breadth of applications, the book provides examples from severaldifferent areas of the social and behavioral sciences. It also illustrates theanalyses using several different software programs. Preferences for com-puter programs change as fast as preferences do for hair styles; thus, it isan advantage that the book is not tied to one computer program. Mostreaders would benefit from analyzing data of their own as they read validity, instrument development and validation, reductionof the number of variables, and sources of bias in measurement, to namejust a few, are subjects supported by high-quality CFA.

7 Almost all researchdata include many variables; therefore, Brown s detailed and careful treat-ment of this important topic will be of benefit in almost all research situa-tions. A gap in the field of multivariate data analysis that has existed for fartoo long has finally been filled. Researchers now have a readable, detailed,and practical discussion of KENNYxSeries Editor s NotePrefacePrefacePrefaceThis book was written for the simple reason that no other book of its kindhad been published before. Although many books on structural equationmodeling (SEM) exist, this is the first book devoted solely to the topic ofconfirmatory factor analysis (CFA). Accordingly, for the first time, manyimportant topics are brought under one cover for example, the similari-ties/differences between exploratory factor analysis (EFA) and CFA, theuse of maximum likelihood EFA procedures as a precursor to CFA, diag-nosing and rectifying the various sources for the ill-fit of a measurementmodel, analysis of mean structures, modeling with multiple groups ( ,MIMIC), CFA scale reliability evaluation, formative indicator models, andhigher-order factor analysis .

8 After covering the fundamentals and varioustypes of CFA in the earlier chapters, in later chapters I address issues likeCFA with non-normal or categorical indicators, handling missing data,and power analysis /sample size determination, which are germane to SEMmodels of any type. Although it is equally important to CFA practice,another reason I included this material was because of the lack of adequatecoverage in preexisting SEM sourcebooks. Thus, I hope the book will serveas a useful guide to researchers working with a latent variable model of anytype. The book is not tied to specific latent variable software packages, andin fact the five most popular programs are featured throughout (Amos,EQS, LISREL, Mplus, SAS/CALIS). However, readers will note that thisbook is the first to provide an extensive treatment of Mplus, a programthat is becoming increasingly popular with applied researchers for its easeof use with complex models and data ( , categorical outcomes, categori-cal latent variables, multilevel data).

9 The target readership of this book is applied researchers and graduatestudents working within any domain of social and behavioral sciencesxi( , psychology, education, political science, management/marketing,sociology, public health). In the classroom, this book can serve as a pri-mary or supplemental text in courses on advanced statistics, factor analy-sis, SEM, or psychometrics/scale development. For applied researchers,this book can be used either as a resource for learning the procedures ofCFA or, for more experienced readers, as a reference guide for dealing withcomplex CFA models or data issues. What each chapter specifically coversis described in Chapter 1. The first five chapters deal with the fundamen-tals of CFA: what the researcher needs to know to conduct a CFA of anytype.

10 Thus, especially for readers new to CFA, it is recommended that thefirst five chapters be read in order, as this material is the foundation for theremainder of the book. Chapters 6 through 10 address specific types ofCFA and other issues such as dealing with missing or categorical data andpower analysis . The reading order of the second group of chapters is lessimportant than for the in quantitative methodology are often slow to be picked upby applied researchers because such methods are usually disseminated in amanner inaccessible to many end users ( , formula-driven articles inmathematical/statistical journals). This is unfortunate, because multi-variate statistics can be readily and properly employed by any researcherprovided that the test s assumptions, steps, common pitfalls, and so on, arelaid out clearly.