Partial Least Squares Path Modeling Hengky Latan • Richard Noonan Editors Partial Least Squares Path Modeling Basic Concepts, Methodological Issues and Applications 123 Editors Hengky Latan Richard Noonan Department of Accounting Institute of International Education STIE Bank BPD Jateng and Petra Stockholm University Christian University Stockholm, Sweden Semarang-Surabaya, Indonesia ISBN 978-3-319-64068-6 ISBN 978-3-319-64069-3 (eBook) DOI 10.1007/978-3-319-64069-3 Library of Congress Control Number: 2017955377 Mathematics Subject Classification (2010): 62H20, 62H25, 62H12, 62F12, 62F03, 62F40, 65C05, 62H30 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland We dedicate this book to the fond memory of Herman O. A. Wold (25 December 1908– 16 February 1992), whose energy and creativity were an inspiration to all of us who had the good fortune to work with him. His pioneering work lives on and forms the base on which this book rests. Foreword I am immensely honored to have been asked to provide a foreword to this volume. An aspiring high-school mathematics teacher, young Karl Jöreskog, is lured into graduate study by celebrated econometrician Herman Wold. In the course of his studies, Jöreskog turns from the mathematics that he loves to statistics. Under Wold’s direction and encouragement, Jöreskog derives a maximum likelihood (ML) approach to estimating confirmatory factor analysis models which yields an inferential 2 distributed test statistic. Wold, a long-time advocate for least squares estimation methods, invents partial least squares (PLS) path modeling as a tool for approximating Jöreskog’s results but without the heavy distributional, computing power and prior knowledge demands of ML estimation. From this origin story, some have concluded that PLS path modeling is inherently a lesser method, and now an anachronism which serves little purpose, given the cheap availability of computing resources and the development of factor analysis estimation methods that are increasingly robust to nonnormal distributions and that address an ever- expanding assortment of complex research situations. Simulation research, using populations defined by factor models, reaches the unsurprising conclusion that the factor-based approach to SEM performed better than composite-based approaches such as PLS path modeling. This general theme, describing factor-based methods as “the real thing” and belittling composite-based alternatives as cheap imitations, runs through a great deal of the methods literature across the social sciences, and no wonder. In the earliest years of the twentieth century, the pioneering works of Charles Spearman had already bound together psychological measurement and factor analysis, making any other analytical method seem deficient. But this identification of “factor analysis” with “measurement” itself hinges on an anachronistic (and now somewhat quaint) philosophy of science. Spearman the empiricist argued that the common factor he extracted or fabricated from data, a common factor which Spearman labeled “gen- eral intelligence” or g, was in fact general intelligence itself. Intelligence, indeed, could be nothing else except the common factor resulting from this analysis of error- prone data, because the realm of legitimate scientific inquiry begins and ends with observable data. In philosophy of science circles, empiricism has long ago broadly vii viii Foreword given way to scientific realism, a perspective that takes unobservable conceptual variables—attributes like intelligence, customer satisfaction, or attitude—to be real entities with their own existence independent of data and statistical models. From a realist perspective, both the common factors in factor-based models and the composites in PLS path modeling are only proxies or empirical substitutes for the actual psychological attributes. Making inferences about the actual psychological attribute on the basis of a statistical model then requires that the researcher establish the validity of each proxy. The mathematics of the indeterminacy of factors and the unreliability of composites give reason enough for researchers to be cautious about the quality of both kinds of proxies. I think it is very important to have alternatives. When there is only one way to do something, there is a tendency to just accept the limitations that come with that single path. It can be hard to even imagine a better way, even if the one available approach is actually rather weak. If there are alternatives, on the other hand, it can be easier to recognize the shortcoming of any one method by comparing it with the others. Moreover, if there are alternatives, then it may be possible to use the strengths of one method to offset or bypass the weaknesses of another method. For example, it was difficult to obtain ML estimates of the “interbattery factor model” until Michael Browne showed how to obtain them by transforming parameter estimates from canonical correlation, a composite-based method. More recently, Theo Dijkstra and colleagues have obtained consistent estimates of factor model parameters as a transformation of PLS path modeling parameter estimates, suggesting the possibility of combining factor-based and composite-based approaches within the same structural equation model. We need to bring the composite-based approaches to SEM and the factor-based approach into the kind of relationship that can enable a true cross-pollination. Viewed as peers—mathematically different tools for accomplishing the same very challenging task of learning about the behavior of unobserved conceptual variables—the methods will be able to borrow from one another and to be inspired by one another, just as Wold and Jöreskog inspired each other. In order to be a genuine participant in such a relationship, the PLS path modeling methodology must continue to grow, evolve, and mature. If PLS path modeling seems either moribund or stuck in the past, outside researchers will not expect to find new insights there and may not bother to look. Unfortunately, PLS path modeling endured a period of years which saw very little growth, even as the factor-based approach to SEM raced ahead. So it is doubly important that new research and advanced applications in this area be strongly encouraged. These days, as it happens, it is hard to keep up with the pace of developments in PLS path modeling. Many exceptional packages are available as either commercial or open-source software, enabling researchers to learn by doing and to actively confront the limits of the known. And as researchers have become more familiar with these tools, they have been driven by need, by curiosity, and by competition to tackle new challenges. For example, one of the major challenges for SEM is dealing with heterogeneity—differentparameter values for different respondents—in all its many Foreword ix aspects. Researchers encounter heterogeneity as differences between known groups, as interaction or moderation effects, as the result of clustering of observations, and as mixtures of distributions within the same population. One by one, methods pioneers have stepped up and provided PLS path modeling procedures to address these issues, while still seeking to minimize distributional assumptions and thus honor the original spirit of Herman Wold’s method. Not every problem has a statistical solution. At the birth of PLS path modeling, one of the virtues claimed for PLS path modeling was its small sample size capabilities. In contrast to the large sample sizes required for maximum likelihood factor analysis, it was noted that PLS path modeling could yield parameter estimates and (jackknife or bootstrap) standard errors even when sample size was very small. This confidence in the small-sample performance of PLS path modeling drew upon a misunderstanding. Yes, PLS path modeling algorithms will function—will yield results and not simply quit or crash—even when sample size is quite small, but the quality and usefulness of such results will be poor. Simulation research, drawing data from correctly specified composite-based populations, has shown that researchers with