Structural Equation Modeling

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Book Review of Basics of Structural Equation Modeling, by Geoffrey M. Maruyama Anne Boomsma Published online: 19 Nov 2009.

To cite this article: Anne Boomsma (2000) Book Review of Basics of Structural Equation Modeling, by Geoffrey M. Maruyama, Structural Equation Modeling: A Multidisciplinary Journal, 7:1, 142-148, DOI: 10.1207/S15328007SEM0701_08 To link to this article: http://dx.doi.org/10.1207/S15328007SEM0701_08

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STRUCTURAL EQUATION MODELING, 7(1), 142–148 Copyright © 2000, Lawrence Erlbaum Associates, Inc.

BOOK REVIEW


Basics of Structural Equation Modeling. Geoffrey M. Maruyama. Thousand Oaks, CA: Sage, 1997, 311 pages, £41.00 (cloth). Reviewed by Anne Boomsma University of Groningen, The Netherlands The rate of publication of books on structural equation modeling (SEM) has shown an almost exponential growth over the last decade, reflecting the popularity of this type of statistical analysis more than its apparent usefulness. Basics of Structural Equation Modeling is yet another book with the goal “to provide readers a good basic understanding of how and why structural equation approaches have come to be used” and “to learn about the logic underlying the use of these approaches, about how they relate to techniques such as regression and factor analysis, about their strengths and shortcomings as compared to alternative methodologies, and about the various methodologies for analyzing structural equation data” (p. 11f.). By and large, that goal is accomplished. The book has four parts, the contents of which will be discussed briefly, followed by a more general evaluation.

PART I.

BACKGROUND

This part includes two chapters: an introductory chapter on “Causal Processes,” and one on the “History and Logic of Structural Equation Modeling.” In this part of the book Maruyama tries to express the usefulness and essence of causal modeling. Almost by definition, causal modeling is seen as an “alternative and complementary methodology to experimentation for examining plausibility of hypothesized models” (p. 7), which is partly remarkable: SEM can hardly ever be a substitute for experimentation. The issue of causality in SEM is not treated with great rigor. In fact, the author’s position is often ambiguous and vague. For example, on the one hand structural equation modeling is presented as similar to causal modeling, and yet, on the other hand already in the first 10 pages a small impression is given of Requests for reprints should be sent to Anne Boomsma, Department of Statistics, Measurement Theory and Information Technology, University of Groningen, Grote Kruisstraat 2/1, 9712 TS Groningen, The Netherlands. E-mail: [email protected]

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some of the controversies involved when referring to causal modeling in the context of SEM. The author distances himself from the feasibility of causal modeling, but accepts causal terminology at the same time—a common attitude in most textbooks. Reference to some of the literature in these matters could have deepened the discussion; see, for example, De Leeuw (1985), Sobel (1995), and Cox and Wermuth (1996). The second chapter is leisurely reading, taking the reader slowly from regression analysis to SEM methodology.

PART II.

BASIC APPROACHES TO MODELING WITH SINGLE OBSERVED MEASURES

This part has four chapters, the first of which handles “The Basics: Path Analysis and Partitioning of Variance.” Although path analysis is historically interesting, today it is more or less set aside by latent variables and errors in variables models. Covered topics like the logic of correlations and covariances are very basic indeed, and part of any first-grade statistics course. The decomposition of an association or correlation into different types of effects is largely illuminating, distinguishing causal (direct and indirect) and noncausal effects (common causes and unanalyzed prior associations). However, the treatment and illustrations of these types of effects is quite talkative; an algebraic approach would have been more direct and could have provided more insight. Chapter 4 deals with “Effects of Collinearity on Regression and Path Analysis.” The main focus is on multicollinearity in regression analysis, not on path models. There is quite a useful reminder of the sources of multicollinearity, and a summary of ways of detecting its occurrence (Table 4.1); however, bringing up explicit references there would have been appreciated. Anyway, this chapter shows originality of presentation. The statement that calculating confidence intervals for correlation coefficients is rather complex, and that it requires converting correlations r to Fisher’s z, should not be taken for granted (see Boomsma, 1977, for an overview of alternatives). What follows is a chapter on “Effects of Random and Nonrandom Error in Path Models,” which includes an important and well-written section about measurement error and components, and makes the transition from path analysis to factor analysis. There is an interesting section on method variance (as opposed to trait variance), and multitrait–multimethod models, with its connections toward convergent and discriminating validity. New to most readers will be that Maruyama considers a covariance between errors of measurement as nonrandom error (p. 87). Chapter 6 on “Recursive and Longitudinal Models” offers a descriptive treatment of issues and problems related to these types of models. Much attention is given to notions of stability and change.

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Maruyama does not fully work out the statistical reasons for analyzing covariance matrices rather than correlation matrices. He just refers to Cudeck (1989), not mentioning estimation methods like weighted least squares in that context. The reader is now halfway through the book. So far, the text is very readable and accessible. It is simple, offers insights, and hardly uses any formulas. It covers the pre-LISREL era, and moves into the future while discussing the advantages and disadvantages of path and regression analysis versus SEM. Although this is relatively old stuff, its presentation is somewhat attractive and original.

PART III.

FACTOR ANALYSIS AND PATH MODELING

This part coincides with chapter 7: “Introducing the Logic of Factor Analysis and Multiple Indicators to Path Modeling.” It introduces confirmatory factor analysis and briefly mentions exploratory factor analysis. The factor model is treated very strongly as a causal rather than a measurement model, owing to terminology (e.g., p. 135). Initially two notations, Y = Pf + U and Y = Pf + e, are used for a factor model. It is unclear why the author does not consistently stick to the familiar LISREL equation y = Λy η + ε when claiming (p. 178) that the book uses LISREL notation. For the initial testing of the plausibility of a model, consistency tests are discussed (p. 154) using the perspective of Costner (1969) and Costner and Schoenberg (1973), in which path analysis approaches and calculations play a central role. This type of plausibility testing is not very statistical, but conceptual insight might be gained if researchers take the time to do such calculations, which is very doubtful. The author claims (p. 160) that the consistency approach is used to remove much about the mysticism that comes from SEM generally, but it is unclear what this means. Structural models are well-defined, there’s nothing mystical about them, and latent variables have always been used in science. In this context, when talking about vanishing tetrads, it would have made sense to refer to the TETRAD program (Scheines, Spirtes, Glymour, & Meek, 1994), and especially to its Purify module.

PART IV.

LATENT VARIABLE STRUCTURAL EQUATION MODELS

The final part includes four chapters, starting with chapter 8: “Putting It All Together: Latent Variable Structural Equation Modeling.” Here the full LISREL model for covariances (not including means) is dispensed, without even considering statistical assumptions.


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The statement that fixing the variance of latent endogenous variables is not an option is not correct (anymore). Given the state of the art of the LISREL program close to the date of publishing, an update of the book should have occurred. This is also apparent from note 14 on page 18, which reflects incorrect as well as outdated information. Of course, that does not take away the appreciation for the section on choosing a reference indicator. It is a misconception to assume, or to suggest, that when the structural part has no degrees of freedom, this is a guarantee for that part not being misspecified (p. 192). In addition, the section on model fitting is superficial. Regarding cross-validation, Camstra (1998) shows that, in a process of model selection, some measures of cross-validation outperform others quite remarkably. As a whole this chapter gives a rather shallow introduction to the LISREL model; it contains the main elements and is certainly not mathematical or statistical in nature. The layout of matrix equations here and in Appendix A is as bad as it can be. Using latent variable structural equation modeling to examine plausibility of models is the subject of chapter 9, which provides “real data” illustrations of structural equation models: a longitudinal path, a nonrecursive multiple-indicator, and a longitudinal multiple-indicator panel model. Their sharing conceptual theme focuses on achievement of students in desegregated schools, more specifically on the relation between achievement and peer acceptance. The examples are good for social psychologists and worrying parents. There is one “but,” however: “Insofar as the model is longitudinal, we definitely should have worked with a covariance matrix, a shortcoming of both the original article and our reanalyses” (p. 205). A sincere confession of misbehavior. The appendixes of chapter 9 give some LISREL, AMOS, and EQS program setups for the examples. However, attached notes saying that the author did not have the EQS program (so he could not run this program to ensure that it works), or mentioning problems with a normal X and Y setup in LISREL 8 without solving them, do not make a good impression. There is also insufficient correspondence between the labels in Illustration 4 of Appendix 9.3 and the chapter’s text. Chapter 10, “Logic of Alternative Models and Significance Tests,” deals with the problem of model fit and model selection. Approaches for setting up series of nested models are discussed, together with some examples illustrating fit tests. Maruyama is overly concerned by the fact that the chi-square model test statistic is affected by the sample size N, even if models are compared in a nested sequence. A relatively extensive outline is presented of different types of fit indexes, about which De Leeuw once wrote, “Unfortunately there seems to be a proliferation of model selection tools, so that it seems likely we will need a tool to select model selection tools in the not too distant future” (1990, p. 240).


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After this chapter, “readers have been exposed to all the basic tools they need to be ‘intelligent’ users of structural equation techniques” (p. 254), Maruyama claims. Unfortunately, that certainly does not hold for the many significant statistical issues in SEM. Chapter 11, “Variations on the Basic Latent Variable Structural Equation Model,” handles three types of models: (a) the comparison of structural models in different populations, including the important topic of dummy variables; (b) second order factor models; and (c) models in which all variables are treated as being endogenous (all-Y models). The latter section is superfluous, because the LISREL 8 version allows for covariances between and within measurement errors of exogenous and endogenous variables. In the final chapter of the book—with the appropriate title, “Wrapping Up”—criticisms on the use of SEM are addressed. As internal criticism, mainly the ever-returning warnings of Cliff (1983) and the article of Breckler (1990) are summarized. Baumrind (1983) and Ling (1982) are viewed as exponents of external criticism, they being members of “a much more sophisticated group that views SEM techniques negatively” (p. 276). Much more sophisticated? Maruyama repeatedly writes that “replication is even more important in SEM research than in experimental work” (p. 272), but whether that’s a fact remains to be seen. Surely replication is often more easily performed in experimental work than in observational studies, where strict replication is frequently impossible (see Rosenbaum, 1995, for feasible statistical alternatives). Both approaches need to answer the question of how robust conclusions from the analysis are against sampling perturbations. In SEM the possible effects of chance capitalization should be evaluated carefully. Finally, a number of fairly complex and less fundamental issues, which have been left out in the preceding chapters, are enumerated (e.g., estimation methods other than maximum likelihood). However, due to the absence of any statistical emphasis, important robustness questions remain backstage (see Hoogland and Boomsma, 1998, for an overview). Additionally, listing gladiators in the field of structural equation modeling (p. 284), whose work ought to be covered and followed, hardly adds anything to the understanding of SEM. As for any rating of scientists, such endeavors are extravagant, and extremely limited due to measurement errors and subjectivity.

GENERAL REMARKS This book is potentially valuable for students and researchers who want an introduction to basic ideas of SEM and its methodological aspects. The reader is assumed to know what an expected value is and should at least have some acquaintance with matrix algebra, but these prerequisites are not really necessary for


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understanding the book’s main contents. In an appendix, a brief introduction to matrix algebra is given. Each chapter concludes with an overview. Some chapters provide discussion questions and some exercises. The discussion questions are rather moderate in content and depth, or inadequate as far as they relate to material not covered in detail by the book and thus require additional knowledge. The subject index is also very limited. Although hardly any errors were detected, the author does not seem to know the difference between bootstrap and jackknife (p. 273). In the program setup for the examples, the old LISREL 8 language (Jöreskog & Sörbom, 1996) is used instead of the easier SIMPLIS command language. Maruyama writes that the equation-based SIMPLIS version exists (p. 283), but he does not use it. Why not? Interestingly, another recent book by Kelloway (1998) also only uses the old LISREL format, refraining from the user-friendly SIMPLIS command language, while pretending at the same time in the introductory chapter that “the intent of the book is to give a ‘user-friendly’ introduction to structural equation modeling” (p. 4). Quite a paradox!

CONCLUSIONS It appears these days that some teachers of courses in structural equation modeling may have enough experience and courage to write a book on this type of analysis. That does not necessarily imply that such volumes are interesting or refreshing. If the reader has not already had a thorough course in SEM, it is doubtful whether any of these books offer more than some occasionally sparkling insights and illuminating examples. As indicated, Maruyama’s book is quite readable, and it has a number of things to offer over other competitive books. One of the author’s strongest points is that he frequently seriously discusses outdated approaches and methodologies to point out their deficiencies, and subsequently makes a progressive path to current potentials of SEM. Maruyama’s book does not aim at teaching how to use SEM software, it tries instead to go back to some basic understanding of the roots of SEM, and to explain what the pros and cons of its use are. Its emphasis is on methodological aspects. Statistics is by no means part of the game Maruyama is involved in. Fundamental concepts and insights (the basic logic underlying path models) is what the author is aiming at. And that is just one, fixed part of the SEM story—the random, statistical component is yet another one. For that very reason this text is more closely related to the book by Duncan (1975) than to that by Bollen (1989), both classics with their own flavor. “Good luck, structural equation modelers!” Maruyama exclaims at the very end. But beware, the analysis of covariance structures requires no luck in setting

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up the model, just a theory base. As far as luck is concerned, the random sample of observations is crucial. There perhaps one might wish to be fortunate, so good luck readers!


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