Abstract

The goal of this chapter is to provide a historical account of structural equation modeling (SEM). To do so I followed the development throughout the twentieth century of the main ideas in the four disciplines that contributed to the development of SEM: biometrics, econometrics, psychometrics, and sociometrics. Special attention is paid to the development of path analysis by Wright and its sociological applications. Also presented are the development of estimation procedures and the formulation of identification issues in econometrics and the beginning of exploratory and confirmatory factor analysis in psychology. The last part of this account presents the synthesis of these ideas in the LISREL model as well as extensions of the original model.

This book describes a family of statistical methods known as structural equation modeling (SEM). SEM is used in a variety of techniques known as “covariance structure analysis”, “latent variable modeling”, “path modeling”, “path modeling with LISREL”, and sometimes it is mistaken for path analysis. This book will help biologists to understand the distinction between SEM and path analysis. The book consists of contributed chapters from biologists as well as leading methodologists in other research fields. We have organized the chapters and their content with the intent of providing a volume that readers may use to learn the methodology and apply it themselves to their research problems. We give the basic formulation of the method as well as technical details on data analysis, interpretation, and reporting. In addition, we provide numerous examples of research designs and applications that are germane to the research needs and interests of organismal biologists. We also provide, as a learning aide, the simulation programs, analysis programs, and data matrices, presented in the book at a website (http://www.usgs.gov/) so that readers may download and run them.

The book is divided into three sections. The first section, “Theory”, describes the SEM model and practical matters of its application. Chapter 1 lays out the mathematics of SEM in a comprehensible fashion. Using an example from behavioral genetics, the authors express their model in what is called LISREL notation, a symbolic language that is commonly used to express SEM models.

Abstract

Although distinctions are commonly made between exploratory and confirmatory models, structural equation modeling (SEM) is not an exploratory statistical method per se. The successful implementation of a structural equation model requires considerable a priori knowledge of the subject matter under investigation. The researcher will usually have a theoretical model in mind to test, and measurement instruments, including latent variables, devised to measure and relate constructs within the model. Research with SEM is a process in which theory is devised, data are collected and analyzed, and models are tested, modified, and confirmed with new data in an iterative fashion. In this context, SEM is rightly viewed as a confirmatory method. As a consequence, a number of epistemological and technical issues require consideration over and above the pure mathematics of the SEM model. In this chapter, we provide background on the philosophical aspects of the study of dependence relationships with SEM, the formulation of latent constructs, model justification, model identification, sample size and power, estimation methods, evaluation of model fit, model modification, interpretation of results, and publication of results. Our objective is to provide a guide that researchers can use to successfully devise and report the results of an SEM study.