Structural equation modeling (SEM) is a statistical methodology that takes a confirmatory (i.e., hypothesis-testing) approach to the analysis of a structural theory bearing on some phenomenon. Typically, this theory represents “causal” processes that generate observations on multiple variables (Bentler, 1988). The term “structural equation modeling” conveys two important aspects of the procedure: (a) that the causal processes under study are represented by a series of structural (i.e., regression) equations, and (b) that these structural relations can be modeled pictorially to enable a clearer conceptualization of the theory under study. The hypothesized model can then be tested statistically in a simultaneous analysis of the entire system of variables to determine the extent to which it is consistent with the data. If goodness-of-fit is adequate, the model argues for the plausibility of postulated relations among variables; if it is inadequate, the tenability of such relations is rejected.

Several aspects of SEM set it apart from the older generation of multivariate procedures. First, as noted above, it takes a confirmatory, rather than an exploratory approach to the data analysis (although aspects of the latter can be addressed). Furthermore, by demanding that the pattern of inter-variable relations be specified a priori, SEM lends itself well to the analysis of data for inferential purposes. By contrast, most other multivariate procedures are essentially descriptive by nature (e.g., exploratory factor analysis), so that hypothesis-testing is difficult if not impossible. Second, whereas traditional multivariate procedures are incapable of either assessing or correcting for measurement error, SEM provides explicit estimates of these error variance parameters. Indeed, alternative methods (e.g., those rooted in regression, or the general linear model) assume that error(s) in the explanatory (i.e., independent) variables vanishes. Thus, applying those methods when there is error in the explanatory variables is tantamount to ignoring error that may lead, ultimately, to serious inaccuracies—especially when the errors are sizable. Such mistakes are avoided when corresponding SEM analyses (in general terms) are used. Third, although data analyses using the former methods are based on observed measurements only, those using SEM procedures can incorporate both unobserved (i.e. latent) and observed variables. Finally, there are no widely and easily applied alternative methods for modeling multivariate relations, or for estimating point and/or interval indirect effects; these important features are available using SEM methodology.

Given these highly desirable characteristics, SEM has become a popular methodology for nonexperimental research, where methods for testing theories are not well developed and ethical considerations make experimental design unfeasible (Bentler, 1980). Structural equation modeling can be utilized very effectively to address numerous research problems involving nonexperimental research; in this book, I illustrate the most common applications (e.g., Chapters 3, 4, 6, 7, 9), as well as some that are less frequently found in the substantive literatures (e.g., Chapters 5, 8, 10, 11, 12, 13). Before showing you how to use the Amos program (Arbuckle, 2015), however, it is essential that I first review key concepts associated with the methodology. We turn now to their brief explanation.

Source: Byrne Barbara M. (2016), *Structural Equation Modeling with Amos: Basic Concepts, Applications, and Programming*, Routledge; 3rd edition.

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