Structural Equation Models
Motivation for this Book Link to heading
Since publication of the first edition of Structural Equation Models, I have been fortunate to maintain an active dialog on structural equations modeling (SEM) with many of my colleagues around the world. I never cease to be surprised with the broad divergence of opinions and myriad applications of SEM methodologies. Statistical methods such as regression and ANOVA rely on datasets of objectively measured constructs. These fail to satisfy a widespread need among researchers to analyze data concerning relationships between hypothesized but unobservable constructs: aesthetics, perceptions, utilities and other human and social constructs. Criticisms of SEM arisen from its lack of fit statistics and indeed the lack of defensible sampling strategies. But my argument is that these problems can be repaired while retaining the desirable features of SEM.
SEM has been applied in both the natural and the social sciences, but it has proven particularly valuable in the social sciences, where researchers apply SEM approaches rather than more structured regression approaches by the inclusion of unobservable (or latent) constructs and by the use of computationally intensive iterative searches for coefficients that fit the data. The expansion of statistical analysis to encompass unmeasurable constructs using SEM, canonical correlation, Likert scale quantification, principal components and factor analysis have vastly extended the scope and relevance of the social sciences over the past century. Subjects that were previously the realm of abstract argumentation have been transported into the mainstream of scientific research.
This new edition of this widely cited book surveys the full range of available structural equation modeling (SEM) methodologies. The book has been updated throughout to reflect the arrival of new software packages, which have made analysis much easier than in the past. Applications in a broad range of disciplines are discussed, particularly in the social sciences where many key concepts are not directly observable. This is the first book to present SEM’s development in its proper historical context–essential to understanding the application, strengths and weaknesses of each particular method. This book also surveys emerging approaches that complement SEM. They have been applied in diverse areas in engineering, including neuroscience for accurate examination of the activity among neural regions during different behaviors. The partial least squares SEM method was contemporaneously developed with PLS regression to address problems in chemistry and spectrography. They improve on predecessor path models that were widely used in genetic research in livestock and agriculture and environmental studies in the elicitation of ecological networks. SEM’s ability to accommodate unobservable theory constructs through latent variables is of significant importance to social scientists. Latent variable theory and application are comprehensively explained and methods are presented for extending their power, including guidelines for data preparation, sample size calculation and the special treatment of Likert scale data. Tables of software, methodologies and fit statistics provide a concise reference for any research program, helping assure that its conclusions are defensible and publishable.
Interest in Structural Equation Models Link to heading
The past two decades have witnessed a remarkable acceleration of interest in structural equations modeling (SEM) methods in many areas of research. In the social sciences, researchers often distinguish SEM approaches from more powerful systems of regression equation approaches by the inclusion of unobservable constructs (called latent variables in the SEM vernacular), and by the use of computationally intensive iterative searches for coefficients that fit the data. The expansion of statistical analysis to encompass unmeasurable constructs using SEM, canonical correlation, Likert scale quantification, principal components and factor analysis have vastly extended the scope and relevance of the social sciences over the past century. Subjects that were previously the realm of abstract argumentation have been transported into the mainstream of scientific research (see I. Allen and Seaman 2007; Altman and Royston 2000). Statistical methods to identify latent constructs underlying observations evolved in the 1930s. Principal component analysis (PCA), factor analysis and other methods look for methods to reduce the dimensionality of a complex multicolinear dataset. Latent factors accounting for most of the similarity or distance of measurements could potentially be inferred from these factors. SEM methods grew out of efforts to infer additional structure between these latent constructs. Many of the seminal studies on structural statistical models in economics took place in the Cowles Commission (then at the University of Chicago) in the 1940s and 1950s and later in the Chicago school of economics from the 1950s on. In a 1976 paper, Robert Lucas of the Chicago school argued that generic additive linear models such as those invoked in the panel regressions commonly used in econometrics, lacked stability and robustness (Lucas Jr 1992). He argued, in what has come to be known as the ‘Lucas critique’, that empirical models are improved when constructs are policy-invariant i.e. structural, implying that they would be unlikely to change whenever the competitive environment or a particular policy changed. Lucas suggested that researchers need to model the “deep structural parameters” (relating to preferences, technology, and resource constraints) that are assumed to govern individual behavior. Structural models in (Lucas Jr 1992) were intended to enable a positive
research program for econometrics, allowing for prediction and real-world decisions. Policy- invariant structural models are constructed through analysis of the underlying dynamics of
the construct relationships and behavior, and are based on a ‘theory’ of how the real-world works. The ‘Lucas critique’ promoted a priori theory building, and this has become common practice in structural equation modeling. It is now standard practice to design the theorized causal structures in an SEM, whether the statistical method is PLS-PA, LISREL or regression approach, prior to statistical estimation. The products of SEM statistical analysis algorithms fall into three groups:
pairwise canonical correlations between pairs of prespecified latent variables computed from observable data (from the so-called partial least squares path analysis, or PLS-PA approaches);
multivariate canonical correlation matrices for prespecified networks of latent variables computed from observable data (from a group of computer intensive search algorithms originating with Karl Jöreskog); and
systems of regression approaches that fit data to networks of observable variables whose clusters are hypothesized to co-vary with latent constructs. Other methods of latent variable analysis are now emerging with the introduction of machine learning new social network analysis.