The power of data-driven decisions is apparent as more and more organizations incorporate sophisticated statistical analyses to guide decision making. The level of usefulness and profit resulting from those decisions is linked directly to the quality of one’s statistical toolkit. How suitable and sophisticated are your tools? I invite you to add one powerful statistical technique to your collection: structural equations models (SEM). This might not be the right tool for your needs, but if it is, you’ll be happy you came across it!
SEM is a framework that brings together regression and factor analysis to facilitate modeling relations between observed and unobserved variables. This framework relies on the analysis of the covariance and mean structure of data, enabling specification of complex, multivariate relations. SEM allows analysts to account for measurement error, specify hypothesized causal chains to identify the mechanisms by which outcomes occur, and account for missing data with cutting-edge algorithms. These key features lead to more accurate estimates of effects that can aid decision making in organizations. Often accompanying SEM are path diagrams that, when drawn correctly, represent the underlying statistical models with full precision. Thus, path diagrams can facilitate specification and interpretation of SEM.
SEM is a framework that brings together regression and factor analysis to facilitate modeling relations between observed and unobserved variables.
Several statistical techniques are subsumed within the SEM framework, including t-tests, ANOVA, ANCOVA, MANOVA, multiple regression, factor analysis, path analysis and measurement error models, among others. What makes SEM special is its flexibility for specifying these or other models and relaxing or imposing constraints that align with theoretical notions. For example, one could fit – simultaneously – two repeated measures ANOVA models to two processes that occur over time, facilitating exploration of the processes’ dynamics as they evolve, while relaxing stringent assumptions of the standard repeated measures ANOVA model.
SEM with unobserved, or latent, variables are particularly useful to fields seeking to study intangible concepts; psychology and education apply SEM widely as they focus on personality, attitudes, achievement, cognition and many other latent constructs. However, latent variables are not unique to these fields; indeed, marketing, management and business, for example, can find value in understanding perceptions, satisfaction, innovation or performance, whereas manufacturing and engineering can benefit from modeling quality, energy and other unobservable factors in industrial processes.
With these seemingly advantageous features, why are SEMs not part of everyone’s toolkit? I hypothesize there are three driving factors:
Accessibility. SEM is a technique taught primarily in graduate social sciences’ programs, so it would be unusual for a classically trained statistician or biostatistician to come across SEM or learn the technical details behind it.
Ease of use. Leading SEM software packages have been historically developed by academics with great understanding of the technique but not enough attention to usability. Moreover, great flexibility sometimes brings great complexity; as analysts aim to solve big challenges with SEM, overly complicated models are prone to specification errors, and ultimately estimation errors.
Domain expertise. Analysts’ knowledge allows them to specify models that align with theory and previous knowledge. In many applications, it is not important to understand why or how certain factors predict an outcome. In these cases, unsupervised models, driven entirely by the data, are an adequate choice, and SEM is not.
Luckily, accessibility and ease of use need no longer be barriers to using SEM. JMP Pro recently introduced an SEM platform to its already rich collection of statistical methods, and this means analysts can find lots of resources for learning how to apply SEM to guide decisions that improve their organizations. The SEM platform in JMP Pro inherits all the interactive and dynamic features that JMP is known for, plus ease of use is at the forefront of its development, with ongoing error checking to alert users to potential issues before they arise in estimation. It has never been easier to add SEM to your statistical toolkit. This sophisticated technique might just be the tool that leads your organization to make better data-driven decisions.
About the Author
Laura Castro-Schilo works on structural equations models in JMP. She is interested in multivariate analysis and its application to different kinds of data – continuous, discrete, ordinal, nominal and even text. Previously, she was Assistant Professor at the L. L. Thurstone Psychometric Laboratory at the University of North Carolina at Chapel Hill. Castro-Schilo has a PhD in quantitative psychology from the University of California, Davis.
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