Structural Equation Modeling (SEM) is complex form of multiple regression that is commonly used in social science research. In many ways, SEM is an amalgamation of factor analysis and path analysis as we shall see. The history of this data analysis approach can be traced all the way back to the beginning of the 20th century.
This post will provide a brief overview of SEM. Specifically, we will look at the role of factory and path analysis in the development of SEM.
The Beginning with Factor and Path Analysis
The foundation of SEM was laid with the development of Spearman’s work with intelligence in the early 20th century. Spearman was trying to trace the various dimensions of intelligence back to a single factor. In the 1930’s Thurstone developed multi-factor analysis as he saw intelligence not as a a single factor as Spearman but rather as several factors. Thurstone also bestowed the gift of factor rotation on the statistical community.
Around the same time (1920’s-1930’s), Wright was developing path analysis. Path analysis relies on manifest variables with the ability to model indirect relationships among variables. This is something that standard regression normally does not do.
In economics, a econometrics was using many of the same ideas as Wright. It was in the early 1950’s that econometricians saw what Wright was doing in his discipline of biometrics.
SEM is Born
In the 1970’s, Joreskog combined the measurement powers of factor analysis with the regression modeling power of path analysis. The factor analysis capabilities of SEM allow it to assess the accuracy of the measurement of the model. The path analysis capabilities of SEM allow it to model direct and indirect relationships among latent variables.
From there, there was an explosion in ways to assess models as well as best practice suggestions. In addition, there are many different software available for conducting SEM analysis. Examples include the LISREL which was the first software available, AMOS which allows the use of a graphical interface.
One software worthy of mentioning is Lavaan. Lavaan is a r package that performs SEM. The primary benefit of Lavaan is that it is available for free. Other software can be exceedingly expensive but Lavaan provides the same features for a price that cannot be beat.
SEM is by far not new to the statistical community. With a history that is almost 100 years old, SEM has been in many ways with the statistical community since the birth of modern statistics.