Innovation with structural equation models

As a doctoral student, I was very interested in structural equation modeling: I joined SEMNET, cataloged SEM packages, took a SEM class with Peter Bentler, turn my class term paper into journal pub and prepared to use SEM for my dissertation. (The lack of normality in the my survey’s DV forced me to instead use logit modeling).

More than a decade later, I’m looking at doing another SEM model and needed to get up to date on current norms. When I was taking my class, fit indices were just becoming common. Now Prof. Bentler has 20,000+ cites for his 1999 paper on fit indices (versus a mere 12,000 for his 1990 paper).

As a quick way to identify those norms was to look for papers mentioning "structural equation" in Research Policy. I looked through the first 25 articles. Some of these papers use SEM cites (or methods) to do a confirmatory factor analysis, a couple don’t mention a specific package.

However, I was able to identify 12 path models estimated using SEM software:

• Only one used Lisrel — and that was published back in January 2004. In the 1980s and 1990s, most SEM papers were written using Lisrel.
• Instead, the most popular package is Amos (7 papers). But that shouldn’t be surprising, because it’s bundled with SPSS, one of the most popular social science stat bundles. (Both SAS and Stata have structural equation modules but it seems like neither are used much).
• While both Amos and Lisrel use traditional covariance modeling, I was not surprised to find that four papers used software based on partial least squares (PLS), Herman Wold’s pioneering prediction algorithm. PLS relaxes distributional assumptions (required by ML covariance modeling) and thus has enviable properties for small samples and cases of non normality (such that some have been deluded into considering it a silver bullet.)

• As with the 1980s LV-PLS package of Jan-Bernd Lohmöller, today’s PLS packages are distributed as freeware. Two articles used PLS-Graph by the pioneer of PLS application to MIS research, Wynne Chin.
• One RP article used SmartPLS, a German freeware package.
• Finally, one used PLS-PM, one of the many structural equation extensions for the open source R package.

In fact, the R repository (CRAN) lists at least seven free packages:

• lavaan: Latent Variable Analysis
• pls: Partial Least Squares and Principal Component regression
• plspm: Tools for Partial Least Squares Path Modeling (PLS-PM)
• RAMpath: Structural Equation Modeling using the reticular action model (RAM) Notation
• rsem: Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
• sem: Structural Equation Models
• semPLS: Structural Equation Modeling Using Partial Least Squares

An eighth add-on for R, the NIH-funded OpenMX, is not distributed via CRAN, but is available for free download. A 2011 analysis by Cardiff University researchers showed that the results were largely the same between the R-derived packages and the commercial packages.

My dissertation was about switching costs by PC software users: psychic switching costs predicted switching decisions better than economic ones. Right now, time is scarcer than money, so my big concern is learning to use a package that’s later orphaned. If I’m going to learn a new package, I figure I’ll pick one of the open source R packages — because the net present value of having to switch in the future is negative, and it’s safe to assume that R (like Linux and Android) isn’t going away any time soon.