Factor-based structural equation modeling with WarpPLS

Dear colleagues:

The link below, for an article forthcoming in the Australasian Marketing Journal (AMJ), provides a discussion on the limitations of using composites in structural equation modeling (SEM). It also discusses a new factor-based method that builds on the classic partial least squares (PLS) technique developed by Herman Wold. This new method, also presented elsewhere (see ISJ article titled “From composites to factors: Bridging the gap between PLS and covariance‐based structural equation modeling”), addresses those limitations of using composites in SEM.

https://www.sciencedirect.com/science/article/abs/pii/S1441358218303215

The article linked above is titled “Factor-based structural equation modeling with WarpPLS”. The discussion in this AMJ article is very applied and, hopefully, conceptually straightforward.

Some of you may be wondering why I am so convinced that, if questionnaires are used for data collection, the resulting data must be factor-based and simply cannot be composite-based. The reason is simple. For question-statements to be devised by researchers, so that indicators measuring latent constructs can be obtained via questionnaires, the mental ideas associated with the constructs must first exist in the minds of the researchers. The direction of causality is clear: from constructs to indicators. This direction of causality gives rise to measurement residuals, which distinguish factors from composites.

Having said that, I believe that we can have what I refer to as "analytic composites", which can be seen as exact linear combinations of indicators. These are unique entities, which are designed to serve specific purposes. Analytic composites are widely used in a variety of fields, including business - e.g., the Dow Jones Industrial Average. With analytic composites, there is no way the original weights can be accurately recovered based on the data. To obtain those weights, one has to either ask the designer or, in the person’s absence, derive the weights from domain-relevant theory.

Remember, the whole point of SEM is to recover the original population parameters based on the sample data collected via questionnaires. The data are the indicators. The original parameters are path coefficients, loadings, weights etc.

In SEM we do not have the original factors at the start of the analysis, we only have the indicators and theory-driven models with structural and measurement components. The new factor-based method discussed in the AMJ article linked above yields correlation-preserving estimates of the factors.

Happy New Year!

Ned