PLS-SEM with factor estimation (PLSF-SEM): An applied discussion in the field of marketing

The article below (mentioned as forthcoming in a recent post; now published!) explains how one can conduct a factor-based PLS structural equation modeling (PLSF-SEM) analysis, with an illustration in the field of marketing, as well as the advantages of using PLSF-SEM in terms of avoidance of type I and II errors.

Kock, N. (2019). Factor-based structural equation modeling with WarpPLS. Australasian Marketing Journal, 27(1), 57-63.

A link to a PDF file is available ().

Abstract:

Structural equation modeling (SEM) is extensively used in marketing research. For various years now, there has been a somewhat heated debate among proponents and detractors of the use of the partial least squares (PLS) method for SEM. The classic PLS design, originally proposed by Herman Wold, has a number of advantages over covariance-based SEM; e.g., minimal model identification demands. However, that design does not base its model parameter recovery approach on the estimation of factors, but on composites, which are exact linear combinations of indicators. This leads to adverse consequences, primarily in the form of unacceptable levels of type I and II errors. Recently a new factor-based method for SEM has been developed, called PLSF, which we discuss in this paper. This method has the advantages of classic PLS, but without the problems inherent in the use of composites. For readers interested in trying it, the PLSF method is implemented in the SEM software WarpPLS.

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

Nonlinearity and type I and II errors in SEM analysis

Many relationships between variables studied in the natural and behavioral sciences seem to be nonlinear, often following a J-curve pattern (a.k.a. U-curve pattern). Other common relationships include the logarithmic, hyperbolic decay, exponential decay, and exponential. These and other relationships are modeled by WarpPLS.

Yet, the vast majority of statistical analysis methods used in the natural and behavioral sciences, from simple correlation analysis to structural equation modeling, assume relationships to be linear in the estimation of coefficients of association (e.g., Pearson correlations, standardized partial regression coefficients).

This may significantly distort results, especially in multivariate analyses, increasing the likelihood that researchers will commit type I and II errors in the same study. A type I error occurs in SEM analysis when an insignificant (the technical term is "non-significant") association is estimated as being significant (i.e., a “false positive”); a type II error occurs when a significant association is estimated as being insignificant (i.e., an existing association is “missed”).

The figure below shows a distribution of points typical of a J-curve pattern involving two variables, disrupted by uncorrelated error. The pattern, however, is modeled as a linear relationship. The line passing through the points is the best linear approximation of the distribution of points. It yields a correlation coefficient of .582. In this situation, the variable on the horizontal axis explains 33.9 percent of the variance of the variable on the vertical axis.

The figure below shows the same J-curve scatter plot pattern, but this time modeled as a nonlinear relationship. The curve passing through the points is the best nonlinear approximation of the distribution of the underlying J-curve, and excludes the uncorrelated error. That is, the curve does not attempt to model the uncorrelated error, only the underlying nonlinear relationship. It yields a correlation coefficient of .983. Here the variable on the horizontal axis explains 96.7 percent of the variance of the variable on the vertical axis.

WarpPLS transforms (or “warps”) J-curve relationship patterns like the one above BEFORE the corresponding path coefficients between each pair of variables are calculated. It does the same for many other nonlinear relationship patterns. In multivariate analyses, this may significantly change the values of the path coefficients, reducing the risk that researchers will commit type I and II errors.

The risk of committing type I and II errors is particularly high when: (a) a block of latent variables includes multiple predictor variables pointing and the same criterion variable; (b) one or more relationships between latent variables are significantly nonlinear; and (c) the predictor latent variables are correlated, even if they clearly measure different constructs (suggested by low variance inflation factors).