Combining composites and factors in PLS-SEM models: A multi-algorithm technique

The article below presents a multi-algorithm technique for combining latent variables estimated as composites or factors into a single model, in the context of structural equation modeling via partial least squares (PLS-SEM).

Kock, N. (2024). Combining composites and factors in PLS-SEM models: A multi-algorithm technique. Data Analysis Perspectives Journal, 5(4), 1-8.

Link to full-text file for this and other DAPJ articles:

https://scriptwarp.com/dapj/#Published_Articles

Abstract:

A multi-algorithm technique is presented for combining latent variables estimated as composites or factors into a single model, in the context of structural equation modeling via partial least squares. The multi-algorithm technique consists of three key steps: selecting composite-based or factor-based outer model analysis algorithms to be used for latent variable estimation; adding the latent variables estimated with the chosen composite-based or factor-based algorithms as new standardized variables; and creating and estimating a final model with the new variables added as single indicators of latent variables.

Best regards to all!

Methods showcase - Using PLSF-SEM in business communication research

The article below discusses how one can employ PLSF-SEM in business communication research. The discussion is generic enough to guide the use of the method in other areas of research. PLSF-SEM builds on partial least squares (PLS) algorithms to generate correlation-preserving factors; the F refers to it being factor-based, as opposed to composite-based. A primer on the use of PLSF-SEM in business communication research is provided, based on an illustrative model inspired by motivating language theory, and where simulated data was analyzed with the software WarpPLS.

Kock, N. (2024). Methods showcase - Using PLSF-SEM in business communication research. International Journal of Business Communication (forthcoming: 23294884241233281).

Link to full-text file for this article:

Methods showcase - Using PLSF-SEM in business communication research.

Abstract:

Structural equation modeling (SEM) is a data analysis method that is widely used in business communication research, as well as research in many other fields, when scholars need to test complex models with multiple outcomes, interactions, or operations across different situations. To date, however, researchers have had to choose between using covariance-based SEM, and dealing with convergence problems; or composite-based SEM, and facing serious methodological issues. This article describes a way to combine strong aspects of both SEM types through PLSF-SEM. By utilizing this novel method, empirical researchers can employ several of the same tests traditionally used in covariance-based SEM, as well as new tests that rely on latent variable estimates, in a succinct and scholarly way. PLSF-SEM builds on partial least squares (PLS) algorithms to generate correlation-preserving factors; the F refers to it being factor-based, as opposed to composite-based. A primer on the use of PLSF-SEM in business communication research is provided, based on an illustrative model inspired by motivating language theory, and where simulated data was analyzed with the software WarpPLS.

Best regards to all!

Contributing to the success of PLS in SEM: An action research perspective

The article below discusses how I employed an action research approach, by working closely with WarpPLS users, to contribute to the success of PLS in SEM. A big thank you to WarpPLS users!

Kock, N. (2023). Contributing to the success of PLS in SEM: An action research perspective. Communications of the Association for Information Systems, 52(1), 730-734.

Link to full-text file for this article:

Contributing to the success of PLS in SEM: An action research perspective

Abstract:

I share with Evermann and Rönkkö (2022) the belief that classic composite-based partial least squares path modeling (PLS-PM) presents shortcomings when used to conduct structural equation modeling (SEM) analyses. The shortcomings can be traced back to one fundamental problem, which is that latent variables (LVs) are approximated in PLS-PM as exact linear combinations of their corresponding indicators. In SEM, each LV is in fact a factor; i.e., a linear combination of the indicators and a measurement residual. My approach to addressing the shortcomings of PLS-PM is rather unique among researchers concerned with quantitative methods. I have employed an action research approach, helping investigators employ SEM in their empirical studies. This has led to my development of a widely used software tool for SEM analyses. I illustrate my action research orientation by discussing three recent methodological developments with which I have been closely involved.

Best regards to all!

Using indicator correlation fit indices in PLS-SEM: Selecting the algorithm with the best fit

The article below explains how one can use indicator correlation fit indices for selecting the analysis algorithm with the best fit in the context of structural equation modeling via partial least squares (PLS-SEM).

Kock, N. (2020). Using indicator correlation fit indices in PLS-SEM: Selecting the algorithm with the best fit. Data Analysis Perspectives Journal, 1(4), 1-4.

A link to a PDF file is available ().

Abstract:

Upon completion of a PLS-SEM analysis, one can obtain the model-implied indicator correlation matrix and compare it with the actual indicator correlation matrix. The latter is obtained directly from the data being analyzed. Indicator correlation fit indices are quantifications of the differences among these two matrices. Our focus in this paper is on the use of indicator correlation fit indices in PLS-SEM for selecting the analysis algorithm with the best fit.

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.

From composites to factors: Bridging the gap between PLS and covariance-based structural equation modeling

How can one bridge the gap between PLS and covariance-based structural equation modeling, by conducting a factor-based PLS structural equation modeling (PLSF-SEM) analysis? This question is addressed through the publication below.

Kock, N. (2019). From composites to factors: Bridging the gap between PLS and covariance-based structural equation modeling. Information Systems Journal, 29(3), 674-706.

A link to a PDF file is available ().

Abstract:

Partial least squares (PLS) methods possess desirable characteristics that have led to their extensive use in the field of information systems, as well as many other fields, for path analyses with latent variables. Such variables are typically conceptualized as factors in structural equation modeling (SEM). In spite of their desirable characteristics, PLS methods suffer from a fundamental problem: unlike covariance-based SEM, they do not deal with factors, but with composites, and as such do not fully account for measurement error. This leads to biased parameters, even as sample sizes grow to infinity. Anchored on a new conceptual foundation, we discuss a method that builds on the consistent PLS technique and that estimates factors, fully accounting for measurement error. We provide evidence that this new method shares the property of statistical consistency with covariance-based SEM, but, like classic PLS methods has greater statistical power. Moreover, our method provides correlation-preserving estimates of the factors, which can be used in a variety of other tests. For readers interested in trying it, the new method is implemented in the software WarpPLS. Our detailed discussion should facilitate the implementation of the method in any numeric computing environment, including open source environments such as R and GNU Octave.

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

Factor-based SEM

There has been a long and in some instances fairly antagonistic debate among proponents and detractors of the use of Wold’s original partial least squares (PLS) algorithms in the context of structural equation modeling (SEM). This debate has been fueled by one key issue: Wold’s original PLS algorithms do not deal with actual factors, as covariance-based SEM algorithms do; but with composites, which are exact linear combinations of indicators. The factor-based SEM algorithms in WarpPLS have been developed specifically to address this perceived limitation of Wold’s original PLS algorithms.

Related YouTube videos:

Conduct a Factor-Based PLS-SEM Analysis with WarpPLS
http://youtu.be/PvXuD5COezU

Use Consistent PLS Factor-Based Algorithms in WarpPLS
http://youtu.be/I5x4SuQHdME