Individual paths can be set as linear or nonlinear in PLS-SEM analyses

In WarpPLS, the “View or change individual inner model analysis algorithm settings” option allows you to set inner model algorithms for individual paths in PLS-SEM analyses; whether these analyses are composite-based or factor-based. That is, for each path a user can select a different algorithm from among the following choices: “Linear”, “Warp2”, “Warp2 Basic”, “Warp3”, and “Warp3 Basic”.

This option is particularly useful in empirical investigations where researchers have solid theoretical reasons to expect certain paths to be associated with nonlinear relationships of particular types. Those researchers may also have solid theoretical reasons to expect certain paths to be associated with linear relationships. Given that one of the main goals of SEM is to test theory, theoretical considerations should be given a very high priority in the selection of algorithms to be used for each path in a model.

There is a short video that illustrates this ().

On a related note - since classic moderating effects analyses already capture nonlinearity, it is usually advisable for users to set moderating paths as linear. They can do this even as they set direct paths as nonlinear. This leads to 2D graphs that are easier to interpret. If users set moderating paths as nonlinear, their interpretation becomes more difficult, as more complex types of moderating relationships are captured.

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.

How to theorize nonlinear relationships and test them: A journal article example

How can a researcher theorize nonlinear relationships and test them? This question is addressed through the publication below, which provides an example of nonlinear theorizing and related empirical analysis. To the best of our knowledge, this is one of the first articles that exemplifies how nonlinear theorizing can be incorporated into a casual model and tested with WarpPLS.

Kock, N., Mayfield, M., Mayfield, J., Sexton, S., & De La Garza, L. (2019). Empathetic leadership: How leader emotional support and understanding influences follower performance. Journal of Leadership and Organizational Studies, 26(2), 217-236.

A link to a PDF file is available ().

Abstract:

This article presents a theory of empathetic leadership and its initial test. Empathetic leadership provides a model of how leader understanding and support improves follower behaviors and affective states. For this article, we explored the link between empathetic leadership and follower performance. Specifically, we tested the causal processes by which empathetic language influences follower performance. These processes include follower job satisfaction and innovation. Findings support model hypotheses and provide preliminary causal support for the model.

A thank you note to the participants in the 2019 PLS Applications Symposium

This is just a thank you note to those who participated, either as presenters or members of the audience, in the 2019 PLS Applications Symposium:

http://plsas.net/

As in previous years, it seems that it was a good idea to run the Symposium as part of the Western Hemispheric Trade Conference. This allowed attendees to take advantage of a subsidized registration fee, and also participate in other Conference sessions and the Conference's social event.

I have been told that the proceedings will be available soon, if they are not available yet, from the Western Hemispheric Trade Conference web site, which can be reached through the Symposium web site (link above).

Also, the full-day workshop on PLS-SEM using the software WarpPLS was well attended. This workshop, conducted by Dr. Jeff Hubona and myself, was fairly hands-on and interactive. Some participants had quite a great deal of expertise in PLS-SEM and WarpPLS. It was a joy to conduct the workshop!

As soon as we define the dates, we will be announcing next year’s PLS Applications Symposium. Like this years’ Symposium, it will take place in Laredo, Texas, probably in the first half of April as well.

Thank you and best regards to all!

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Ned Kock

Symposium Chair

http://plsas.net

PLS Applications Symposium; 3 - 5 April 2019; Laredo, Texas (Abstract submissions accepted until 15 February 2019)

PLS Applications Symposium; 3 - 5 April 2019; Laredo, Texas

(Abstract submissions accepted until 15 February 2019)

*** Only abstracts are needed for the submissions ***

The partial least squares (PLS) method has increasingly been used in a variety of fields of research and practice, particularly in the context of PLS-based structural equation modeling (SEM). The focus of this Symposium is on the application of PLS-based methods, from a multidisciplinary perspective. For types of submissions, deadlines, and other details, please visit the Symposium’s web site:

http://plsas.net

*** Workshop on PLS-SEM ***

On 3 April 2019 a full-day workshop on PLS-SEM will be conducted by Dr. Ned Kock and Dr. Geoffrey Hubona, using the software WarpPLS. Dr. Kock is the original developer of this software, which is one of the leading PLS-SEM tools today; used by thousands of researchers from a wide variety of disciplines, and from many different countries. Dr. Hubona has extensive experience conducting research and teaching topics related to PLS-SEM, using WarpPLS and a variety of other tools. This workshop will be hands-on and interactive, and will have two parts: (a) basic PLS-SEM issues, conducted in the morning (9 am - 12 noon) by Dr. Hubona; and (b) intermediate and advanced PLS-SEM issues, conducted in the afternoon (2 pm - 5 pm) by Dr. Kock. Participants may attend either one, or both of the two parts.

The following topics, among others, will be covered - Running a Full PLS-SEM Analysis - Conducting a Moderating Effects Analysis - Viewing Moderating Effects via 3D and 2D Graphs - Creating and Using Second Order Latent Variables - Viewing Indirect and Total Effects - Viewing Skewness and Kurtosis of Manifest and Latent Variables - Viewing Nonlinear Relationships - Solving Collinearity Problems - Conducting a Factor-Based PLS-SEM Analysis - Using Consistent PLS Factor-Based Algorithms - Exploring Statistical Power and Minimum Sample Sizes - Exploring Conditional Probabilistic Queries - Exploring Full Latent Growth - Conducting Multi-Group Analyses - Assessing Measurement Invariance - Creating Analytic Composites.

-----------------------------------------------------------

Ned Kock

Symposium Chair

http://plsas.net

One-tailed or two-tailed P values in PLS-SEM?

Should P values associated with path coefficients, as well as with other coefficients such as weights and loadings, be one-tailed or two-tailed? This question is addressed through the publication below.

Kock, N. (2015). One-tailed or two-tailed P values in PLS-SEM? International Journal of e-Collaboration, 11(2), 1-7.

PDF file:

http://cits.tamiu.edu/kock/pubs/journals/2015JournalIJeC2/Kock_2015_IJeC_OneTwoTailedPLSSEM.pdf

Abstract:

Should P values associated with path coefficients, as well as with other coefficients such as weights and loadings, be one-tailed or two-tailed? This question is answered in the context of structural equation modeling employing the partial least squares method (PLS-SEM), based on an illustrative model of the effect of e-collaboration technology use on job performance. A one-tailed test is recommended if the coefficient is assumed to have a sign (positive or negative), which should be reflected in the hypothesis that refers to the corresponding association. If no assumptions are made about coefficient sign, a two-tailed test is recommended. These recommendations apply to many other statistical methods that employ P values; including path analyses in general, with or without latent variables, plus univariate and multivariate regression analyses.

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