Tuesday, November 24, 2015

Nonlinear analyses versus data segmentation in PLS-SEM

Those who conduct PLS-SEM analyses employing software other than WarpPLS and data segmentation approaches such as FIMIX-PLS may want to also conduct their analyses with WarpPLS, using a nonlinear algorithm, and compare the results against those obtained with data segmentation.

Data segmentation assumes the presence of underlying heterogeneity, which is also assumed (and accounted for) in a nonlinear analysis. The differences are that a nonlinear analysis assumes that the heterogeneity is somewhat uniform (a more reasonable assumption than that of “fragmented” heterogeneity), and that the heterogeneity can be described by nonlinear functions.

In WarpPLS users can define a main general type of nonlinear function for each structural link in their models.

Additionally, the “View focused relationship graphs with segments” options of WarpPLS allow users to view graphs that focus on the best-fitting line or curve, that exclude data points to provide the effect of zooming in on the best-fitting line or curve area, and that show curves as linear segments. The segments are shown with their respective beta coefficients and with or without P values (see figure below).

The options available are: “View focused multivariate relationship graph with segments (standardized scales)”, “View focused multivariate relationship graph with segments (standardized scales, P values)”, “View focused multivariate relationship graph with segments (unstandardized scales)”, “View focused bivariate relationship graph with segments (standardized scales)”, “View focused bivariate relationship graph with segments (standardized scales, P values)”, and “View focused bivariate relationship graph with segments (unstandardized scales)”.

The number of segments shown in the graphs above depends on the absolute effect segmentation delta chosen by the user using the “Settings” menu option. This absolute effect segmentation delta is the change (or delta) threshold in the first derivative of the nonlinear function depicting the relationship before a new segment is started.

For example, a delta of 0.1 means that in each segment the first derivative of the nonlinear function depicting the relationship does not vary more than 0.1. Since the first derivative does not change in linear relationships, segmentation only occurs in nonlinear relationships.

This graph segmentation option allows for the identification of unobserved heterogeneity without a corresponding reduction in sample size, providing a convenient alternative in this respect to data segmentation approaches such as FIMIX-PLS.

See the latest version of the User Manual for more details. The User Manual is available from the web site below.


Saturday, July 11, 2015

Testing for common method bias in PLS-SEM using full collinearity VIFs

Full collinearity variance inflation factors (VIFs) can be used for common method bias tests that are more conservative than, and arguably superior to, the traditionally used tests relying on exploratory factor analyses. Full collinearity VIFs and their use for common method bias tests, as well as other tests, are addressed in the following publications (also available from WarpPLS.com):

Kock, N. (2015). Common method bias in PLS-SEM: A full collinearity assessment approach. International Journal of e-Collaboration, 11(4), 1-10.

PDF file:


Kock, N., & Lynn, G.S. (2012). Lateral collinearity and misleading results in variance-based SEM: An illustration and recommendations. Journal of the Association for Information Systems, 13(7), 546-580.

PDF file:


Essentially, testing for the existence of common method bias through this method entails comparing the full collinearity VIFs calculated by WarpPLS for all latent variables to the threshold of 3.3 (or 5.0, if factor-based algorithms are used). If all full collinearity VIFs are equal to or lower than the threshold, this can be seen as an indication that the model is free from common method bias.

The formative-reflective measurement dichotomy

I have been asked several times in the past about the formative-reflective measurement dichotomy, and whether formative measurement should be used at all. Recently there seems to be an emerging belief shared among various methodological researchers that formative measurement should not be used, under any circumstances. My view on the issue is not as extreme, and is summarized through the text below, taken from page 127 of the article whose full text link is also provided. The references cited are available from the article.

Kock, N., & Mayfield, M. (2015). PLS-based SEM algorithms: The good neighbor assumption, collinearity, and nonlinearity. Information Management and Business Review, 7(2), 113-130.

"The formative-reflective measurement dichotomy is intimately related to a characteristic shared by the PLS-based SEM algorithms discussed here. These algorithms generate approximations of factors via exact linear combinations of indicators, without explicitly modeling measurement error. Recently new PLS-based SEM algorithms have been proposed that explicitly model measurement error (Kock, 2014). These new algorithms suggest that formative and reflective latent variables may be conceptually the same, but at the ends of a reliability scale, where reliability can be measured through the Cronbach’s alpha coefficient (Cronbach, 1951; Kline, 2010).

That is, a properly designed formative latent variable would typically have a lower reliability than a properly designed reflective latent variable. Nevertheless, both reliabilities would have to satisfy the same criterion – be above a certain threshold (e.g., .7). While reflective latent variables can achieve high reliabilities with few indicators (e.g., 3), formative latent variables require more indicators (e.g., 10). This mathematical property is in fact consistent with formative measurement theory, where many different facets of the same construct should be measured so that the corresponding formative latent variable can be seen as a complete depiction of the underlying formative construct.

Future research opportunities stem from the above discussion, leading to important methodological questions. What is the best measure of reliability to be used? It is possible that the composite reliability coefficient (Kock, 2013) is a better choice than the Cronbach’s alpha coefficient. Will the new PLS-based SEM algorithms that explicitly model measurement error (Kock, 2014) obviate the need for the classic algorithms discussed here, or will the new algorithms have a more limited scope of applicability? Will formative measurement be re-conceptualized as being at the low end of a reliability scale that also includes reflective measurement, providing a unified view of what could be seen as an artificial dichotomy? These and other related methodological questions give a glimpse of the exciting future of PLS-based SEM."

Tuesday, April 21, 2015

PLS Applications Symposium; 15 - 17 April 2015; Laredo, Texas

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).

As an emerging method, its users often face challenges in successfully publishing PLS-based research, hence the theme of this year's Symposium: Successfully publishing PLS-based research.

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:


Ned Kock
Symposium Chair

Thursday, March 26, 2015

WarpPLS 5.0 upgraded to stable

Dear colleagues:

Version 5.0 of WarpPLS is now available as a stable version. You can download and install it for a free trial from:


This version was initially released as a beta version and was later upgraded to stable. It has undergone extensive testing in-house prior to its release as a beta version, and has been in the hands of users for several months prior to its upgrade to stable.

The full User Manual is also available for download from the web site above separately from the software. See this document, and the link below to a previous post, for more details about this new version.



Thursday, January 1, 2015

WarpPLS 5.0 now available: Factor-based PLS-SEM algorithms, rotating 3D graphs, normality tests, missing data imputation methods, and more!

Dear colleagues:

Version 5.0 of WarpPLS is now available, as a beta version. You can download and install it for a free trial from:


The full User Manual is also available for download from the web site above separately from the software.

Some important notes for users of previous versions:

- There is no need to uninstall previous versions of WarpPLS to be able to install and use this new version.

- Users of previous versions can use the same license information that they already have; it will work for version 5.0 for the remainder of their license periods.

- Project files generated with previous versions are automatically converted to version 5.0 project files. Users are notified of that by the software, and given the opportunity not to convert the files if they so wish.

- The MATLAB Compiler Runtime 7.14, used in this version, is the same as the one used in versions 2.0-4.0. Therefore, if you already have one of those versions of WarpPLS installed on your computer, you should not reinstall the Runtime.

WarpPLS is a powerful PLS-based structural equation modeling (SEM) software. Since its first release in 2009, its user base has grown steadily, now comprising more than 7,000 users in over 33 countries.

Some of its most distinguishing features are the following:

- Very easy to use, with a step-by-step user interface guide.

- Implements classic (composite-based) as well as factor-based PLS algorithms.

- Identifies nonlinear relationships, and estimates path coefficients accordingly.

- Also models linear relationships, using classic and factor-based PLS algorithms.

- Models reflective and formative variables, as well as moderating effects.

- Calculates P values, model fit and quality indices, and full collinearity coefficients.

- Calculates indirect effects for paths with 2, 3 etc. segments; as well as total effects.

- Calculates several causality assessment coefficients.

- Provides a number of graphs, including zoomed 2D graphs, and 3D graphs.

At the beginning of the User Manual you will see a list of new features in this version, some of which are listed below together with related YouTube videos. The User Manual has more details on how these new features can be useful in SEM analyses.

- There has been a long and in some instances fairly antagonistic debate among proponents and detractors of the use of Wold’s original PLS algorithms in the context of 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 new factor-based algorithms provided in this version have been developed specifically to address this perceived limitation of Wold’s original PLS algorithms.

Related YouTube video:
Conduct a Factor-Based PLS-SEM Analysis with WarpPLS

- An extended set of descriptive statistics is now provided for both indicators and latent variables. The descriptive statistics provided include: minimum and maximum values, medians, modes, skewness and excess kurtosis coefficients, as well as results of unimodality and normality tests. These are now complemented by histograms, which can be viewed on the screen and saved as files.

- Often the use of PLS-based SEM methods is justified based on them making no data normality assumptions, but typically without any accompanying test of normality! This is addressed in this version through various outputs of unimodality and normality tests, which are now provided for all indicators and latent variables.

Related YouTube video:
View Skewness and Kurtosis in WarpPLS

- Rocky and smooth 3D graphs can now be viewed with data points excluded. Corresponding graphs with data points included are also available. The 3D graph displays with data points excluded are analogous to those used in the focused 2D graphs. Additionally, users can now incrementally rotate 3D graphs in the following directions: up, down, left, and right.

Related YouTube video:
View Moderating Effects via 3D and 2D Graphs in WarpPLS

- An extended set of “stable” P value calculation methods is now available to users: Stable1, Stable2, and Stable3. The Stable1 method was the software’s default up until version 4.0, when it was called simply the “stable” method. The Stable2 and Stable3 methods have been developed as alternatives to the Stable1 method that rely on the direct application of exponential smoothing formulas, and that can thus be more easily implemented and tested by methodological researchers.

- Several missing data imputation methods are now available to users: Arithmetic Mean Imputation (the software’s default), Multiple Regression Imputation, Hierarchical Regression Imputation, Stochastic Multiple Regression Imputation, and Stochastic Hierarchical Regression Imputation. Extensive simulations suggest that these methods perform fairly well in the context of PLS-based SEM (including Arithmetic Mean Imputation), even with as much as 30 percent of data missing.

Related YouTube video:
View and Change Missing Data Imputation Settings in WarpPLS