Multi-Group analysis in WarpPls (measurement invariance)

[Kunal]

Hi Everyone,

I'm using WarpPls and after examining the path coefficients of the two different groups for significant differences I wanted to establish measurement invariance to ensure that the same construct is being measured across the  specified groups).

Now for analysing path cooefficiant differences im applying the pooled standard error method using the excel Spreadsheet provided by Ned: http://www.scriptwarp.com/warppls/rscs/Kock_2013_MultiGroup.xls
This analysis is fine.

Now to establish measurement invariance I am using the same spreadsheet. However I was wondering weather I use item loadings or indicator weights. I was under the impression that item loadings are used but I read a paper from Neds doctrol student and in it indicator weights are used.

Can someone please clarify?

And to further deepen the discussion: Regarding measurement invariance is there any rule of thumb that indicates how many items per construct can be significantly different before it can be declared that measurement invariance for the specific construct is not given (for example if in a 3 item construct 1 item is significantly different between the two groups can the construct still be used in multi-Group analysis)?

Thx for your input

Best regards,
Kunal Mohan, Ph.D, MBA

[José Luis Roldán]

Dear Kunal,

Perhaps, the below paper could be useful for you.

Multi-Group Invariance Testing: An Illustrative Comparison of PLS Permutation and Covariance-Based SEM Invariance Analysis
Wynne W. Chin, Annette M. Mills, Douglas J. Steel, and Andrew Schwarz

Proceedings: 7th International Conference on Partial Least Squares and Related Methods 1 May 19-May 22, 2012 • Houston, Texas, USA

https://www.dropbox.com/s/5g9pthibim98xs7/PLS2012_Chin_Mills_etal.pdf

Best regards,

José L. Roldán

José L. Roldán

jlro...@us.es

http://personal.us.es/jlroldan

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[Ned Kock]

I think this is a good question Kunal.

 

Since each LV score is ultimately calculated by multiplying the weights and the indicator scores, I would suggest using the weights. The weights are the key components of the measurement model.

 

In PLS algorithms each LV score is ultimately calculated as a weighted sum of its indicators, regardless of whether the LV refers to a formative or reflective construct, or calculated using a “reflective mode” or “formative mode” (e.g., PLS modes A or B, respectively).

 

In practice, using weights or loadings should not make a big difference in the measurement invariance test using the multi-group comparison formula in Excel, because the weights and loadings (unrotated) are redundant measures.

 

Using weights also helps avoid confusion. There is only one value reported for each weight by WarpPLS. There is more than one reported for each loading, as WarpPLS also reports rotated loadings.

 

The paper linked by Jose is also very good. I am linking it again below for clarity, so that everybody knows what we are referring to.

 

https://www.dropbox.com/s/5g9pthibim98xs7/PLS2012_Chin_Mills_etal.pdf

 

This paper compares a CB-SEM approach (using the chi-squared statistic) with a PLS-SEM permutation approach for testing measurement invariance. Unfortunately, this approach is not implemented in WarpPLS as described.

 

As a side note, you cannot go wrong reading papers by Wynne Chin and some of his close collaborators, such as Jason Thatcher and Annette Mills.

 

I had the opportunity to chat with Wynne recently (a few days ago). He is always helpful, a gentleman, and a genius.

 

I happen to like contrarian views as well, such as those of Dale Goodhue and colleagues (see link below) and of Mikko Rönkkö and colleagues. I also met and chatted with Dale and Ron a few days ago. Contrarian views, when put forth in a scholarly way, invariably lead to scientific progress.

 

http://www.misq.org/does-pls-have-advantages-for-small-sample-size-or-non-normal-data.html

 

I hope some of these folks will join us at the PLS Applications Symposium, where hopefully we’ll be able to distill key lessons in terms that are accessible to PLS users.

 

http://plsas.net

 

Scholarly debate is always useful, in my opinion. Unfortunately it often tends to become polarized and personal.

 

Ned

[David Gefen]

You may also wish to consult the MISQ guidelines at

 

Gefen, David , Rigdon, Ed and Straub, Detmar W. “An Update and Extension to SEM Guidelines for Administrative and Social Science Research” MANAGEMENT INFORMATION SYSTEMS QUARTERLY 35.2 (Jun 2011)III-XIV

 

              David

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[ela...@yahoo.com]

Hi,

After reading regarding use of Multi group Analysis, I have another question. suppose you have developed a model and you want to see weather there is any difference between SME's Vs Large scale enterprises. Suppose that you divide the data into two groups as per SME and Large Scale enterprises. You run the analysis separately for each group and find significant difference across the groups. Does it mean that your industry type has acted as a moderator.  This is very crucial.. as checking invariance across the groups is quite common in operations management domain. So if the Beta value of the paths changes , it ultimately also means that type of industry has a significant influence.. is this approach means that there is moderation.

[Ned Kock]

Hi Kunal.

 

Indeed, a multi-group analysis is in fact a moderating effects analysis, where the grouping variable is the moderator. However, there is a twist to this story.

 

Before going into the twist, here is an example of one such analysis in the context of PLS-based SEM.

 

Let us say you collected data in two different countries. When you do a multi-group analysis employing one of the procedures discussed in the blog post linked below, you are doing the equivalent to testing the moderating effect of the variable country on each of the paths in your model.

 

http://bit.ly/15wbflh

 

The twist is that a traditional multi-group analysis (as in the link provided above) would “hide” the multivariate adjustments that would happen if the interaction variables were added to the model.

 

In other words, in traditional multi-group analyses the interaction variables associated with the moderating effects, one for each path, are not included in the model.

 

Given this, results of traditional multi-group analyses should be taken with caution, as the multivariate interactions and their effects, which will be “hidden”, could significantly alter the results and related interpretations.

 

This can be particularly problematic when the interaction variables, if added to the model, would have led to full collinearity VIFs greater than 3.3. See article below, available in full-text format from http://warppls.com.

 

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.

 

This is an example of the many pressing PLS-based SEM methodological issues that need attention. We need multi-group tests with outputs that allow researchers to rule out the possibility of problems associated with “hiding” the effects of multivariate adjustments.

 

At this point my suggestion to those using traditional multi-group analyses in the context of PLS-based SEM is to include a note of caution in their papers about the possible problems discussed above.

 

Ned

[CMR]

Hi

 

This article might be useful to take a look at moderation, nonlinear effects and multi-group analysis:

·         Rigdon, E. E., Ringle, C. M., & Sarstedt, M. 2010. Structural Modeling of Heterogeneous Data with Partial Least Squares. In N. K. Malhotra (Ed.), Review of Marketing Research: 255-296. Armonk: Sharpe.

 

You may want to check this article on PLS-SEM multi-group analysis (PLS-MGA):

·         Sarstedt, M., Henseler, J., & Ringle, C. M. 2011. Multi-Group Analysis in Partial Least Squares (PLS) Path Modeling: Alternative Methods and Empirical Results. In M. Sarstedt, M. Schwaiger and C. R. Taylor (Eds.), Advances in International Marketing, Volume 22: 195-218: Emerald Group Publishing Limited.
http://www.marketing.ovgu.de/marketing_media/Forschung/Publikation/2011_Sarstedt_et_al.pdf

·         Rigdon, E. E., Ringle, C. M., Sarstedt, M., & Gudergan, S. P. 2011. Assessing Heterogeneity in Customer Satisfaction Studies: Across Industry Similarities and Within Industry Differences. Advances in International Marketing, 22: 169-194.

 

In these articles, we call for a check of  heterogeneity as standard evaluation in PLS-SEM:

·         Becker, J.-M., Rai, A., Ringle, C. M., & Völckner, F. 2013. Discovering Unobserved Heterogeneity in Structural Equation Models to Avert Validity Threats. MIS Quarterly, 37(3): 665-694.

·         Hair, J. F., Sarstedt, M., Ringle, C. M., & Mena, J. A. 2012. An Assessment of the Use of Partial Least Squares Structural Equation Modeling in Marketing Research. Journal of the Academy of Marketing Science, 40(3): 414-433.

·         Hair, J. F., Ringle, C. M., & Sarstedt, M. 2013. Partial Least Squares Structural Equation Modeling: Rigorous Applications, Better Results and Higher Acceptance. Long Range Planning, 46(1-2): 1-12.

 

Besides, here are some other articles, which tackle the issue of segmentation and heterogeneity in PLS-SEM:

·         Ringle, C. M., Sarstedt, M., & Mooi, E. A. 2010. Response-Based Segmentation Using Finite Mixture Partial Least Squares: Theoretical Foundations and an Application to American Customer Satisfaction Index Data. Annals of Information Systems, 8: 19-49.

·         Ringle, C. M., Sarstedt, M., Schlittgen, R., & Taylor, C. R. 2013. PLS Path Modeling and Evolutionary Segmentation. Journal of Business Research, 66(9): 1318-1324.

·         Ringle, C. M., Sarstedt, M., & Schlittgen, R. 2013. Genetic Algorithm Segmentation in Partial Least Squares Structural Equation Modeling. OR Spectrum, DOI: 10.1007/s00291-013-0320-0.

·         Ringle, C. M., Sarstedt, M., & Zimmermann, L. 2011. Customer Satisfaction with Commercial Airlines: The Role of Perceived Safety and Purpose of Travel. Journal of Marketing Theory and Practice, 19(4): 459-472.

·         Ringle, C. M., Wende, S., & Will, A. 2010. Finite Mixture Partial Least Squares Analysis: Methodology and Numerical Examples. In V. Esposito Vinzi, W. W. Chin, J. Henseler and H. Wang (Eds.), Handbook of Partial Least Squares: Concepts, Methods and Applications  (Springer Handbooks of Computational Statistics Series, vol. II): 195-218. Heidelberg, Dordrecht, London, New York: Springer.

·         Sarstedt, M. 2008. A Review of Recent Approaches for Capturing Heterogeneity in Partial Least Squares Path Modelling. Journal of Modelling in Management, 3(2): 140-161.

·         Sarstedt, M., Becker, J.-M., Ringle, C. M., & Schwaiger, M. 2011. Uncovering and Treating Unobserved Heterogeneity with FIMIX-PLS: Which Model Selection Criterion Provides an Appropriate Number of Segments? Schmalenbach Business Review, 63(1): 34-62.

·         Sarstedt, M., & Ringle, C. M. 2010. Treating Unobserved Heterogeneity in PLS Path Modelling: A Comparison of FIMIX-PLS with Different Data Analysis Strategies. Journal of Applied Statistics, 37(8): 1299-1318.

·         Sarstedt, M., Schwaiger, M., & Ringle, C. M. 2009. Do We Fully Understand the Critical Success Factors of Customer Satisfaction with Industrial Goods? - Extending Festge and Schwaiger’s Model to Account for Unobserved Heterogeneity. Journal of Business Market Management, 3(3): 185-206.

·         Völckner, F., Sattler, H., Hennig-Thurau, T., & Ringle, C. M. 2010. The Role of Parent Brand Quality for Service Brand Extension Success. Journal of Service Research, 13(4): 359-361.

 

You may want to check www.smartpls.de à Announcements à Literature to access these articles

 

Best

Christian Ringle

www.tuhh.de/hrmo