PLS is broadly applied in modern business research. This forum is the right place for discussions on the use of PLS in the fields of Marketing, Strategic Management, Information Technology etc.
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Real name and title: Abdulrahman Aljabr


Post by AAljabr » Mon Jan 18, 2016 3:22 pm

Hi all,

I have read the paper "Testing Measurement Invariance of Composites Using Partial Least Squares". Also, I have consulted other related papers (Henseler et al. 2016) and (Rigdon, 2012).

Regarding the issue related to the composites and factors, what I understood from the paper "Testing measurement invariance of composites using partial least squares", is that all constructs in PLS are composites, and these composites can be built on either formative or reflective measurement models. Also, in the empirical example section, the authors used the MICOM model invaraince test with formative and reflective constructs.

On page 20 and 21:
" We use the corporate reputation model (Schwaiger, 2004), as shown with its latent variables in
Figure 5, to provide a MICOM example with empirical data......... While the exogenous latent variables
(i.e., QUAL, PERF, CSOR, ATTR) represent composites that build on a formative measurement model
(Mode A), the endogenous latent variables (i.e., LIKE, COMP, CUSL) are composites with a reflective
measurement model (Mode A)

However, what I understood from Henseler et al 2016 paper "PLS path modeling in new technology research: updated guidelins", is that PLS can contain two types of constructs, namely, factors and composites.

On page 4:
"PLS path models can contain two different forms of construct measurement: factor
models or composite models (see Rigdon, 2012, for a nice comparison of both types
of measurement models). The factor model hypothesizes that the variance of a set of
indicators can be perfectly explained by the existence of one unobserved variable (the
common factor) and individual random error. It is the standard model of behavioral
research. In Figure 1, the exogenous construct ξ and the endogenous construct η are
modeled as factors. In contrast, composites are formed as linear combinations of their
respective indicators. The composite model does not impose any restrictions on the
covariances between indicators of the same construct, i.e. it relaxes the assumption that
all the covariation between a block of indicators is explained by a common factor.
The composites serve as proxies for the scientific concept under investigation
(Ketterlinus et al., 1989; Rigdon, 2012; Maraun and Halpin, 2008; Tenenhaus, 2008)[1].
The fact that composite models are less restrictive than factor models makes it likely
that they have a higher overall model fit (Landis et al., 2000).

On page 6:
"In some PLS path modeling software (e.g. SmartPLS and PLS-Graph), the depicted
direction of arrows in the measurement model does not indicate whether a factor or
composite model is estimated, but whether correlation weights (Mode A, represented by
arrows pointing from a construct to its indicators) or regression weights (Mode B,
represented by arrows pointing from indicators to their construct) shall be used to create
the proxy. In both cases PLS will estimate a composite model. Indicator weights estimated
by Mode B are consistent (Dijkstra, 2010) whereas indicators weights estimated by
Mode A are not, but the latter excel in out-of-sample prediction (Rigdon, 2012)

In addition, what I understood is that MICOM is suitable for composites, and there are other model invariance tests for factor models.
On page 13:
"There is a plethora of papers discussing how to assess the measurement invariance of factor
models (see e.g. French and Finch, 2006), there is only one approach for assessing the
measurement invariance of composite models (Henseler et al., forthcoming).

From the above, the distinction between reflective constructs and factor models is not clear to me.

1. What is the real difference between reflective constructs and factor models? What would be a reflective composite and what would be a factor? And how the difference is transferred to the PLS context in terms of model specification?

2. Can I use the MICOM for both reflective and formative constructs? if not, how can I test for measurement model invariance test for reflective constructs. I could not find a suitable model invariance test for reflective constructs that is available in SmartPLS 3. The program provides the permutation p values for the difference between the two groups in terms of, for example, AVE and composite reliability. Should I use these for reflective constructs? Isn't similar to Ringle et al. (2011) approach when they tested for measurement invariance for their model's reflective constructs.


Henseler, J., Hubona, G., & Ray, P. A. (2016). Using PLS path modeling in new technology research: updated guidelines. Industrial Management & Data Systems, 116(1), 2-20

Henseler, J., Ringle, C.M. and Sarstedt, M. (forthcoming), “Testing measurement invariance of
composites using partial least squares”, International Marketing Review (in print).

Rigdon, E.E. (2012), "Rethinking partial least squares path modeling: in praise of simple
methods", Long Range Planning, Vol. 45 Nos 5/6, pp. 341-358.

Ringle, C. M., Sarstedt, M. and Zimmermann, L. (2011), "Customer Satisfaction with Commercial
Airlines: The Role of Perceived Safety and Purpose of Travel", Journal of Marketing Theory and
Practice, Vol. 19 No. 4, pp. 459-472.

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Post by janschreier » Sun Jul 17, 2016 9:04 pm

hi there,

I know this post is quite old, but right now I am thinking about the same issues and would be glad to see some experts join the discussion.

A good source for further reading should be this paper (it actually has a literal quote of your question in it ;):
Estimation issues with PLS and CBSEM: Where the bias lies!
by Sarstedt et al. 2016 ... D&el=1_x_3

in this paper, this one is also mentioned: ... ion_Models

from my understanding I would give the following remarks to your questions:
- in a factor model you are talking about the underlying factors that cannot be directly measured but can only be made visible by watching at indicators that (partially) reflect the factors. Thus a factor model is always reflective.

For now that's my two cents and I will re-read the papers mentioned by you and me again to find an answer (and hope for somebody else to join the discussion)

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Post by Piddzilla » Tue Nov 22, 2016 11:30 am


I am also struggling to understand the difference between common factors and composites in a PLS setting.

There seems to be a difference between the common factors/composites distinction on the one hand and reflective models/formative models distinction on the other. At the same time, I have never seen any good examples in the literature of a composite that has not been formatively modelled. I think it would be a good idea, for the sake of clarity, to include such examples in the tutorials and text books etc.

Also, to make things even more confusing, according to the literature, SmartPLS assumes that models are composite models, which means that reflective models (Mode A) would be treated as composite models by default. The PLSc algorithm is, as far as I understand, the method one should use when analyzing a common factor model. This implies that there is a difference between Mode A in PLS and Mode A in PLSc and that this difference has more to do with the common factor/composite distinction than with the reflective/formative distinction. Also, I have read that PLSc should not be treated merely as a "more strict" PLS algorithm, since it is based on a fundamentally different measurement philosophy with goals that are more in line with CB-SEM than with PLS-SEM. Then I read other sources that claim that PLS works just fine for common factor models as well.

So, how do I know if my model is a common factor model or a reflective composite model? What is the difference? Is the difference, if any, purely theoretical, or does it affect the choices I have to make in SmartPLS and what estimates I should focus on? What would be the possible consequences on estimations, results, and so forth if one, i.e., models data as composites when, in fact, they should be treated as common factors? What would be a typical (empirical) example of a set of reflective composite indicators compared to typical set of common factor indicators?

As far as I understand, it is crucial to sort out whether your data come from a "common factor population" or from a "composite population" before proceeding with the SEM analysis. How I make this distinction is what I would like to find out.

Thank you!

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Real name and title: Jan Schreier


Post by janschreier » Tue Nov 22, 2016 3:05 pm

hi Peter,

you ask excellent questions. To put it simple, I would say that the diversion from formative/reflective towards composite/common factor is a still ongoing discussion between the methodolgists that advance PLS.
Now I see three types of PLS users: the first group just take the existings methods and apply them to their data and walk away with the results, while (few) others in the second group seek to understand what the methods do and where the issues lie but their main focus is their orginial research and PLS is just a tool, for the third group PLS is a main research subject itself. As soon as people from the first group face a strict reviewer, they end up in the second group, too ;)
(persons of group one would stop reading here and walk away with simply saying composite instead of formative and common factor instead of reflective from now on)

at the moment the gap between group three and two for my perspective is quite large as it requires to read a lot of papers and also sometimes to have some background knowledge on relevant players in those discussions. currently I think the best method to close your own knowledge-gap is either to read a lot and discuss online (from my point of view, the best place is the SEMNET mailing lists archives to be found here: ), or to visit trainings or conferences where you can directly discuss with the major stakeholders personally.

hope that helps and maybe someone reads this and decides to create some youtube videos or short articles that give practical answers to the latest developments in PLS.

best regards, Jan

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Post by Piddzilla » Wed Nov 23, 2016 11:23 am

Hi Jan and thanks for your quick reply!

Ok, then my gut feeling the last few days has been correct - that this is an ongoing discussion and maybe there is no clear answer to all questions. I definitely belong to group two and I try to read as much as I can about the most recent findings and guidlines for this.

/ Peter

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Real name and title: Abdulrahman Aljabr


Post by AAljabr » Thu Dec 29, 2016 1:33 pm

Hi All,

Please read the following paper, which I found to be very helpful:
Sarstedt, M., Hair, J. F., Ringle, C. M., Thiele, K. O., & Gudergan, S. P. (2016). Estimation issues with PLS and CBSEM: Where the bias lies!. Journal of Business Research, 69(10), 3998-4010.

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