## PLS Algorithm vs PLSc Algorithm LVscores issue

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KIHO KWON
PLS Junior User
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Joined: Tue May 15, 2018 1:37 am
Real name and title: Mr. KIHO KWON

### PLS Algorithm vs PLSc Algorithm LVscores issue

hi.
when I use PLS Algorithm, the results show up Latent Variable scores.
On the other hand, when I use PLSc Algorithm, Latent Variable scores is not shown in smartpls3.
I can only see Latent variable correlations and covariances.

May I ask why this kind of situation happen?
If I want Latent variable scores in smartpls3, Should I use only PLS Algorithm?

My model has reflective-reflective 2nd order construct. So I'd like to use two-step approach as my references did.
Therefore, I have to get Latent Variable scores.

jmbecker
SmartPLS Developer
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Joined: Tue Mar 28, 2006 11:09 am
Real name and title: Dr. Jan-Michael Becker

### Re: PLS Algorithm vs PLSc Algorithm LVscores issue

KIHO KWON wrote:
Wed May 16, 2018 1:55 am
If I want Latent variable scores in smartpls3, Should I use only PLS Algorithm?
Yes!

The reason is quite simple: PLSc tries to mimic a common factor model. However, in a common factor model there is not one determinate set of factor (or latent variable) scores that is consistent with the model. There are an infinite many possible scores. The problem is called factor indeterminacy. Therefore, it is not possible to provide a LV score.
PLS on the other side is a method of composites. It explicitly uses the latent variables scores as part of its estimation process. Therefore, you get on set of LV scores that are consistent with your results (i.e., loadings, path coefficients, weights, etc.).

If you have a higher-order construct it would be possible to use the two-stage approach with PLSc only on the second-stage. But you need to manually calculate and set the reliability of the second stage higher-order construct (you can do that by double-clicking on the LV in the path diagramm).
Dr. Jan-Michael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de

AAljabr
PLS Expert User
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Joined: Wed Jan 06, 2016 11:52 pm
Real name and title: Abdulrahman Aljabr

### Re: PLS Algorithm vs PLSc Algorithm LVscores issue

Hello,

Many thanks for discussing this important topic.

As PLS estimates composites, which themselves, according to a group of researchers, can be reflective or formative [see Sarstedt et al (2016)], does the factor indeterminacy issue exist for reflective composites?

Another group of PLS researchers seem to follow the classification of common factors (i.e., reflective constructs), causal formative constructs and composite formative constructs [e.g., Henseler (2017)]. Given PLS's ability to estimate reflective constructs (i.e., common factors) and composite formative constructs, following this construct classification indicates that reflective constructs estimated by PLS may suffer the factor indeterminacy issue. Is this correct?

Many thanks

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.[/size]

Henseler, J. (2017). Bridging design and behavioural research with variance-based structural equation modeling. Journal of advertising, 46(1), 178-192

jmbecker
SmartPLS Developer
Posts: 1129
Joined: Tue Mar 28, 2006 11:09 am
Real name and title: Dr. Jan-Michael Becker

### Re: PLS Algorithm vs PLSc Algorithm LVscores issue

You need to distinguish between the conceptual (theoretical) orientation of the construct (reflective, formative) and the statistical tool to estimate constructs (composites or common factors).

In standard PLS all constructs are estimated using composites. Composites are always determinate and thus you will get a latent variable score for them, regardless of whether you think the construct is reflective or formative. The estimation of the composite is usually slightly different (assuming Mode A for reflective and Mode B for formative constructs), but they are always composites.

In PLSc the results of all parameters that involve a reflective constructs are corrected to reflect common factor model relations. Thus, you use initially a normal PLS model with composites (which have a latent variable score), but then you transform the results to mimic a common factor model. The initial composite results (and thus the latent variable scores) are then not anymore conformable with the new results. Thus, we do not provide latent variable scores in PLSc as they do not conform to the results of the common factor model (because common factors are indeterminate and there exist no one single latent variable score like for composites).
Dr. Jan-Michael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de

AAljabr
PLS Expert User
Posts: 33
Joined: Wed Jan 06, 2016 11:52 pm
Real name and title: Abdulrahman Aljabr

### Re: PLS Algorithm vs PLSc Algorithm LVscores issue

Dear Dr. Becker,

Many thanks for the clarification.

Best regards,