Applying POS-PLS

[Maximilian]

Hi everyone,

first of all, thanks for providing this forum! It really helps with some issues regarding SmartPLS! I've got two questions regarding POS-PLS.

1. The first one is probably pretty simple to answer, however, I just want to make sure. When applying POS-PLS, I get segment assignments for all "units". I'm wondering, how they are corresponding to my original data set. For example, "unit 0" is assigned to segment 2. How do I know, which of my survey participant is "unit 0"? Is it as simple as just copying the segment assignment and pasting it as new column into my original data set? Are the participants of both data sets (the segment assignment and the original data set) in the same order automatically?

2. The other question is more general. There are several options, when conducting POS-PLS. I can choose to do an initial separation by RANDOM ASSIGNMENT or FIMIX SEGMENTATION. In Hair and Hult (2016): A Primer on PLS-SEM it is suggested to first run FIMIX-PLS and only afterwards running POS-PLS with the sgment number suggested by FIMIX-PLS, does that mean, FIMIX-Sgmentation should be used as initial separation? And shall I use pre-segmentation additionally in the first round? And what kind of optimization criteion can be recommended?

Scholars opinions on these matters would be highly appreciated since I cannot find any answers to these questions online.

Thanks you so much in advance,
Max

[jmbecker]

1. Yes.

2. In applications of the PLS-POS we found that it works quite well based on a FIMIX-PLS starting solution. In addition, you have the advantage of determining the number of segments in FIMIX-PLS. Thus, I would generally recommend this. Only if this gives very strange results or you expect strong heterogeneity in your formative measures, I would use the random assignment with the pre-segmentation in the first round (this is the original PLS-POS algorithm). It does not make sense to combine FIMIX and pre-segmentation as the pre-segmentation would "overwrite" the FIMIX solution.
In the published simulations we only used "Sum of all construct R-Squares". It works quite well when you have very well defined groups (strong heterogeneity). If heterogeneity is not so well defined it might give you a solution with one smaller exceptionally good group (i.e., high R²) and one larger bad group (i.e, low R²). Thus, it separates well predicting from not so well predicting observation. That might sometimes be useful, but we found that the groups are often hard to interpret (especially the bad group with low R²). In contrast, we found in many applications that the segmentation solution is often better interpretable with "Sum of all construct Weighted R-Squares" as it improves groups more equally.
The difference between "all constructs" and "target construct" is that you can choose a construct for which the R² will be optimized in the segmentation process. This is only meaningful if you have a strong focus on that target construct (for example, in a customer satisfaction study on satisfaction) and are not particularly interested in explaining the other constructs. Usually you would want to optimize the whole model. If you have only one endogenous (dependent) construct there is no difference between the two options.

[Maximilian]

Dear Dr. Becker,

Thank you so much für your fast and precise answer! It really is helpful.

Unfortunately, some questions remain:
1. Is FIMIX-PLS even applicable when my data is non-normally distributed at all (Likert Scales).
2. Is POS-PLS able to handle reflective-reflective higher-order constructs / second-order constructs? I’ve got one within my model (credibility) and I am asking, because the R^2 matrix shows R^2s for my two lower order construct (trustworthiness and expertise) and tries to optimize them, which seems kind of strange to me.
3. Fortunately, average R^2s are given, when applying POS-PLS, so that one can easily compare different segment solutions regarding their explanatory power, however, Q^2s are not given. Is there any possibility to compare average Q^2s amongst the different sgment-solutions without actually performing the PLS algorithm for every segment in all the different segment-solutions?

I ask these questions, since (according to my interpretation) so far neither the FIMIX-PLS, nor the POS-PLS (random assignment, pre-segmentation) suggests a single clear segmentation possibility, especially not since results vary a lot when applying the algorithm several times (see attachment).

However, there seems to be unobserved heterogeneity, which is why I want to define segments.

Thanks for any comment or suggestion!

[jmbecker]

1. It depends on the level of non-normality. In my experience Mixture-Algorithms work quite well with modest deviations from normality. If you have highly skewed data (exponential family, etc.) they don't work as well.

2. Good questions. I have never tried that. The questions would be: do you expect heterogeneity within your second-order model or not? If not, you can only optimize by target construct. Otherwise the second-order model will always be part of the optimization procedure.
Using the two-stage approach could help. Although it is not recommended for reflective-reflective type models, the difference is usually quite small.

3. No. You have to calculate Q² for your final segmentation solution by applying Blindfolding separately.

[Maximilian]

Dear Dr. Becker,

thank you very much for your helpful answer. I did as you suggested. The only thing I'm, still wondering about is the fact that path coefficients as well as R^2s change tremendously when I run the algorithm several times. Especially path coefficients vary a lot. Is there a certain procedure to follow, or how do I pick one of the segment solutions (most of them are not interpretable very good, while others deliver good results)?