Modeling HCMs

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katarina86
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Real name and title: PhD Katarina Njegic Assistant Professor

Modeling HCMs

Post by katarina86 »

Hi everyone! I read the book Advanced Issues in PLS-SEM and it's great! I learned a lot of new things! However, I have some questions regarding HCMs that I couldn't find the answer on.

I have a model that has two HOCs, that are both reflective-formative: Market orientation (MO), that consists of 3 reflective LOCs, and export performance(EP) that consists of two LOCs. I also have 3 first order constructs in the model, and I want to check if MO affects EP indirectly through competitive advantage (it is a first order construct).

My questions are:
Which is the best approach to use in this situation- repeated indicator or two-stage?
How to calculate the indirect effect MO->CompetitiveAdv->EP when I use repeated indicator approach? In the section "Specific Indirect Effects" this effect is not statistically significant, but the effects MO->CompAdv->StratEP and MO->CompAdv->EconEP are both significant. Also, when I use repeated indicator, I don't know how to calculate R2 for HOCs.
When I use two-stage approach: I'm not sure how should I model first-order constructs on the second stage. Should I use latent variable scores as indicators for the first-order constructs on the second stage, or should I use again all the indicators that I used in the first stage. I'm also not sure when to do the analysis of unobserved heterogeneity- on the first or on the second stage?

Thank you for the answers,
Katarina
jmbecker
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Real name and title: Dr. Jan-Michael Becker

Re: Modeling HCMs

Post by jmbecker »

1) You may read the paper by Becker, J. M., Klein, K., & Wetzels, M. (2012). Hierarchical latent variable models in PLS-SEM: guidelines for using reflective-formative type models. Long Range Planning, 45(5-6), 359-394. They provide recommendations on when to use repeated or two-stage approach.
Generally, I found it in empirical applications that the sample size does matter. Two-stage appears to be more robust with smaller sample sizes, while repeated-indicator approach is better with larger sample sizes, but generally they should not differ much.
In your case I would probably use the two-stage approach because it is indeed easier to interpret the mediation, because the repeated-indicator approach you also need to take the effects via the lower order constructs.
For the first-order constructs that are not part of a higher-order construct you want to model them with all their original indicators in the second stage.

If you want to analyze unobserved heterogeneity, it depends on where you expect heterogeneity. In the paths on the higher-level? In the (measurement) relations of the lower-level? Both?
In the first case you can use the second stage model. In the second and third case you are probably better of using a repeated indicator approach.

Do you have enough data points for such a complex model + heterogeneity analysis (i.e., grouping of the data which needs minimum requirements for each group).
Dr. Jan-Michael Becker, BI Norwegian Business School, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de
katarina86
PLS Junior User
Posts: 7
Joined: Thu Feb 21, 2019 9:44 am
Real name and title: PhD Katarina Njegic Assistant Professor

Re: Modeling HCMs

Post by katarina86 »

Dear Professor Backer,

Thank you very much for all the answers. I also read the paper you suggested and it helped me a lot to understand better HCMs.

Regarding unobserved heterogeneity, I wanted to test it in order to see if it affects results substantially and to obtain the evidence that the results are valid. I have 121 observations, and the model has 4 independent variables and maximum of 5 arrows pointing at a construct. I ran FIMIX Segmentation procedure (with repeated indicator approach) and I obtained the results I attached. Based on the AIC4 and BIC, one segment solution is better, but is it enough to conclude that the heterogeneity does not affect the results, or should I also run POS?

Thank you very much for your time and dedication!

Kind regards,
Katarina
Attachments
segment sizes
segment sizes
2.png (3.96 KiB) Viewed 65044 times
Fit Indices
Fit Indices
1.png (15.33 KiB) Viewed 65045 times
jmbecker
SmartPLS Developer
Posts: 1281
Joined: Tue Mar 28, 2006 11:09 am
Real name and title: Dr. Jan-Michael Becker

Re: Modeling HCMs

Post by jmbecker »

Purely based on the AIC4 and BIC you cannot conclude that no heterogeneity exists.
First, you should better use AIC3 and CAIC as advised in Sarstedt, Marko, Jan-Michael Becker, Christian Ringle and Manfred Schwaiger (2011). Uncovering and Treating Unobserved Heterogeneity with FIMIX-PLS: Which Model Selection Criterion Provides an Appropriate Number of Segments?, Schmalenbach Business Review, 63 (1), 139-151.
If they agree and show only one segment you have a large likelihood that no heterogeneity exists. However, if they do not agree, there may be any segement between CAIC (lower bound) and AIC3 (upper bound) possible (including those that they indicate). For example, CAIC pointing at 1 and AIC3 pointing at 4, then it could be 1, 2, 3, or 4 segments.

Sarstedt, Ringle, and Hair (2018) show a systematic process of applying FIMIX that is strongly data driven and also includes the EN criterion.

Becker et al. (2013) develop a more theory driven approach to uncover heterogeneity and to determine the number of segments.

Nevertheless, you datasize is quite small to uncover unobserved heterogeneity. To estimate latent segments you actually want to have a sample size of at least a 100 per segment I would recommend.

Sarstedt, M., Christian M. Ringle, and Hair, J. F. (2018). Treating Unobserved Heterogeneity in PLS-SEM: A Multi-method Approach. In H. Latan & R. Noonan (Eds.), Partial least squares structural equation modeling: Basic concepts, methodological issues and applications. New York: Springer.
Becker, J.-M., A. Rai, C. M. Ringle, and F. Völckner (2013). "Discovering Unobserved Heterogeneity in Structural Equation Models to Avert Validity Threats." MIS Quarterly, 37(3), 665-694.
Dr. Jan-Michael Becker, BI Norwegian Business School, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de
katarina86
PLS Junior User
Posts: 7
Joined: Thu Feb 21, 2019 9:44 am
Real name and title: PhD Katarina Njegic Assistant Professor

Re: Modeling HCMs

Post by katarina86 »

Thank you very much, professor, for all the answers and the literature. It is really helpful.

Best wishes,
Katarina
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