sample size requirements

[Ahamed AFM Jalal]

Dear All,

The question I am going to ask may be a silly one to some of you, however I am asking for some expert opinion.

I have a very simple model with three latent variables, namely A,B,C, where A affect B, and B affect C. A has 5 items, B has 5 items and C has 4 items. There is a moderator “language skill” which moderate A to B and B to C relationship. Two groups of people are in the language skill category, one who knows 2 languages and the rest. All together I have 56 sets of data.

Now, it would be my pleasure to know is a sample size of 56 is enough to run the aforesaid model in WarpPls? Any alternative suggestion is appreciable.

Best regards

Jalal Ahamed  

[Ned Kock]

A small sample size requirement is often mentioned as one of the attractive characteristics of PLS-based SEM.

 

So what is the minimum sample size for a PLS-based SEM analysis?

 

I will answer this now in a simplified way, based on the notion of degrees of freedom. Later I will give a more thorough answer based on effect size (and thus statistical power) considerations as well.

 

Based on ideas underlying the theory of degrees of freedom (Walker, 1940) applied to regression, a reasonable estimate of the minimum required sample size is 10 times the maximum number of variables (manifest or latent) influencing the calculation of latent variable scores in the latent variable equations (outer or inner).

 

To illustrate what this means, let us consider a model with three latent variables: A, B and C. Let us assume that A and B point at C; and that A has 5 indicators, B has 3 indicators, and C has 7 indicators.

 

If the inner model is NOT allowed to influence the outer model, the minimum required sample size is 10x7=70. This is the case with WarpPLS; the inner model is NOT allowed to influence the outer model, no matter what algorithm is chosen – even if the algorithm is nonlinear.

 

If the inner model is allowed to influence the outer model, the minimum required sample size is 10x(7+2)=90. This is the case with software tools that conduct PLS-based SEM through one of Lohmöller’s (1989) “good neighbor” modes; namely modes A, B and MIMIC.

 

The 7+2 term refers to C, which has 7 indicators and 2 latent variables pointing at it. With “good neighbor” modes, C is calculated based on its 7 indicators AND the scores of the 2 latent variables that point at it.

 

Stated in simpler terms, with WarpPLS the minimum required sample size is 10 times the larger of these two numbers: (a) the maximum number of indicators in any latent variable; or (b) the maximum number of latent variables pointing at another latent variable in the model.

 

References

 

Lohmöller, J.-B. (1989). Latent variable path modeling with partial least squares. Heidelberg, Germany: Physica-Verlag.

 

Walker, H. M. (1940). Degrees of freedom. Journal of Educational Psychology, 31(4), 253–269.

[Muhammad Asim Tufail]

Dear Professor Ned Kock,

I have prepared and presented the manuscript attached with this mail in which I considered the power analysis for the sample size. Do you think it is the right approach when to define sample size in case of PLS path Modelling?

If so, I dont mind if any one would like to refer to this paper but it is just a conference paper.

I also request your kind self to advise if this paper can be published in a journal? (meaning is it good enough)? and request for any advise on the journal title.

Hoping in anticipation of your kind response.

Best regards.

P.S. Dear Ahamad AFM Jalal.

If the professor feels this is the  right way to report on sample size, in respect to effect size, you may refer this paper. Thank you.

--
You received this message because you are subscribed to the Google
Groups "PLS-SEM" group.
To post to this group, send email to pls...@googlegroups.com
To unsubscribe from this group, send email to
pls-sem+u...@googlegroups.com

--

Muhammad Asim Tufail.
Student Ambassador (Pakistan).
H/P: +60-17-4992696
School of HBP, USM, Malaysia.

http://www.ips.usm.my/ambassador/?page_id=649

"I think we risk becoming the best informed society that has ever died of ignorance." - Ruben Blades

[Ned Kock]

Hi Muhammad.

 

If I were you, I would run a full collinearity test on your model. Some of your betas are so high as to strongly suggest lateral collinearity. If that is indeed the case, for possible solutions see the paper below, available from www.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.

 

With lateral collinearity present, frequently the impression that one gets is that some effects are very strong, and that very small samples sizes are required to reject the null. Unfortunately, that is a “mirage”.

[Muhammad Asim Tufail]

Dear Professor Ned Kock,

Thank you very much for your kind input I am to do as you have advised as soon as I have digested the paper. 

With reference to the sample size, effect size and the power analysis would you please comment that it is the right way to do it?

Best regards and much gratitude.

--

You received this message because you are subscribed to the Google
Groups "PLS-SEM" group.
To post to this group, send email to pls...@googlegroups.com
To unsubscribe from this group, send email to
pls-sem+u...@googlegroups.com

[Ned Kock]

Hi Muhammad. The issue of model-wide collinearity is critical in the context of your sample size calculation. WarpPLS calculates block and full collinearity estimates automatically.