Sample size: minimum R2 method

Questions about the implementation and application of the PLS-SEM method, that are not related to the usage of the SmartPLS software.
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WanderSea
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Real name and title: Filippo Marino

Sample size: minimum R2 method

Post by WanderSea »

Hi everyone!

I'm conducting for the first time a PLS-SEM analysis and I'm following the Hair Jr. et al. (2014) primer's guidelines. I already read other threads about the sample size determination on the forum and I've also conducted a power analysis using G*power.

However, I wanted to ask you for clarification about the example in the sample size section of Hair's book:
"For instance, independent variables in the measurement and structural models is five, one would need 70 observations to achieve a statistical power of 80% for detecting R2 values of at least 0.25 (with a 5% probability of error)."
Does this mean that by failing to reach the 70 observations the model would be reliable only to measure higher R2 values (eg 0.25<R2<0.5) since those require smaller sample sizes?

I'd really appreciate your help.

Thank you,
Filippo
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cringle
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Re: Sample size: minimum R2 method

Post by cringle »

In principle, you are on the right track. In the second edition of the book, the explications have been slightly modified. Here, one looks at an effect size level and the required sample size.

The attached pictures provide further explications.

Please note that these are technical considerations. Reaching the minimum sample size does not necessarily mean that your data is good for the analysis. You need a representative sample and - with regards to the analyzed population - this should be easily several hundred and thousands of observations and/or require the use of a weighting variable to ensure the representativeness of your results (see weighted PLS: https://www.smartpls.com/documentation/ ... ighted-pls).

Best
Christian
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WanderSea
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Real name and title: Filippo Marino

Re: Sample size: minimum R2 method

Post by WanderSea »

Dear Dr Ringle,

thank you very much for your reply and your help.

For my study, I was following the 1st version of your primer book, therefore for a statistical power of 80%, α=5%, and 7 independent variables leading to a dependent variable, I considered to reach at least 166 observations (or 228 for α=1%).
I collected 249 observations, which accordingly to your latest explications - based on f2 - still meet the required minimum sample size.

Now I have a second question. For my research, I also wanted to check for heterogeneity, since the respondents' data was from two close but different natural protected areas. From the MGA I found 3 significantly different path coefficients. This suggests that I should analyse the two groups separately.
However, their sizes are quite different: 173 and 76.
Therefore, if I want to make a comparison and draw conclusions about the subsamples differences, does it mean that the smallest sample would limit my analysis to an effect size of f2=0.15 (min sample size of 55, for α=5% and stat power of 80%)?

Thank you again for your help,
Filippo
jmbecker
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Re: Sample size: minimum R2 method

Post by jmbecker »

Yes, you have to consider the minimum sample size requirements for each group if you want to do a MGA.
Dr. Jan-Michael Becker, BI Norwegian Business School, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
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dnirmala
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Re: Sample size: minimum R2 method

Post by dnirmala »

cringle wrote: Mon Dec 03, 2018 10:06 am In principle, you are on the right track. In the second edition of the book, the explications have been slightly modified. Here, one looks at an effect size level and the required sample size.

The attached pictures provide further explications.

Please note that these are technical considerations. Reaching the minimum sample size does not necessarily mean that your data is good for the analysis. You need a representative sample and - with regards to the analyzed population - this should be easily several hundred and thousands of observations and/or require the use of a weighting variable to ensure the representativeness of your results (see weighted PLS: https://www.smartpls.com/documentation/ ... ighted-pls).

Best
Christian
Dear Prof. Ringle

This sample size table differs from the one presented in the book (Hair Jr et al., 2016). Could you please explain the difference between these tables? The values in (Hair Jr et al., 2016) are based on Cohen (1992). What is the basis for the sample sizes in the below table? A reference to this table?

Also, what is the difference between "Linear multiple regression: Fixed Model, R2 deviation from zero" and "Linear multiple regression: Fixed Model, single regression coefficient."?

Thank you!

Regards
dasun
jmbecker
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Re: Sample size: minimum R2 method

Post by jmbecker »

I think the difference lies exactly in the difference between "Linear multiple regression: Fixed Model, R2 deviation from zero" and "Linear multiple regression: Fixed Model, single regression coefficient."

The first is the power of a regression models' F-test to find that the R² is different from zero, so that all predictors together explain significant variance.

The second is the power for regression models' path coefficient test to find that the effect is different from zero.

I would say that the second is the more relevant test in most situations.

Another approach not available in G*Power is the approach suggest by Ned Kock to use the Inverse Square Root Method, because it directly works with standardized path coefficients, what is what you are usually concerned about in PLS.
The G*Power approach required translation of the coefficient into an effect size measure.

Kock, N., & Hadaya, P. (2018). Minimum Sample Size Estimation in PLS‐SEM: The Inverse Square Root and Gamma‐exponential Methods. Information Systems Journal, 28(1) 227-261.
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
dnirmala
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Real name and title: Mr. Dasun M

Re: Sample size: minimum R2 method

Post by dnirmala »

jmbecker wrote: Thu Aug 24, 2023 9:25 am I think the difference lies exactly in the difference between "Linear multiple regression: Fixed Model, R2 deviation from zero" and "Linear multiple regression: Fixed Model, single regression coefficient."

The first is the power of a regression models' F-test to find that the R² is different from zero, so that all predictors together explain significant variance.

The second is the power for regression models' path coefficient test to find that the effect is different from zero.

I would say that the second is the more relevant test in most situations.

Another approach not available in G*Power is the approach suggest by Ned Kock to use the Inverse Square Root Method, because it directly works with standardized path coefficients, what is what you are usually concerned about in PLS.
The G*Power approach required translation of the coefficient into an effect size measure.

Kock, N., & Hadaya, P. (2018). Minimum Sample Size Estimation in PLS‐SEM: The Inverse Square Root and Gamma‐exponential Methods. Information Systems Journal, 28(1) 227-261.
Dear Dr. Becker

Thank you for the clarification.

Can I trouble you for any literature or resources which explains about these two options?

Regards
Dasun
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