QUESTION: About The 10 Times Rule (PLS-MGA)

[MMVS]

"When engaging in PLS-MGA, researchers need to ensure that the number of observations in each group meets the rules of thumb for minimum sample size requirements (Chapter 1). As the maximum number of arrows pointing at a latent variable is three, we would need 3 · 10 = 30 observations per group, according to the 10 times rule. Following the more rigorous recommendations from a power analysis (Chapter 1), 59 observations per group are needed to detect R2 values of around 0.25 at a significance level of 5% and a power level of 80%. Therefore, the group-specific sample sizes can be considered sufficiently large.” - page 250, Hair Jr. et al. (2013)

Hair Jr., J. F., G. T. M. Hult, C. Ringle, and M. Sarstedt. 2013. A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM): Sage Publications.
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SITUATION:
In my research, the maximum number of arrows pointing at a latent variable is 4. Thus, according to the 10 times rule, I would need to have a minimum of 40 cases per group. I have a total of 509 cases. However, when I was about to conduct a PLS-MGA for the observable Age grouping, I discovered that I have the following:
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Age_18 or younger(1) = 40 records
Age_19-25 years old(2) = 163 records
Age_26-35 years old(3) = 173 records
Age_36 or above(4) = 133 records
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Age_18 or younger - seems to fall just right in the ballpark. However, "a more rigorous recommendations from a power analysis (Chapter 1), suggests that 59 observations per group are needed to detect a meaningful R2.."

QUESTION(S):
1.) Should I still consider running PLS-MGA for the AGE group? If so, would it mean that the results (e.g. R2 values) will be less than the power level of 80%?

2.) Does disregarding "Age_18 or younger" group make any difference or would it make the results more meaningful?

Similarly, I generated a sub-group for INCOME and found one group that falls below the 59 observation recommendation.
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Less than $10,000(1) = 122 records
$10,001 – $30,000(2) = 158 records
$30,001 – $50,000(3) = 112 records
$50,001 or more(4) = 76 records
Prefer Not to Answer(5) = 41 records
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QUESTION: Will unchecking "Prefer Not to Answer(5) = 41 records" in the PLS-MGA option help obtain a power level higher than 80%?

Please advice. Any help would be appreciated. Thank you in advance!

Regards,
Mark

[Hengkov]

Hi,

First, I do not really support the analysis of PLS-MGA done using demographic variables such as age or income.
When you run PLS-MGA, then the cultivated amount of your sample should be the same or almost the same. For the analysis of PLS always considered power analysis. Moreover, to run PLS-MGA with more than two groups of samples considered somewhat difficult, because it is done gradually and the result is still questionable. Why do not you just divide it into two groups?

Greetings,

[MMVS]

Hi everyone!

I just want to give you guys an update, I did run the MGA analysis anyway. I found that the results were satisfactory enough, and was able to conclude similar findings as with my original data set. However, groups with cases lower than the power analysis recommendation undoubtedly showed more insignificant path relationships. For cultivating the samples, I let the bootstrapping process run its course and handle it. But as a precaution, I cited that more data is needed to come up with a better proper conclusion for these groups.

Regards,
Mark

[Anita]

Hi

please note that you have to pay attention to the significance level required for testing your hypothesis in addition to the 19 times rule.
i did not know this myself but recently i read a book titled as" a primer on partial least squares structural equation modeling" by Josepj F. Hair and i noticed that. in the mentioned book there is a table defining the sample size based on the significance level and maximum number of arrows.

good luck