High Significance but Low R2,f2 and q2 - is this normal?

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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arcticarrow
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High Significance but Low R2,f2 and q2 - is this normal?

Post by arcticarrow »

Hi all,

I am pretty new to PLS and SEM. I have the following result as attached. I read from the book that a path coefficient of 0.2 is significant. As i see my data, the t-value shows they are at 0.01 significance level. However, it's the low R^2 value that concerns me.

I thought about since my study is on human behaviour, a low R^2 is possible. But I am just not so sure considering also the F^2 and Q^2 values.

Do you have any idea or, or any good suggested articles on showing people how to interpret low R2 value? I just need a bit guidance so I can make solid argument in my work.

Highly appreciated.

PS: My model is basically a single dependent variable with single arrow pointing to all the other 5 dependent variables. All are reflective. you can ignore the name, it was just for showing the idea only.

Thanks!
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janschreier
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Real name and title: Jan Schreier

Re: High Significance but Low R2,f2 and q2 - is this normal?

Post by janschreier »

I think it would help if you would post the model (if you don't want to give away the names, copy the model and change the names). right now it is hard to exactly tell what you have, especially since you talk about variables only and not about constructs at all.
jmbecker
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Real name and title: Dr. Jan-Michael Becker

Re: High Significance but Low R2,f2 and q2 - is this normal?

Post by jmbecker »

There is no surprise in your results. With just a single predictor your R² values can directly be calculated from the path coefficients by p²=R², because there is not multicollinearity affecting your model and the standardized path coefficient is actaully the correlation of the two variables/constructs.
For example 0,34²=0.1156 (rounded 0.12 which is your R²). f² and q² also follow directly from these results, because if you delete that one predictor you will explain nothing, because no predictor is left. To get really high R² in a single predictor model you need really strong relations (path coefficients/correlations), because only one variable is there to explain the variance of your dependent variable.
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
arcticarrow
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Re: High Significance but Low R2,f2 and q2 - is this normal?

Post by arcticarrow »

Thanks for the great reply. Basically the model is like a STAR. Envy is the only exo.construct (prediator) with 10 Reflective indicators.

All the other Endo.Constructs have 5 to 10 Reflective Indicators. So the Envy construct have multiple single arrow pointing to each Endo.Constructs (Human Behavior 1, Human Behavior 2.... Human Behavior 5).


I got it now that since there is only one exo construct, hence the relatively lower R2 value.

my question is, Hair.Book mentioned Path Coefficient > 0.2 can be used to consider if a hypothesis is supported if the R2 value is good, but R2 value varies from discpline, I am not sure how to interpret if my hypothesis is supported or not. My supervisor just "hint" that there are good logical reasons for Low R2, but she didnt explain.

Any paper or insight you could share I will appreciate very very much. Thanks.

PS. another funny question is, I know there are doubts on the 10 times rule of the sample size requirement. But in this case, since Max. number of arrows pointing at a construct is .. "ONE", does it mean I only need 10 samples? That sounds too little. My supervisor allows me to use this 10 time rules, but still..... Anyway, I have around 220 samples.
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