negative f² (f square), negative q² (q square)
negative f² (f square), negative q² (q square)
Hello everyone,
I have used the search function and actually this question has come up already, but has not been answered yet.
1) In my model I come up with some very low and also negative (yet also close to zero) f² s. Although the f² s are never negative for the link when I exclude an exogenous variable that directly effects an endogenous variable, they sometimes become negative for the indirect effect on an endogenous variable "further down the road". How to interpret this negative f² s?
2) When assessing q², I have a similar problem. Judging from the Q² s each endogenous variable has predictive relevance. But when I exclude the exogenous variables one by one, the q² s for LV links with indirect effects become negative (yet, also very close to zero). Same question here: how to interpret the negative q² s? Is there a paper, which I could quote that justifies to interpret the f² and q² for direct effects only?
Thanks a lot for any help!!
I have used the search function and actually this question has come up already, but has not been answered yet.
1) In my model I come up with some very low and also negative (yet also close to zero) f² s. Although the f² s are never negative for the link when I exclude an exogenous variable that directly effects an endogenous variable, they sometimes become negative for the indirect effect on an endogenous variable "further down the road". How to interpret this negative f² s?
2) When assessing q², I have a similar problem. Judging from the Q² s each endogenous variable has predictive relevance. But when I exclude the exogenous variables one by one, the q² s for LV links with indirect effects become negative (yet, also very close to zero). Same question here: how to interpret the negative q² s? Is there a paper, which I could quote that justifies to interpret the f² and q² for direct effects only?
Thanks a lot for any help!!

 PLS Expert User
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 Joined: Sat Jul 25, 2009 1:34 pm
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Hey Martin,
I think your negative f2 and q2 are one and the same problem. As you have wrote R2 cannot be negative. Therefore f2 should not be negative also. In some situation it could be that R2 get smaller with an further independent variable because of the stepwise algorithms of PLS. Like OLS PLS tries to minimize the error term of the dependet variable. If PLS have more then one dependent variable it could happen that with a new further variable f2 become lower. I suppose that f2 is very small in your case. Because your negative f2 depends on the stepwise algorithms of PLS I would ignore it. That means I would report it with 0 what means variable have not any impact. But that is only my opinion!
Best regards,
Christian
I think your negative f2 and q2 are one and the same problem. As you have wrote R2 cannot be negative. Therefore f2 should not be negative also. In some situation it could be that R2 get smaller with an further independent variable because of the stepwise algorithms of PLS. Like OLS PLS tries to minimize the error term of the dependet variable. If PLS have more then one dependent variable it could happen that with a new further variable f2 become lower. I suppose that f2 is very small in your case. Because your negative f2 depends on the stepwise algorithms of PLS I would ignore it. That means I would report it with 0 what means variable have not any impact. But that is only my opinion!
Best regards,
Christian
Thanks a lot
Hey Christian!
Thanks a lot for your reply, that helps a lot!
Martin
Thanks a lot for your reply, that helps a lot!
Martin

 PLS Senior User
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 Joined: Thu Jun 24, 2010 5:38 am
 Real name and title:
Hi, Do you mean this f square (the effect size):
I got the negative value due to the R square (with moderator) is bigger than R square (without moderator)
the result:
Agreed with Christian and this is from my thesis
"f2 value represent the strength of moderator effects. Chin (2003, 2010) and Cohen (1988) proposed that 0.02 is a weak, from 0.15 is a moderate, and above 0.35 is a strong.
However Limayem (2001) has different argument about f2 value
I got the negative value due to the R square (with moderator) is bigger than R square (without moderator)
the result:
Agreed with Christian and this is from my thesis
"f2 value represent the strength of moderator effects. Chin (2003, 2010) and Cohen (1988) proposed that 0.02 is a weak, from 0.15 is a moderate, and above 0.35 is a strong.
However Limayem (2001) has different argument about f2 value

 PLS Junior User
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 Joined: Thu Jul 26, 2007 2:07 am
 Real name and title: Reem Ayouby, Ph.D.
 Contact:
Hi!iris_afandiphd wrote:Hi, Do you mean this f square (the effect size):
I got the negative value due to the R square (with moderator) is bigger than R square (without moderator)
the result:
Agreed with Christian and this is from my thesis
"f2 value represent the strength of moderator effects. Chin (2003, 2010) and Cohen (1988) proposed that 0.02 is a weak, from 0.15 is a moderate, and above 0.35 is a strong.
However Limayem (2001) has different argument about f2 value
Could you please provide the full reference for Limayem (2001).
Thanks,
Reem
Reem Ayouby, Ph.D.
reemayouby.com
reemayouby.com
Maybe it would have been smarter to post my question here:
so in any case here is the link to my Topic: How do I calculate fsquared and qsquared?
viewtopic.php?t=1623
so in any case here is the link to my Topic: How do I calculate fsquared and qsquared?
viewtopic.php?t=1623

 PLS Junior User
 Posts: 2
 Joined: Thu Jun 27, 2019 8:28 pm
 Real name and title: Stephanie Gapud, Instructor, Spring Hill College, Mobile AL USA
Re: negative f² (f square), negative q² (q square)
Following this discussion
I got a positive f² but a negative q².
How can that be?
I got a positive f² but a negative q².
How can that be?

 SmartPLS Developer
 Posts: 1287
 Joined: Tue Mar 28, 2006 11:09 am
 Real name and title: Dr. JanMichael Becker
Re: negative f² (f square), negative q² (q square)
A predictor with positive f² and negative q² seems to contribute to overfitting.
f² measures explanatory power (withinsample fit), while q² measures predictive power (outofsample fit). If you overfit, you have high explanatory power (your model explains the data very well), but you cannot generalize beyond the observations used to estimate the model (i.e., truely predict).
However, blindfolding has some weaknesses. I would crosscheck the result with PLSpredict.
f² measures explanatory power (withinsample fit), while q² measures predictive power (outofsample fit). If you overfit, you have high explanatory power (your model explains the data very well), but you cannot generalize beyond the observations used to estimate the model (i.e., truely predict).
However, blindfolding has some weaknesses. I would crosscheck the result with PLSpredict.
Dr. JanMichael 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
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de

 PLS Junior User
 Posts: 2
 Joined: Thu Jun 27, 2019 8:28 pm
 Real name and title: Stephanie Gapud, Instructor, Spring Hill College, Mobile AL USA
Re: negative f² (f square), negative q² (q square)
thank you I will run PLS predict

 PLS Junior User
 Posts: 1
 Joined: Sun May 12, 2024 6:45 am
 Real name and title: Prateek dirghangi
Re: negative f² (f square), negative q² (q square)
jmbecker wrote: ↑Fri Jul 12, 2019 11:31 am
A predictor with positive f² and negative q² seems to contribute to overfitting.
f² measures explanatory power (withinsample fit), while q² measures predictive power (outofsample fit). If you overfit, you have high explanatory power (your model explains the data very well), but you cannot generalize beyond the observations used to estimate the model (i.e., truely predict).
Hello @jmbecker, I am in this situation at present. can you provide some citations for this statement "A predictor with positive f² and negative q² seems to contribute to overfitting" would really help. Thanks in advance