## negative f² (f square), negative q² (q square)

nicefreak
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### 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!!

christian.nitzl
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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

nicefreak
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### Thanks a lot

Hey Christian!

Martin

iris_afandiphd
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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

rayouby
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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
Hi!

Could you please provide the full reference for Limayem (2001).

Thanks,
Reem
Reem Ayouby, M.Sc.
Ph.D. Student
JMSB, Concordia University
Reem.Ayouby@gmail.com
r_ayouby@jmsb.concordia.ca

AMunoz
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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 f-squared and q-squared?

viewtopic.php?t=1623

sgapud
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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?

jmbecker
SmartPLS Developer
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Real name and title: Dr. Jan-Michael 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 (within-sample fit), while q² measures predictive power (out-of-sample 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 cross-check the result with PLSpredict.
Dr. Jan-Michael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker