[R-meta] Testing of moderators in rma()
Samuel Knapp
samuel.knapp at tum.de
Tue Oct 24 23:29:05 CEST 2017
Many thanks, that made it very clear.
For the first case, would the null hypothesis not have to be b0=b1=b2?
This is how I understood your explanation.
To me, the eqn (eg. b1=0) look very similar between both examples.
Best regards
On 24/10/17 23:21, James Pustejovsky wrote:
> Samuel,
>
> These two omnibus tests have very different interpretations. Say that
> you have a moderator with three levels, A, B, C.
>
> If you fit the model with an intercept, as in
> yi = b0 + b1 X1i + b2 X2i + ei,
> then b0 will be the average effect size for the reference level (say
> this is A), b1 will be the difference in average effect sizes
> comparing B versus A, and b2 will be the difference in average effect
> sizes comparing C versus A. The omnibus test in this case is for the
> null hypothesis that b1 = 0 and b2 = 0, i.e., that the average effect
> sizes are all equal to b0*. *Note too that this omnibus test would
> have 2 degrees of freedom.
>
> If you fit the model without an intercept, as in
> yi = b1 X1i + b2 X2i + b3 X3i + ei,
> then b1 will be the average effect size for studies with level A, b2
> will be the average effect size for studies with level B, and b3 will
> be the average effect size for studies with level C. The omnibus test
> in this case is for the null hypothesis that b1 = 0, b2 = 0, and b3 =
> 0, i.e., that the average effect sizes are all equal to zero. Note too
> that this omnibus test would have 3 degrees of freedom.
>
> So the two omnibus tests are quite different, and there is no reason
> to expect that they should be consistent with each other.
>
> James
>
> On Tue, Oct 24, 2017 at 3:55 PM, Samuel Knapp <samuel.knapp at tum.de
> <mailto:samuel.knapp at tum.de>> wrote:
>
> Dear all,
>
> I have a problem in finding the right test for the inclusion of
> moderators, or actually I'm not sure if I should include the
> intercept term or not. What troubles me, is that the removal of
> the intercept term, has a very big effect on the omnibus test of
> the moderators.
>
> The model: rma.mv <http://rma.mv>() with an additional random
> effect (study), a variance-covariance matrix for the sampling
> variances and covariances (Lajeunesse correction).
>
> I want to test species as a moderator. When I include the
> intercept, the moderator effect is not significant (P=0.2779), and
> when I remove the intercept P<0.001. I started to remove the
> intercept to get the average effects for levels for each species
> and the z-test for each species. However, no I'm not sure anymore,
> what the different interpretation of moderator test for the two
> different models are.
>
> Thanks a lot!
>
> ### Model with intercept:
>
> > specmodel <- rma.mv
> <http://rma.mv>(yi~species,V=varmat,random=~1|study/myo,data=metadat,method="REML")
> > summary(specmodel)
>
> Multivariate Meta-Analysis Model (k = 166; method: REML)
>
> logLik Deviance AIC BIC AICc
> 12.8545 -25.7089 22.2911 93.5666 32.3751
>
> Variance Components:
>
> estim sqrt nlvls fixed factor
> sigma^2.1 0.0216 0.1470 39 no study
> sigma^2.2 0.0300 0.1732 166 no study/myo
>
> Test for Residual Heterogeneity:
> QE(df = 144) = 1386.5618, p-val < .0001
>
> Test of Moderators (coefficient(s) 2:22):
> QM(df = 21) = 24.3187, p-val = 0.2779
>
> ### Model without intercept:
>
> > specmodel <- rma.mv
> <http://rma.mv>(yi~species-1,V=varmat,random=~1|study/myo,data=metadat,method="REML")
> > summary(specmodel)
>
> Multivariate Meta-Analysis Model (k = 166; method: REML)
>
> logLik Deviance AIC BIC AICc
> 12.8545 -25.7089 22.2911 93.5666 32.3751
>
> Variance Components:
>
> estim sqrt nlvls fixed factor
> sigma^2.1 0.0216 0.1470 39 no study
> sigma^2.2 0.0300 0.1732 166 no study/myo
>
> Test for Residual Heterogeneity:
> QE(df = 144) = 1386.5618, p-val < .0001
>
> Test of Moderators (coefficient(s) 1:22):
> QM(df = 22) = 61.9539, p-val < .0001
>
>
> --
> Samuel Knapp
>
> Lehrstuhl für Pflanzenernährung
> Technische Universität München
> (Chair of Plant Nutrition
> Technical University of Munich)
>
> Emil-Ramann-Strasse 2
> D-85354 Freising
>
> Tel. +49 8161 71-3578 <tel:%2B49%208161%2071-3578>
> samuel.knapp at tum.de <mailto:samuel.knapp at tum.de>
> www.researchgate.net/profile/Samuel_Knapp
> <http://www.researchgate.net/profile/Samuel_Knapp>
>
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