[R-meta] Testing of moderators in rma()

[Samuel Knapp]

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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