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

[Samuel Knapp]

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() 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(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(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	
samuel.knapp at tum.de
www.researchgate.net/profile/Samuel_Knapp