[R-meta] Testing of moderators in rma()
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> 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() 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,ran
dom=~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,r
andom=~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 f?r Pflanzenern?hrung
Technische Universit?t M?nchen
(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
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