[R-meta] Different outputs by comparing random-effects model with a MLMA without intercept

Dear Wolfgang and All,

I am conducting a meta-analysis to evaluate potential bias of a fixed
predictor with two subgroups (predictor: yes and no). Because I found a
bias, I removed the values of subgroup "yes" and performed a random-effects
model. However, when I compared the output of the first model without
intercept with the output of the random effects model, I obtained different
results, especially in the estimation of confidence intervals. I was
expecting to found similar results because the model without intercept
tests if the average outcome differs from zero. Can you explain in which
case this can happen? Every help is welcome.


model1=rma.mv(yi, vi, mods=~predictor-1, random = list (~1|effectsizeID,
~1|studyID, ~1|speciesID), R=list(speciesID=phylogenetic_correlation),
data=h)

#Multivariate Meta-Analysis Model (k = 1850; method: REML)
#
#Variance Components:
#                    estim     sqrt      nlvls  fixed        factor     R
#sigma^2.1  0.0145  0.1204   1850    no  effectsizeID   no
#sigma^2.2  0.0195  0.1397    468     no       studyID     no
#sigma^2.3  0.2386  0.4885    348     no     speciesID   yes
#
#Test for Residual Heterogeneity:
#QE(df = 1848) = 10797.5993, p-val < .0001
#
#Test of Moderators (coefficients 1:2):
#QM(df = 2) = 17.6736, p-val = 0.0001
#
*#Model Results:*
*#                          estimate      se        zval       pval
ci.lb <http://ci.lb>   ci.ub *
*#potential_sceno     0.2843  0.1659  1.7141  0.0865  -0.0408  0.6095  *.
#potential_sceyes    0.3741  0.1668  2.2421  0.0250   0.0471  0.7011  *
#---
#Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1


model2=rma.mv(zf, vzf, random = list (~1|effectsizeID, ~1|studyID,
~1|speciesID), R=list(speciesID=phylogenetic_correlation),
data=subset(h,potential_sce=="no"))

#Multivariate Meta-Analysis Model (k = 1072; method: REML)
#
#Variance Components:
#            estim    sqrt  nlvls  fixed        factor    R
#sigma^2.1  0.0140  0.1184   1072     no  effectsizeID   no
#sigma^2.2  0.0394  0.1986    264     no       studyID   no
#sigma^2.3  0.0377  0.1943    240     no     speciesID  yes
#
#Test for Heterogeneity:
#Q(df = 1071) = 4834.5911, p-val < .0001
#
*#Model Results:*
*#estimate      se    zval    pval   ci.lb <http://ci.lb>   ci.ub *
*#  0.2989  0.0720  4.1494  <.0001  0.1577  0.4401  *** *
#---
#Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1


I used another data set to conduct the same approach and obtained similar
results:

dat <- dat.bangertdrowns2004
rbind(head(dat, 10), tail(dat, 10))
dat <- dat[!apply(dat[,c("length", "wic", "feedback", "info", "pers",
"imag", "meta")], 1, anyNA),]

head(dat)

random.model=rma.mv(yi, vi, random=list(~1|id, ~1|author), structure="UN",
data=subset(dat, subject=="Math"))

random.model

*#Math*
*#Model Results:*
*#  estimate      se    zval         pval   ci.lb <http://ci.lb>   ci.ub *
*#    0.2106  0.0705  2.9899  0.0028  0.0726  0.3487  ***

mixed.model=rma.mv(yi, vi, mods=~subject-1, random=list(~1|id, ~1|author),
structure="UN", data=dat)

anova(mixed.model,btt=2)

*#Math*
*#  estimate      se       zval    pval       ci.lb <http://ci.lb>   ci.ub*
*#    0.2100  0.0697   3.0122  0.0026   0.0734  0.3467*

Best wishes,

Rafael.