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

[Viechtbauer, Wolfgang (SP)]

Dear Rafael,

Let's try this again (instead of sending an empty mail -- sorry about that!).

Indeed, the results differ because model2 estimates the variance components only based on the subset, while model1 estimates those variances based on all data. You would have to allow the variance components to differ for the "no" and "yes" levels of 'potential_sce' in 'model1' for the results to be identical. Actually, even then, I don't think you would get the exact same results, since you make use of the 'R' argument. Due to the correlation across species, the estimate (and SE) of 'potential_sceno' and 'potential_sceno' will be influenced by whatever species are included in the dataset. In the subset, certain species are not included (240 instead of 348), which is another reason why there are differences.

Best,
Wolfgang

-----Original Message-----
From: Michael Dewey [mailto:lists using dewey.myzen.co.uk] 
Sent: Thursday, 07 March, 2019 18:06
To: Rafael Rios; Viechtbauer, Wolfgang (SP); r-sig-meta-analysis using r-project.org
Subject: Re: [R-meta] Different outputs by comparing random-effects model with a MLMA without intercept

Dear Rafael

I think this may be related to the issue outlined by Wolfgang in this 
section of the web-site

http://www.metafor-project.org/doku.php/tips:comp_two_independent_estimates

Michael

On 07/03/2019 16:46, Rafael Rios wrote:
> 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.
> __________________________________________________________
> 
> Dr. Rafael Rios Moura
> *scientia amabilis*
> 
> Behavioral Ecologist, Ph.D.
> Postdoctoral Researcher
> Universidade Estadual de Campinas (UNICAMP)
> Campinas, São Paulo, Brazil
> 
> ORCID: http://orcid.org/0000-0002-7911-4734
> Currículo Lattes: http://lattes.cnpq.br/4264357546465157
> Research Gate: https://www.researchgate.net/profile/Rafael_Rios_Moura2