# [R-meta] Questions about Omnibus tests

Rafael Rios bior@f@elrm @ending from gm@il@com
Tue Oct 30 06:15:34 CET 2018

```Dear Wolfgang,

Thank you for the very helpful advices! I will be grateful if you could
help me again with my new questions. I organized them in the topics bellow.

1. Does the QM-test, with an intercept in the model, evaluates if the
average true outcomes of subgroups differ from the reference level or from
0? I found a p>0.05, probably meaning that there is no difference among
subgroups. However, if you analyze the graph, there a higher effect size
for the subgroup of female choice compared to others. So, I am not sure
about the best approach to evaluate differences among outcomes. Why are the
graph results so different from the QM-test with an intercept in the model?
Should I evaluate results using anova(meta,btt=1:3)?

You also suggested that the script for pairwise comparisons was wrong.
According to the link that you provided, it can also be drawn
as summary(glht(meta, linfct=rbind(c(0,0,1), c(0,1,0), c(0,-1,1))),
test=adjusted("none")). Was the argument linfct=rbind(c(0,0,1)) used to
compare the subgroups of female choice (reference level) and male choice?
What am I evaluating by using summary(glht(meta,
linfct=rbind(female=c(1,0,0), male=c(0,1,0))), test=Chisqtest())?

2. Thank you for the correction of I² formula. What is the best approach to
measure heterogeneity in a multilevel meta-analysis? Maybe, this one:
http://www.metafor-project.org/doku.php/tips:i2_multilevel_multivariate

3. I used the standard deviation to weight the effect sizes, according to
Zaykin (2011). Is variance a better measure of weight than se in a
multilevel meta-analysis? Reference: D. V. Zaykin, Optimally weighted
Z-test is a powerful method for combining probabilities in meta-analysis.
J. Evol. Biol. 24, 1836–1841 (2011).

4. Finally, I agree with the exclusion of potential_sce as a random
variable. However, I need to control for this variable. An alternative
could be to include this potential_sce as a fixed variable. Is this model
more appropriate?: meta=rma.mv(zf, sezf, mods=~mate_choice+potential_sce,
random = list (~1|effectsizeID, ~1|studyID, ~1|species1), data = h_mc).

Thank you again for the help.

Best wishes,

Rafael.
__________________________________________________________

Dr. Rafael Rios Moura
*scientia amabilis*

Behavioral Ecologist, PhD
Postdoctoral Researcher
Campinas, São Paulo, Brazil

Currículo Lattes: http://lattes.cnpq.br/4264357546465157
ORCID: http://orcid.org/0000-0002-7911-4734
Research Gate: https://www.researchgate.net/profile/Rafael_Rios_Moura2

<http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4244908A8>

Em qui, 25 de out de 2018 às 16:59, Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> escreveu:

> Dear Rafael,
>
> With an intercept in the model, the QM-test tests all coefficients except
> for the intercept. In this case, those coefficients reflect differences
> relative to the reference level defined by the intercept. So, the QM-test
> tells you whether the average true outcome is different for the various
> levels or not. The QM-test is not significant, so there is no
> (statistically significant) evidence that the average true outcome differs
> across the various levels.
>
> The intercept is significantly different from 0, but this is a completely
> different hypothesis and has nothing to do with the QM-test here. The
> intercept is the estimated average true outcome for the reference level.
> Whether it is different from 0 has nothing to do with whether the other
> levels are different from the reference level.
>
>
> http://www.metafor-project.org/doku.php/tips:testing_factors_lincoms
>
> You are also not conducting pairwise comparisons. Your code computes the
> estimated average true outcome for various pairs of levels and then chi^2
> tests with df=2 are conducted to test the null hypothesis that both of
> these average true outcomes are significantly different from 0. That is not
> testing for the *difference* between the two levels. The pairwise
> comparisons are:
>
> summary(glht(meta, linfct=rbind(c(1,0,0)-c(1,1,0))), test=Chisqtest())
> summary(glht(meta, linfct=rbind(c(1,0,0)-c(1,0,1))), test=Chisqtest())
> summary(glht(meta, linfct=rbind(c(1,0,1)-c(1,1,0))), test=Chisqtest())
>
> The first two are unnecessary, since the contrasts between the reference
> level and the second and third level are already part of the model output.
> All of these are not significant.
>
> As for the negative I^2 value: You are not using the correct formula. It
> should be: 100*(106.866-102)/106.866. This can still yield a negative value
> (in general, not in this case), in which case the value is just set to 0.
> BUT: This equation comes from the standard random-effects model (and
> assumes that we are using the DL-estimator). You are fitting a more complex
> model (and using REML estimation), so the usefulness of this equation in
> this context is debatable.
>
> Finally, the model you are fitting is incorrectly specified. First, you
> are setting the second argument of rma.mv() to 'sezf' (which is
> apparently the SE of the estimates). However, the second argument is for
> specifying the *variances* (or an entire var-cov matrix). Second, you need
> to add random effects corresponding to the individual estimates to the
> model. Adding 'study-level' random effects does not replace the
> 'estimate-level' random effects in multilevel models, they both need to be
>
>
> http://www.metafor-project.org/doku.php/analyses:konstantopoulos2011#a_common_mistake_in_the_three-level_model
>
> So, you should be using:
>
> meta <- rma.mv(zf, vzf, mods = ~ mate_choice, random = list (~1|studyID,
> ~1|effectsizeID, ~1|species1, ~1|potential_sce), data = h_mc)
>
> Whether it is appropriate/useful to add random effects corresponding to
> the levels of 'potential_sce' is also debatable. This variable only has two
> levels, so the estimate of the variance component for this factor is going
> to be very imprecise (see confint(meta, sigma2=4) after fitting the model
> above). The estimated variance for this factor turns out to be 0 here, so
> this is identical to dropping this random effect altogether, so in the end
> it does not matter.
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: R-sig-meta-analysis [mailto:
> r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Rafael Rios
> Sent: Thursday, 25 October, 2018 21:13
> To: Michael Dewey
> Cc: r-sig-meta-analysis using r-project.org
> Subject: Re: [R-meta] Questions about Omnibus tests
>
> Dear Michael,
>
> Thank you for the help. Indeed, I found a significant p-value in the
> QM-test by removing the intercept or using btt(1:3) argumment in the
> function rma.mv. However, using such approach, I am testing if each mean
> outcome is different than zero. However, I need to test differences among
> subgroups by including a value of reference. Such approach needs the
> inclusion of intercept:
> http://www.metafor-project.org/doku.php/tips:multiple_factors_interactions
>
> I am not sure about the correct approach and what results to report. Can I
> really use the QM-test without the intercept to test differences among
> subgroups?
>
> Best wishes,
>
> Rafael.
> __________________________________________________________
>
> Dr. Rafael Rios Moura
> *scientia amabilis*
>
> Behavioral Ecologist, PhD
> Postdoctoral Researcher
> Campinas, São Paulo, Brazil
>
> Currículo Lattes: http://lattes.cnpq.br/4264357546465157
> ORCID: http://orcid.org/0000-0002-7911-4734
> Research Gate: https://www.researchgate.net/profile/Rafael_Rios_Moura2
>
> Em qui, 25 de out de 2018 às 12:33, Michael Dewey <lists using dewey.myzen.co.uk
> >
> escreveu:
>
> > Dear Rafael
> >
> > I think the issue is that the test of the intercept tests whether that
> > might be zero whereas the test of the moderator tests whether the other
> > two coefficients are zero. If you remove the intercept from the model
> > you should get a test for the moderator with 3 df (not 2 as at pesent)
> > which tests whether all three coefficients are zero which seems to be
> > what you are after.
> >
> > Michael
> >
> > On 25/10/2018 16:00, Rafael Rios wrote:
> > > Dear Wolfgang and All,
> > >
> > > I am conducting a meta-analysis to evaluate the effects of mate choice
> > > on the outcome. My dataset and script follow on attach. I found
> > > conflicting results with the omnibus test. The QM-test had a
> > > non-significant p-value, while z-test shows a significant p-value for
> > > the intercerpt (corresponding to the treatment of female choice). When
> I
> > > undertook pairwise comparisons, I also found differences among
> > > treatments consistent with the z-test results. You can also observe
> > > these differences in the graph. What exactly is each test (QM and z)
> > > evaluating? Why is QM-test reporting a p-value higher than 0.05, even
> > > when there is differences in pairwise comparisons? I also found a
> > > negative value for I². Is there any problem with the model to report
> > > such result? My questions are organized inside the script. Any help
> will
> > > be welcome.
> > >
> > > Best wishes,
> > >
> > > Rafael.
> > > __________________________________________________________
> > >
> > > Dr. Rafael Rios Moura
> > > /scientia amabilis/
> > >
> > > Behavioral Ecologist, PhD
> > > Postdoctoral Researcher