# [R-meta] Why total variation differs in two rma.mv models?

Yefeng Yang ye|eng@y@ng1 @end|ng |rom un@w@edu@@u
Tue Jan 10 12:34:03 CET 2023

```Dear Yuhang,

Just add to Wolfgang's explanation. If you have basic knowledge of regression analysis, you will understand that it is expected that m2 would have less total variance than m1. This is basically the aim of why you added the a priori moderators to a meta-analytic model - explain the heterogeneity. However, as Wolfgang pointed out, if the moderators you added to the model do not account for any of the heterogeneity, the residual heterogeneity might be even larger than that from a null model - this is somewhat counterintuitive, but it can happen in the context of meta-analysis.

Best,
Yefeng
________________________________
From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> on behalf of Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
Sent: Tuesday, 10 January 2023 18:12
To: r-sig-meta-analysis using r-project.org <r-sig-meta-analysis using r-project.org>
Cc: yh342 using nau.edu <yh342 using nau.edu>
Subject: Re: [R-meta] Why total variation differs in two rma.mv models?

Dear Yuhang,

If the moderators account for (at least some of the) heterogeneity, then this is exactly what should happen (in m2, the variance components reflect heterogeneity not accounted for by the moderators).

Best,
Wolfgang

>Dear Colleagues,
>
>I have fit an intercept-only model like:
>
>m1 = rma.mv(yi ~ 1, V=V, random = ~1|study/effect)
>
>And then the same model with some moderators:
>
>m2 = rma.mv(yi ~ mod1*mod2 + X1 + X2, V=V, random = ~1|study/effect)
>
>When I compare the **total variation** (sum of the variance components)
>across the two models, "m1" has a much larger estimate than "m2".
>
>I wonder how that could be when both models use the same set of effect
>sizes?
>
>Thank you so much!
>Yuhang Hu

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