# [R-meta] Two ways to calculate subgroup and overall average effect sizes

Nathan Pace n.l.pace at utah.edu
Thu Aug 24 00:44:18 CEST 2017

```Hi Wolfgang,

I have a k = 29 SMD meta analysis.

The moderator is a three level factor.

painearly1surgery.rma <- rma(yi = yi, vi = vi, mods = ~ surgery,
data = painearly.df, test = 'knha', digits = 3)

painearly2surgery.rma.mv <- rma.mv(yi = yi, V = vi, mods = ~ surgery,
random = ~ surgery | study, struct = 'DIAG',
data = painearly.df, test = 't', digits = 3)

There is a nearly 10 fold variation in the individual tau^2s.

Variance Components:

outer factor: study   (nlvls = 29)
inner factor: surgery (nlvls = 3)

estim   sqrt  k.lvl  fixed  level
tau^2.1    0.082  0.287      8     no   open
tau^2.2    0.759  0.871     10     no    lap
tau^2.3    0.086  0.294     11     no  other

The average tau^2 is:

tau^2 (estimated amount of residual heterogeneity):     0.312 (SE = 0.110)
tau (square root of estimated tau^2 value):             0.559

The omnibus test of moderators  is not rejected in either model.

Test of Moderators (coefficient(s) 2:3):  (average tau^2)
F(df1 = 2, df2 = 26) = 2.082, p-val = 0.145

Test of Moderators (coefficient(s) 2:3):  (individual tau^2)
F(df1 = 2, df2 = 26) = 2.643, p-val = 0.090

Is there a meaningful statistical comparison of the individual tau^2s?

Are there other ways to compare the model fits (AIC or BIC)?

The anova function won’t mix rma.uni and rma.mv objects.

Nathan

```

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