# [R-meta] Why am I getting different means when conducting multilevel meta-analysis with factorial moderator vs. as subgroups?

Maximilian Theisen Theisen at stud.uni-heidelberg.de
Wed Apr 18 18:09:12 CEST 2018

```Hello!

I am conducting a multilevel meta-analysis using metafor in R. I have
effect sizes ("esid") nested within samples ("sampleid") nested within
publications ("studyid"). I have four subgroups ("task.type").
The mean effect sizes for each subgroup differ depending on whether I
use task.type as a moderator or run the rma.mv command for each subgroup
independently.

This is the code I use with task.type as moderator:
multi.task <- rma.mv(yi=g, V = var.g, data=df, random=list(~ 1 | esid,
~1 | sampleid, ~1 | studyid), mods=~factor(task.type)-1)

Multivariate Meta-Analysis Model (k = 142; method: REML)

Variance Components:

estim    sqrt  nlvls  fixed    factor
sigma^2.1  0.0942  0.3069    142     no      esid
sigma^2.2  0.7769  0.8814     29     no  sampleid
sigma^2.3  0.0000  0.0001     25     no   studyid

Test for Residual Heterogeneity:
QE(df = 138) = 950.2971, p-val < .0001

Test of Moderators (coefficient(s) 1:4):
QM(df = 4) = 29.9283, p-val < .0001

Model Results:

estimate      se     zval    pval    ci.lb    ci.ub
factor(task)1    0.6072  0.2360   2.5729  0.0101   0.1446   1.0697   *
factor(task)2   -0.5173  0.2559  -2.0212  0.0433  -1.0189  -0.0157   *
factor(task)3    0.5755  0.2048   2.8100  0.0050   0.1741   0.9769  **
factor(task)4    0.6173  0.4333   1.4246  0.1543  -0.2320   1.4665

This is the one I use when computing the model for each task.type
individually:
random=list(~ 1 | esid, ~ 1 |sampleid, ~ 1 | studyid))

Multivariate Meta-Analysis Model (k = 27; method: REML)

Variance Components:

estim    sqrt  nlvls  fixed    factor
sigma^2.1  0.1685  0.4105     27     no      esid
sigma^2.2  0.1307  0.3616      7     no  sampleid
sigma^2.3  0.1307  0.3616      7     no   studyid

Test for Heterogeneity:
Q(df = 26) = 115.1759, p-val < .0001

Model Results:

estimate      se     zval    pval    ci.lb   ci.ub
-0.0649  0.2289  -0.2836  0.7767  -0.5135  0.3837

estimate      se    zval    pval    ci.lb   ci.ub
0.3374  0.6983  0.4832  0.6290  -1.0312  1.7060

estimate      se    zval    pval   ci.lb   ci.ub
0.3862  0.1254  3.0808  0.0021  0.1405  0.6319  **

estimate      se    zval    pval    ci.lb   ci.ub
0.6126  0.3409  1.7971  0.0723  -0.0555  1.2807  .

Why are the results so different?

Best,
Max

```