# [R-meta] Modeling dependent effect sizes (MASEM/TSSEM)

Marius Wuketich m@riu@wuketich @ending from gm@il@com
Sat Nov 17 15:32:39 CET 2018

```Dear colleagues,

I have a question about different approaches to modeling dependent effect
sizes. I'm doing a TSSEM study (based on correlation coefficients)
according to Mike Cheung in metaSEM. My path model is a model with one
independent and one dependent variable and three mediators.

A small part of my work deals with different methods to consider dependent
effect strengths in a MASEM analysis. I would like to compare the results
of the following three methods:

1. simple averaging the effect sizes

2. the approach of Wilson/Polanin/Lipsey 2016 (
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4905597/) - a combination of a
three-level hierarchical model and TSSEM

3. the robust variance estimation according to Tipton/Hedges/Johnson 2010 (
https://onlinelibrary.wiley.com/doi/abs/10.1002/jrsm.5) for the first part
of the TSSEM

With the third approach, I now have a basic understanding problem - how do
I have to specify my model in metafor for the robust approach?

K_ID = Study ID

ESID = Effect sizes ID

Second approach (three-level-model):

Step1 <-rma.mv(yi=r, V=N_INV,

data=dataset,

random=list(~1|K_ID,~1|ESID),

method="ML", mods=~factor(Zelle)-1)

summary (Step1)

Third approach (robust variance approach):

Step1 <-rma.mv(yi=r, V=N_INV,

data=Robust1,

random= ~1|K_ID,

method="ML", mods=~factor(Zelle)-1)

summary (Step1)

step2 <- robust(Step1, cluster = Robust1\$K_ID, adjust = TRUE)

summary(step2)

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Is that specified correctly yet? It just seems too simple to me.

Best,

Marius

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