# [R-meta] Calculating effect size for subsets of data

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Wed Sep 2 11:40:27 CEST 2020

```Dear Tarun,

If I understand you correctly, then there should be 16 different combinations of A, B, C, and D but one of them (A=B=C=D=0) cannot occur, so essentially there are 15 combinations that were observed. As a result, you should have gotten a warning when fitting the model that a redundant predictor was dropped from the model. Let's consider a simpler case with just A and B:

set.seed(1234)
k <- 900
A <- c(rep(0,k/3), rep(1,k/3), rep(1,k/3))
B <- c(rep(1,k/3), rep(0,k/3), rep(1,k/3))
vi <- rep(.01, k)
yi <- rnorm(k, 0.5 * A + 0.1 * B + 0.3*A*B, sqrt(vi))

A <- factor(A)
B <- factor(B)

res <- rma(yi, vi, mods = ~ A*B)
res

These are the model results:

estimate      se      zval    pval    ci.lb    ci.ub
intrcpt   -0.3019  0.0100  -30.1904  <.0001  -0.3215  -0.2823  ***
A1         0.7963  0.0082   97.5319  <.0001   0.7803   0.8123  ***
B1         0.4032  0.0082   49.3825  <.0001   0.3872   0.4192  ***

The results are a bit tricky to interpret, so I would suggest a different parameterization:

res <- rma(yi, vi, mods = ~ A:B + 0)
res

estimate      se      zval    pval   ci.lb   ci.ub
A1:B0    0.4944  0.0058   85.6397  <.0001  0.4831  0.5058  ***
A0:B1    0.1013  0.0058   17.5462  <.0001  0.0900  0.1126  ***
A1:B1    0.8976  0.0058  155.4771  <.0001  0.8863  0.9090  ***

Now we can clearly see that A1:B0 is the estimated effect when A is given alone, A0:B1 is the estimated effect when B is given alone, and A1:B1 is the estimated effect when A and B are given together.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org]
>On Behalf Of Tarun Khanna
>Sent: Monday, 31 August, 2020 13:11
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] Calculating effect size for subsets of data
>
>Dear all,
>
>I am conducting a meta-analysis of effect of certain interventions on
>household energy consumption. In my data set I have a dummy variable for
>each of the sub-interventions: A,B,C,D such that intersection of A=0 & B=0 &
>C=0 & D=0 is zero. Each effect size may be associated with multiple
>interventions though.
>
>I have calculated an aggregate effect size across interventions and then
>effect size by sub-intervention. But I also want to compare if the effect of
>the sub-interventions differs from each other. I thought about including the
>sub-regression dummies as controls in the meta regression:
>
>rma (yi, vi, method = "REML", data = data, mods ~ A*B*C*D)
>
>The problem in interpreting the output of this regression is that there is
>no base category left for the intercept to denote. Can I perhaps run the
>model by supressing the intercept? Or what would be the interpretation of
>the intercept in this case?
>
>
>Best
>
>Tarun
>Tarun Khanna
>PhD Researcher
>Hertie School
>
>Friedrichstraße 180
>10117 Berlin ∙ Germany
>khanna using hertie-school.org ∙ www.hertie-school.org<http://www.hertie-
>school.org/>
```