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

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 at r-project.org]
On Behalf Of Tarun Khanna
Sent: Monday, 31 August, 2020 13:11
To: r-sig-meta-analysis at 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?

Thanks in advance!

Best

Tarun
Tarun Khanna
PhD Researcher
Hertie School

Friedrichstra?e 180
10117 Berlin ? Germany
khanna at hertie-school.org ? www.hertie-school.org<http://www.hertie-
school.org/>