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

[Tarun Khanna]

Dear Wolfgang,


I am following up on a question that we discussed a few weeks ago regarding meta-analysis for different combinations of data. This is regarding interpreting the results.


label    beta    se      pvalues         upper_lim       lower_lim
Social Comparison                 0.102           0.057           0.077           0.214          (0.011)
Feedback                  0.076           0.033           0.020           0.140           0.012
Feedback+Social           0.104           0.043           0.016           0.189           0.020
Monetary Incentives               0.261           0.042           0.000           0.344           0.178
Social+Monetary           0.034           0.081           0.674           0.193          (0.125)
Feedback+Monetary                 0.176           0.060           0.003           0.293           0.060
Social+Monetary+Feedback                  0.338           0.139           0.015           0.611           0.065
Motivation                0.131           0.052           0.012           0.233           0.029
Feedback+Motivation               0.152           0.047           0.001           0.243           0.061
Social+Feedback+Motivation                0.212           0.087           0.015           0.383           0.041


I ran the model as you suggested. The model reveals differences in the average effect size the different combinations but the condifence levels of these estimates overlap. In my opinion that does not mean that the differences are not statistically significant as we don't necessarily test for significance of differences. Or do these results mean we can't say anything about the differences? In a regression model I would run a F test with Ho : b1-b2 = 0. Can we do the same here?


Best

Tarun




Tarun Khanna

Research Associate


Hertie School


Friedrichstraße 180

10117 Berlin ∙ Germany
khanna using hertie-school.org ∙ www.hertie-school.org<http://www.hertie-school.org/>

________________________________
From: Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
Sent: 02 September 2020 11:40:27
To: Tarun Khanna; r-sig-meta-analysis using r-project.org
Subject: RE: 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 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?
>
>Thanks in advance!
>
>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-<http://www.hertie-school.org<http://www.hertie->
>school.org/>

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