# [R-meta] Question about escalc, proportion ES, and nested data

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Wed Feb 2 11:17:09 CET 2022

```Dear Jordan,

Please see below for my responses.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Harris, Jordan L
>Sent: Tuesday, 01 February, 2022 22:50
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] Question about escalc, proportion ES, and nested data
>
>Hi List Members,
>
>I am a graduate student who is new to R and meta-analyses, and I have been
>running into problems getting my code sorted out.
>
>I am conducting a meta-analysis to explore how the structure of psychopathology
>changes across childhood and adolescence. My effect size of interest is
>represented by a proportion score that is conceptualized as ratio of variance
>accounted for by a general factor, called "general_es" (i.e., general / general +
>specific). These data do not currently have a sampling variance, nor have
>transformed effect sizes been calculated. I have 3 levels of nested data: Level 1
>= "timepoint_id", Level 2 = "sample_id", Level 1 = "study_id" which account for
>non-independence of data. Here, I will call my data file "dat."
>
>  1.  How should I structure the escalc command to derive a "yi" and "V" values
>needed for the rma.mv analysis? Would my measure be "PLO"?

"PLO" is for binomial data, which is not what you appear to have. A logit transformation may in itself be useful for proportions (however derived), but the calculation of the sampling variance in escalc() assumes that each proportion was calculated based on a random variable that follows a binomial distribution.

Ideally, one would need the standard errors of the proportions, which should come from whatever method/model was used to obtain those proportions. Then one can use the delta method to obtain the sampling variances of the logit-transformed proportions.

Getting the covariance between sampling errors would be even more difficult (multiple proportions obtained from the same sample will have non-zero correlations between the sampling errors).

>  2.  Would this structure be acceptable: rma.mv(yi, vi, random = ~ 1 |
>study_id/sample_id/timepoint_id, data=dat)?

Possibly, but it is impossible to answer this properly without further details. For example, this model assumes constant correlation across timepoints, regardless of how far they are apart.

And as noted above, this model would not account for non-independent sampling errors.

>Thanks,
>Jordan

```