[R-meta] Calculating covariances in multivariate meta-analysis

[Mark White]

Thanks Wolfgang! I'll try to implement that. One of the other issues is
that, in two of the studies, *everyone* has *every* measure of x_k and y_k
(where k is the study). However, in another, I observe both types of x_k,
but only *one* type of y_k:

# A tibble: 20 x 4
   ill_imm_auth ksu_auth ill_imm_prej ksu_prej
          <dbl>    <dbl>        <dbl>    <dbl>
 1        5.375       NA          4.2      2.0
 2        1.500       NA          3.4      3.8
 3        2.875       NA          4.4      3.6
 4        3.250       NA          4.2      2.6
 5        4.125       NA          4.6      4.8
 6        2.750       NA          2.6      3.6
 7        2.875       NA          2.4      2.4
 8        6.000       NA          2.8      3.0
 9        5.875       NA          4.6      2.0
10        3.875       NA          3.8      2.4
11           NA    1.000          3.4      2.6
12           NA    2.375          3.2      4.0
13           NA    3.500          3.4      2.4
14           NA    1.000          4.0      1.6
15           NA    1.000          3.2      1.0
16           NA    2.500          2.2      1.6
17           NA    1.125          1.0      1.2
18           NA    2.500          4.2      1.6
19           NA    1.000          1.8      1.0
20           NA    2.750          3.0      2.4

Since I just want to know the meta-analytic average (y ~ 1), is there a
simpler way than making this matrix?

On Wed, Jan 17, 2018 at 3:09 PM, Viechtbauer Wolfgang (SP) <
wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:

> Indeed, the computations are a *huge* pain. I wrote this a while ago:
>
> https://gist.github.com/wviechtb/700983ab0bde94bed7c645fce770f8e9
>
> It will go into metafor at some point.
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-
> bounces at r-project.org] On Behalf Of Mark White
> Sent: Wednesday, 17 January, 2018 19:03
> To: James Pustejovsky
> Cc: r-sig-meta-analysis at r-project.org
> Subject: Re: [R-meta] Calculating covariances in multivariate meta-analysis
>
> James,
>
> Thank you—I have looked at that citation (and similar ones mentioned in the
> documentation for metafor::rma.mv); yes, they do appear to be somewhat of
> a
> pain.
>
> The goal here is simple: All I want is the overall, meta-analytic
> correlation and confidence interval. That is, a multivariate estimate for y
> ~ 1 (i.e., metafor::rma.mv(yi, V)).
>
> Mark
>
> On Wed, Jan 17, 2018 at 11:30 AM, James Pustejovsky <jepusto at gmail.com>
> wrote:
>
> > Mark,
> >
> > The formulas needed to calculate the covariances are given in the
> > following reference:
> >
> > Olkin, I., & Finn, J. (1990). Testing correlated correlations.
> >> Psychological Bulletin, 108(2), 330–333.
> >
> >
> > Unfortunately they're a bit complicated, a pain in the rear to program,
> > and sometimes return non-positive definite covariance matrices that
> create
> > problems at the meta-analysis stage. If you've got the raw data, a
> cleaner
> > approach would be to use a basic bootstrap (i.e., re-sampling cases) for
> > the set of correlations you want to meta-analyze.
> >
> > But a larger question might be relevant here: what is the goal of
> > conducting a multi-variate meta-analysis on these correlations? Is it to
> > come up with a synthetic correlation matrix? To understand heterogeneity
> > across studies in the correlations? Depending on your answer--and given
> > that you have access to the raw data--other statistical approaches (other
> > than MV meta-analysis) might be equally or better suited for the problem.
> >
> > James
> >
> > On Wed, Jan 17, 2018 at 9:17 AM, Mark White <markhwhiteii at gmail.com>
> > wrote:
> >
> >> Hello all,
> >>
> >> I have 8 studies in my dissertation; I want to meta-analyze the
> >> correlation
> >> between focal variable X and outcome Y. Let variables for Study 1 be x1
> >> and
> >> y1, Study 2 be x2 and y2, etc. However, I also have *various
> measurements
> >> *of
> >> each construct in some studies. For example, in Study 1, I have the
> >> correlation between x1_1 and y1_1, as well as x1_2 and y1_2. And in
> Study
> >> 2, I have the correlation between x2_1 and y2_1 as well as x2_2 and
> y2_2.
> >> In Study 3, I have these all the way up to x3_10 and y3_10.
> >>
> >> I want to perform a multivariate meta-analysis, since I have all of the
> >> raw
> >> data. My question: How do I calculate the covariates between these
> >> correlations? I know I want to end up with a covariance matrix where the
> >> diagonal is the variance, off-diagonal the covariances (with all zeros
> >> where they are from different studies). In the analysis examples on the
> >> metafor website, these are already calculated for the user. How do I
> >> calculate these from my raw data?
> >>
> >> Thank you,
> >> Mark
>

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