# [R-meta] Computing var-covariance matrix with correlations of six non-independent outcomes

Mika Manninen m|xu89 @end|ng |rom gm@||@com
Tue Jul 7 21:53:07 CEST 2020

```James,

Thank you so much for replying.

The dataset (8 studies out of 25 included) can be created with the
following code:

###Creating vectors for the outcome, study, motivation, effect size, and
variance estimate

#Total effects/outcomes
outcome <- c(1:28)

#Study
study <- c(1,1,1,1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,6,7,8,8,8,8,8,8)

#Six different motivation types measured in the studies
motivation <- c(1,3,4,5,6,1,3,4,5,1,3,4,5,6,1,3,4,5,6,6,6,6,1,2,3,4,5,6)

#Hedges g:s
g <- c(0.6068, 0.0603, 0.2684, -0.0886, 0.0415, 1.592, 1.4031, 0.7928,
0.2013, 0.541, 0.1169,
0.3129, -0.0275, -0.3536, 1.5886, 2.7218, -1.6273, -0.4375, -1.0695,
-0.1247, -0.1038,
-0.2706, 0.2045, -0.2701, 0.3763, -0.7371, -0.0666, 0.2789)

#Variance estimates
v <- c( 0.0162, 0.0155, 0.0157, 0.0155, 0.0155, 0.1889,
0.17875984,0.15484225,
0.14432401, 0.0329, 0.0318, 0.0322, 0.0318, 0.0323, 0.1886, 0.2758,
0.1909, 0.147, 0.164, 0.0067, 0.0028, 0.004, 0.0726, 0.0729, 0.0735,
0.0771, 0.0723, 0.073)

###Dataset matrix with different levels and motivation types
meta <- cbind(outcome, study, motivation, g, v)
View(meta)

I created 6x6 correlation matrices (with 15 unique correlations) for the
eight included studies. I am not sure if this is the most sensible approach
as only a few studies have measured all six outcomes. Value NA reflects the
absence of a correlation (absence of that one or both of the motivation
types in the study). The row and column numbers (1-6) correspond to the
variable motivation in the created dataset.

### Correlation matrices for studies 1-8

study1c <- rbind(c(1, "NA", .96, .34, -.33, -.66), c("NA", "NA", "NA",
"NA", "NA", "NA"), c(.96, "NA", 1, .55, -.12, -.50),
c(.34, "NA", .55, 1, .53, .05), c(-.33, "NA", -.12, .53,
1, .72), c(-.66, "NA", -.50, .05, .72, 1))

study2c <- rbind(c(1, "NA", .96, .34, -.33, "NA"), c("NA", "NA", "NA",
"NA", "NA", "NA"), c(.96, "NA", 1, .55, -.12, "NA"),
c(.34, "NA", .55, 1, .53, "NA"), c(-.33, "NA", -.12, .53,
1, "NA"), c("NA", "NA", "NA", "NA", "NA", "NA"))

study3c <- rbind(c(1, "NA", .96, .34, -.33, -.66), c("NA", "NA", "NA",
"NA", "NA", "NA"), c(.96, "NA", 1, .55, -.12, -.50),
c(.34, "NA", .55, 1, .53, .05), c(-.33, "NA", -.12, .53,
1, .72), c(-.66, "NA", -.50, .05, .72, 1))

study4c <- rbind(c(1, "NA", .85, .35, .06, -.44), c("NA", "NA", "NA", "NA",
"NA", "NA"), c(.85, "NA", 1, .59, .46, -.14),
c(.35, "NA", .59, 1, .71, .27), c(.06, "NA", .46, .71, 1,
.52), c(-.44, "NA", -.14, .27, .52, 1))

study5c <- rbind(c("NA", "NA", "NA", "NA", "NA", "NA"), c("NA", "NA", "NA",
"NA", "NA", "NA"), c("NA", "NA", "NA", "NA", "NA", "NA"),
c("NA", "NA", "NA", "NA", "NA", "NA"), c("NA", "NA", "NA",
"NA", "NA", "NA"), c("NA", "NA", "NA", "NA", "NA", 1))

study6c <- rbind(c("NA", "NA", "NA", "NA", "NA", "NA"), c("NA", "NA", "NA",
"NA", "NA", "NA"), c("NA", "NA", "NA", "NA", "NA", "NA"),
c("NA", "NA", "NA", "NA", "NA", "NA"), c("NA", "NA", "NA",
"NA", "NA", "NA"), c("NA", "NA", "NA", "NA", "NA", 1))

study7c <- rbind(c("NA", "NA", "NA", "NA", "NA", "NA"), c("NA", "NA", "NA",
"NA", "NA", "NA"), c("NA", "NA", "NA", "NA", "NA", "NA"),
c("NA", "NA", "NA", "NA", "NA", "NA"), c("NA", "NA", "NA",
"NA", "NA", "NA"), c("NA", "NA", "NA", "NA", "NA", 1))

study8c <- rbind(c(1, .79, .84, .24, -.20, -.50), c(.79, 1, .93, .47, .00,
-.31), c(.84, .93, 1, .57, -.07, -.52),
c(.24, .47, .57, 1, .43, .01), c(-.20, .00, -.07, .43,
1, .55), c(-.50, -.31, -.52, .01, .55, 1))

#list with all the correlations matrices

corlist <- list(study1c, study2c, study3c, study4c, study5c, study6c,
study7c, study8c)

Mika

ti 7. heinäk. 2020 klo 19.54 James Pustejovsky (jepusto using gmail.com)
kirjoitti:

> Hi Mika,
>
> To add to Wolfgang's question, could you tell us a little bit more about
> how you have structured the data on correlations between types of
> motivation? Is it just one correlation matrix (6X6 matrix, with 1 + 2 + 3 +
> 4 + 5 = 15 unique correlations)? Or is it study-specific?
>
> This sort of calculation is a bit tricky to carry out so I am not
> surprised that you haven't found a solution in the listserv archives. If
> you are willing to share your dataset (or a subset thereof, say 3-4 studies
> worth of data), it may make it easier for us to help problem solve.
>
> James
>
> On Tue, Jul 7, 2020 at 11:42 AM Viechtbauer, Wolfgang (SP) <
> wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>
>> Dear Mika,
>>
>> What effect size measure are you using for the meta-analysis?
>>
>> Best,
>> Wolfgang
>>
>> >-----Original Message-----
>> >From: R-sig-meta-analysis [mailto:
>> r-sig-meta-analysis-bounces using r-project.org]
>> >On Behalf Of Mika Manninen
>> >Sent: Tuesday, 07 July, 2020 18:10
>> >To: r-sig-meta-analysis using r-project.org
>> >Subject: [R-meta] Computing var-covariance matrix with correlations of
>> six
>> >non-independent outcomes
>> >
>> >Hello,
>> >
>> >I am doing a meta-analysis looking at the effect of a teaching
>> intervention
>> >(versus control) on six types of motivation/behavioral regulation.
>> >Theoretically and empirically these constructs form a continuum in which
>> >the continuum neighbors are most strongly positively correlated and the
>> >furthest from one another most negatively correlated.
>> >
>> >I have 95 effects. These effects come from 25 studies, each reporting
>> >scores for between 1-6 motivation types. The number of effects per
>> >motivation ranges from 22 to 13. In some studies, they have measured only
>> >one or two types whereas in others they have measured 5 or all 6 types of
>> >motivation.
>> >
>> >I originally ran a separate random-effects meta-analysis for all the six
>> >outcomes. However, I got feedback that the dependency of the motivation
>> >types should be taken into account and a 3-level meta-analysis was
>> >recommended. After looking into it, the 3-level model seems to be a worse
>> >approach than the multivariate approach.
>> >
>> >As is not usually the case, I have succeeded in gathering all
>> correlations
>> >between all the motivation types for all studies (some from original
>> >reporting and some from previous meta-analysis findings).
>> >
>> >My question is, how do I compute the V-matrix for this data in order to
>> run
>> >the multivariate analysis? I read the whole archive but I could not find
>> a
>> >clear answer to the problem.
>> >
>> >Thank you very much in advance,
>> >
>> >Mika
>>
>> _______________________________________________
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>> R-sig-meta-analysis using r-project.org
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>>
>

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