[R-meta] Non-positive definite covariance matrix for rma.mv

[Viechtbauer, Wolfgang (NP)]

Dear Pia,

You use vcalc() as follows:

> V <- vcalc(vi=ES_all$vi, cluster=DatMA$id_database)

This assumes a correlation of 1 within clusters. An example:

dat <- data.frame(study=c(1,1,1,2,3,3), vi=runif(6, .01, .10))
V <- vcalc(vi, cluster=study, data=dat)
blsplit(V, dat$study, fun=cov2cor)

I don't think this is what you intended. If you have multiple observations within clusters, then you indicate this to the function via 'obs' combined with 'rho' to provide the correlation:

dat <- data.frame(study=c(1,1,1,2,3,3), obs=c(1,2,3,1,1,2), vi=runif(6, .01, .10))
V <- vcalc(vi, cluster=study, obs=obs, data=dat, rho=0.6)
blsplit(V, dat$study, fun=cov2cor)

Best,
Wolfgang

> -----Original Message-----
> From: Pia-Magdalena Schmidt <pia-magdalena.schmidt using uni-bonn.de>
> Sent: Wednesday, September 4, 2024 15:05
> To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-
> project.org>; James Pustejovsky <jepusto using gmail.com>
> Cc: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
> Subject: Re: [R-meta] Non-positive definite covariance matrix for rma.mv
>
> Dear all,
> although this issue has been raised recently (see below), I would highly
> appreciate your advice, particularly regarding whether I might use nearPD to
> approximate a PD V matrix.
> I am running a meta-analysis with 30 studies, 11 of which report more than
> one effect size (2 or 3).
> Therefore, I would like to fit a random-effects model using the rma.mv
> function to account for these dependencies.
> I used vcalc to approximate the var cov matrix and received the following
> warning for all clusters (11) with more than one effect size: “The var-cov
> matrix appears to be not positive definite in cluster x”.
> The correlation (r= 0.6) used is an approximation based on available raw
> data.
> I inspected the eigenvalues of the according submatrices and found 3
> negative eigenvalues close to 0, else values near 0 (see the values below).
> If I round the values accordingly to your previous emails, the matrix is
> semi-PD.
> I am wondering whether I might use the nearPD function to be able to fit the
> rma.mv model to my data?
> Best,
> Pia
>
> ES_all <- escalc(measure="SMCC", m1i=DatMA$'1_drug_mean',
> sd1i=DatMA$'1_drug_sd', ni = DatMA$'1_n', m2i=DatMA$'1_plc_mean',
> sd2i=DatMA$'1_plc_sd', pi=DatMA$'1_p_value', ri = DatMA$'1_ri')
>
> V <- vcalc(vi=ES_all $vi, cluster=DatMA$id_database)
>
> res <- rma.mv(yi=ES_all$yi, V, random = ~ 1 | id_database/effect_id, data =
> DatMA)
>
> eigenvalues:
> $`1`
> [1] 0.335876
> $`2`
> [1] 6.788500e+00 3.552714e-15 0.000000e+00
> $`3`
> [1] 0.2049939
> $`4`
> [1] 0.1275193
> $`5`
> [1] 2.792778e-01 1.387779e-17
> $`6`
> [1] 0.1974481
> $`7`
> [1] 0.2392147
> $`8`
> [1] 0.09561453
> $`9`
> [1] 0.1023009
> $`10`
> [1] 7.202168e-02 6.938894e-18
> $`11`
> [1] 0.08839118
> $`12`
> [1] 0.05667013
> $`13`
> [1] 2.160967e-01 5.551115e-17 -1.387779e-17
> $`14`
> [1] 1.906503e-01 5.551115e-17 0.000000e+00
> $`15`
> [1] 0.2379626
> $`16`
> [1] 1.060134e+00 5.551115e-17
> $`17`
> [1] 4.879074e-02 1.734723e-18
> $`18`
> [1] 0.1956611
> $`19`
> [1] 0.1319664
> $`20`
> [1] 4.783856e-01 1.665335e-16 2.775558e-17
> $`21`
> [1] 0.07701826
> $`22`
> [1] 0.08400946
> $`23`
> [1] 0.4219658
> $`24`
> [1] 3.485124e+00 -5.551115e-17
> $`25`
> [1] 4.095845e-01 -2.775558e-17
> $`26`
> [1] 0.1124492
> $`27`
> [1] 0.09964694
> $`28`
> [1] 2.130419e-01 6.938894e-18
> $`29`
> [1] 0.2391303
> $`30`
> [1] 0.122081
>
> round(eigen(V)$values, 8)
>
> [1] 6.78849973 3.48512378 1.06013363 0.47838557 0.42196575 0.40958453
> 0.33587598 0.27927780 0.23921468 0.23913035 0.23796263 0.21609670 0.21304191
> [14] 0.20499394 0.19744806 0.19566106 0.19065030 0.13196637 0.12751926
> 0.12208097 0.11244916 0.10230087 0.09964694 0.09561453 0.08839118 0.08400946
> [27] 0.07701826 0.07202168 0.05667013 0.04879074 0.00000000 0.00000000
> 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
> [40] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000