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

[Pia-Magdalena Schmidt]

Dear Wolfgang,
Many thanks for pointing that out! That was indeed not what I had intended, 
and the change has solved the problem.
Best,
Pia

On Mi, 4 Sep 2024 14:03:39 +0000
  Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl> 
wrote:
> 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