# [R-meta] Variance-covariance is not positive definite.

Ana Benítez @ben|tez81 @end|ng |rom gm@||@com
Thu Sep 26 13:32:56 CEST 2019

```Dear Wolfgang,

Apologies for sending the text in rich-text format. Here I copy-paste the
original message and I additionally attach a piece of code to solve the
issue. I got the code from Alfredo Sánchez-Tojar but he claims he got it
from someone else, maybe even you Wolfgang. The code is this:

# this function is to make sure that a is matrix positive-definitive
# it uses the function nearPD in the Matrix package to compute the
# nearest positive definite matrix to an approximate one
# Function reused from: https://osf.io/ayxrt/

PDfunc <- function(matrix){
require(Matrix)
if(corpcor::is.positive.definite(matrix) == T){
x <- corDiag
}else{
x <- Matrix::nearPD(matrix)
}
mat <- x\$mat
return(mat)
}

# is the matrix positive-definitive? No, run PDfunc to make it
# so. If a matrix is not positive-definite, it won't work

is.positive.definite(varcovar) # FALSE
varcovar  <-PDfunc(varcovar)
is.positive.definite(varcovar) # TRUE

And this is my original email in case someone is interested:

Dear Wolfgang and meta-analysis list subscribers,

I am running a muti-level meta-regression in which I have several
comparisons using a common control for some of the studies. My effect size
is the log response ratio (RR) and I have as random effects Study, Effect
size ID and Species nested in Family and Order. I am also rerunning the
same analysis using a phylogenetic correlation matrix instead of nesting
species in higher taxonomic taxa (see end of the message).

To calculate the var-covar matrix I have used Wolfgang’s code:

calc.v <- function(x) {
v <- matrix(x\$sd_m[1]^2 / (x\$N_m[1] * x\$Mean_m[1]^2), nrow=nrow(x),
ncol=nrow(x))
diag(v) <- x\$var
v
}
#make sure we order the database by the variable we are splitting on
(CommonControl)
mamdata <- mamdata[order(mamdata\$CommonControl),]

Vmam<- bldiag(lapply(split(mamdata, mamdata\$CommonControl), calc.v))

Yet, when I run the meta-analysis, and although I get reasonable results, I
get the warning: 'V' appears to be not positive definite. See results here:

Multivariate Meta-Analysis Model (k = 705; method: REML)

logLik   Deviance        AIC        BIC       AICc
116.6641  -233.3282  -219.3282  -187.4407  -219.1671

Variance Components:

estim    sqrt  nlvls  fixed                        factor
sigma^2.1  0.0149  0.1223    131     no                     Reference
sigma^2.2  0.0275  0.1657    705     no                            ID
sigma^2.3  0.0013  0.0363     13     no                         Order
sigma^2.4  0.0069  0.0831     37     no                  Order/Family
sigma^2.5  0.0242  0.1554    167     no  Order/Family/Species.nominal

Test of Moderators (coefficient(s) 2):
QM(df = 1) = 18.0854, p-val < .0001

Model Results:

estimate      se     zval    pval    ci.lb    ci.ub
intrcpt       0.1768  0.0636   2.7780  0.0055   0.0521   0.3015   **
logmass   -0.0880  0.0207  -4.2527  <.0001  -0.1286  -0.0475  ***

I have also tried computing the var-covar matrix using the script provided
by Moatt et al. 2016, The effect of dietary restriction on reproduction: a
meta-analytic perspective. BMC evolutionary biology, 16(1), 199, available
modified the script to calculate the var-covar matrix for RR as:

# create square matrix matching N of ES, filled with zeros
V <- matrix(0,nrow = dim(mamdata)[1],ncol = dim(mamdata)[1])
rownames(V) <- mamdata\$ID
colnames(V) <- mamdata\$ID

# find start and end coordinates for the subsets
shared_coord <-
which(mamdata\$CommonControl%in%mamdata\$CommonControl[duplicated(mamdata\$CommonControl)]==TRUE)
shared_coord

# matrix of combinations of coordinates for each experiment with shared
control
combinations <- do.call("rbind", tapply(shared_coord,
mamdata[shared_coord,"CommonControl"], function(x) t(combn(x,2))))
combinations

# calculate covariance values between ES values at the positions in
shared_list and place them on the matrix
for (i in 1:dim(combinations)[1]){
p1 <- combinations[i,1]
p2 <- combinations[i,2]
p1_p2_cov <- mamdata\$sd_m[1]^2 / (mamdata\$N_m[1] * mamdata\$Mean_m[1]^2)
V[p1,p2] <- p1_p2_cov
V[p2,p1] <- p1_p2_cov
}

# add the diagonal - use df\$var as matrix diagonal
diag(V) <-  mamdata\$var

Using this approach the results are pretty similar but I still get the
warning: 'V' appears to be not positive definite.

Multivariate Meta-Analysis Model (k = 705; method: REML)

logLik   Deviance        AIC        BIC       AICc
115.2436  -230.4872  -216.4872  -184.5997  -216.3261

Variance Components:

estim    sqrt  nlvls  fixed                        factor
sigma^2.1  0.0153  0.1238    131     no                     Reference
sigma^2.2  0.0274  0.1656    705     no                            ID
sigma^2.3  0.0014  0.0370     13     no                         Order
sigma^2.4  0.0070  0.0836     37     no                  Order/Family
sigma^2.5  0.0242  0.1554    167     no  Order/Family/Species.nominal

Test of Moderators (coefficient(s) 2):
QM(df = 1) = 18.3750, p-val < .0001

Model Results:

estimate      se     zval    pval    ci.lb    ci.ub
intrcpt       0.1799  0.0639   2.8159  0.0049   0.0547   0.3051   **
logmass   -0.0890  0.0208  -4.2866  <.0001  -0.1298  -0.0483  ***

Needless to say that when I run the phylogenetic meta-analysis I also get
the warning. Results below:

Multivariate Meta-Analysis Model (k = 702; method: REML)

logLik   Deviance        AIC        BIC       AICc
115.2222  -230.4445  -218.4445  -191.1380  -218.3233

Variance Components:

estim    sqrt  nlvls  fixed           factor    R
sigma^2.1  0.0135  0.1161    131     no        Reference   no
sigma^2.2  0.0276  0.1662    702     no               ID   no
sigma^2.3  0.0274  0.1654    164     no             SPID   no
sigma^2.4  0.0090  0.0951    161     no  Species.nominal  yes

Test of Moderators (coefficient(s) 2):
QM(df = 1) = 17.6159, p-val < .0001

Model Results:

estimate      se     zval    pval    ci.lb    ci.ub
intrcpt   0.1486  0.0744   1.9979  0.0457   0.0028   0.2943    *
logmass   -0.0792  0.0189  -4.1971  <.0001  -0.1162  -0.0422  ***

My question is whether I should be worried by the warning or not and if so,
how I can fix it.

Best,

Ana

El mar., 24 sept. 2019 a las 13:12, Viechtbauer, Wolfgang (SP) (<
wolfgang.viechtbauer using maastrichtuniversity.nl>) escribió:
>
> Dear Ana,
>
> Please send messages to this list in plain text (no HTML / rich-text
emails). As you can see below, your message includes lots of superfluous
empty lines, which makes it hard to read.
>
> Based on what you posted, it is not possible to determine why the
construction of the V matrix leads to a non-positive definite matrix. We
would have to see the actual dataset (mamdata). The only thing I can
suggest to check is that the common control group is always given by
variables Mean_m, sd_m, and N_m and not the other three variables that are
used for the comparison groups. Also, how was variable 'var' computed? Was
it computed using escalc() or was this computed based on other software? In
the latter case, the computation used may not match up with what the
calc.v() function below uses for computing the covariances.
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: R-sig-meta-analysis [mailto:
r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Ana Benítez
> Sent: Thursday, 19 September, 2019 12:14
> To: r-sig-meta-analysis using r-project.org
> Subject: [R-meta] Variance-covariance is not positive definite.
>
> Dear Wolfgang and meta-analysis list subscribers,
>
>
>
> I am running a muti-level meta-regression in which I have several
> comparisons using a common control for some of the studies. My effect size
> is the log response ratio (RR) and I have as random effects Study, Effect
> size ID and Species nested in Family and Order. I am also rerunning the
> same analysis using a phylogenetic correlation matrix instead of nesting
> species in higher taxonomic taxa (see end of the message).
>
>
>
> To calculate the var-covar matrix I have used Wolfgang’s code:
>
>
>
> calc.v <- function(x) {
>
>   v <- matrix(x\$sd_m[1]^2 / (x\$N_m[1] * x\$Mean_m[1]^2), nrow=nrow(x),
> ncol=nrow(x))
>
>   diag(v) <- x\$var
>
>   v
>
> }
>
>
> #make sure we order the database by the variable we are splitting on
> (CommonControl)
>
> mamdata <- mamdata[order(mamdata\$CommonControl),]
>
>
>
> Vmam<- bldiag(lapply(split(mamdata, mamdata\$CommonControl), calc.v))
>
>
>
>
> Yet, when I run the meta-analysis, and although I get reasonable results,
I
> get the warning: 'V' appears to be not positive definite. See results
here:
>
>
>
> Multivariate Meta-Analysis Model (k = 705; method: REML)
>
>
>
>    logLik   Deviance        AIC        BIC       AICc
>
>  116.6641  -233.3282  -219.3282  -187.4407  -219.1671
>
>
>
> Variance Components:
>
>
>
>             estim    sqrt  nlvls  fixed                        factor
>
> sigma^2.1  0.0149  0.1223    131     no                     Reference
>
> sigma^2.2  0.0275  0.1657    705     no                            ID
>
> sigma^2.3  0.0013  0.0363     13     no                         Order
>
> sigma^2.4  0.0069  0.0831     37     no                  Order/Family
>
> sigma^2.5  0.0242  0.1554    167     no  Order/Family/Species.nominal
>
>
>
> Test of Moderators (coefficient(s) 2):
>
> QM(df = 1) = 18.0854, p-val < .0001
>
>
>
> Model Results:
>
>
>
>                         estimate      se     zval    pval    ci.lb
> ci.ub
>
> intrcpt              0.1768  0.0636   2.7780  0.0055   0.0521   0.3015
**
>
> logmass           -0.0880  0.0207  -4.2527  <.0001  -0.1286  -0.0475  ***
>
>
>
> I have also tried computing the var-covar matrix using the script provided
> by Moatt et al. 2016, The effect of dietary restriction on reproduction: a
> meta-analytic perspective. BMC evolutionary biology, 16(1), 199, available
> modified the script to calculate the var-covar matrix for RR as:
>
>
>
> # create square matrix matching N of ES, filled with zeros
>
> V <- matrix(0,nrow = dim(mamdata)[1],ncol = dim(mamdata)[1])
>
> rownames(V) <- mamdata\$ID
>
> colnames(V) <- mamdata\$ID
>
>
>
> # find start and end coordinates for the subsets
>
> shared_coord <-
>
which(mamdata\$CommonControl%in%mamdata\$CommonControl[duplicated(mamdata\$CommonControl)]==TRUE)
>
> shared_coord
>
>
>
> # matrix of combinations of coordinates for each experiment with shared
> control
>
> combinations <- do.call("rbind", tapply(shared_coord,
> mamdata[shared_coord,"CommonControl"], function(x) t(combn(x,2))))
>
> combinations
>
>
>
> # calculate covariance values between ES values at the positions in
> shared_list and place them on the matrix
>
> for (i in 1:dim(combinations)[1]){
>
>   p1 <- combinations[i,1]
>
>   p2 <- combinations[i,2]
>
>   p1_p2_cov <- mamdata\$sd_m[1]^2 / (mamdata\$N_m[1] * mamdata\$Mean_m[1]^2)
>
>   V[p1,p2] <- p1_p2_cov
>
>   V[p2,p1] <- p1_p2_cov
>
> }
>
>
>
> # add the diagonal - use df\$var as matrix diagonal
>
> diag(V) <-  mamdata\$var
>
>
>
>
>
> Using this approach the results are pretty similar but I still get the
> warning: 'V' appears to be not positive definite.
>
>
>
> Multivariate Meta-Analysis Model (k = 705; method: REML)
>
>
>
>    logLik   Deviance        AIC        BIC       AICc
>
>  115.2436  -230.4872  -216.4872  -184.5997  -216.3261
>
>
>
> Variance Components:
>
>
>
>             estim    sqrt  nlvls  fixed                        factor
>
> sigma^2.1  0.0153  0.1238    131     no                     Reference
>
> sigma^2.2  0.0274  0.1656    705     no                            ID
>
> sigma^2.3  0.0014  0.0370     13     no                         Order
>
> sigma^2.4  0.0070  0.0836     37     no                  Order/Family
>
> sigma^2.5  0.0242  0.1554    167     no  Order/Family/Species.nominal
>
>
>
> Test of Moderators (coefficient(s) 2):
>
> QM(df = 1) = 18.3750, p-val < .0001
>
>
>
> Model Results:
>
>
>
>                         estimate      se     zval    pval    ci.lb
> ci.ub
>
> intrcpt              0.1799  0.0639   2.8159  0.0049   0.0547   0.3051
**
>
> logmass           -0.0890  0.0208  -4.2866  <.0001  -0.1298  -0.0483  ***
>
>
>
> Needless to say that when I run the phylogenetic meta-analysis I also get
> the warning. Results below:
>
>
>
> Multivariate Meta-Analysis Model (k = 702; method: REML)
>
>
>
>    logLik   Deviance        AIC        BIC       AICc
>
>  115.2222  -230.4445  -218.4445  -191.1380  -218.3233
>
>
>
> Variance Components:
>
>
>
>             estim    sqrt  nlvls  fixed           factor    R
>
> sigma^2.1  0.0135  0.1161    131     no        Reference   no
>
> sigma^2.2  0.0276  0.1662    702     no               ID   no
>
> sigma^2.3  0.0274  0.1654    164     no             SPID   no
>
> sigma^2.4  0.0090  0.0951    161     no  Species.nominal  yes
>
>
>
> Test of Moderators (coefficient(s) 2):
>
> QM(df = 1) = 17.6159, p-val < .0001
>
>
>
> Model Results:
>
>
>
>                         estimate      se     zval    pval    ci.lb
> ci.ub
>
> intrcpt               0.1486  0.0744   1.9979  0.0457   0.0028   0.2943
*
>
> logmass           -0.0792  0.0189  -4.1971  <.0001  -0.1162  -0.0422  ***
>
>
>
> My question is whether I should be worried by the warning or not and if
so,
> how I can fix it.
>
>
> Best,
>
> Ana
>
>
> --
> Ana Benítez López
>
> Juan de la Cierva-Incorporación Postdoctoral Fellow
> The Integrative Ecology Group (http://ebd10.ebd.csic.es/)
> Estación Biológica de Doñana (CSIC)
> Avenida Américo Vespucio, 26, 41092, Sevilla, Spain
> Phone: 954 46 67 00 ext. 1451
>
>  https://www.researchgate.net/profile/Ana_Benitez-Lopez
>
> orcid.org/0000-0002-6432-1837
>
> http://www.environmentalevidencejournal.org/

--
Ana Benítez López

Juan de la Cierva-Incorporación Postdoctoral Fellow
The Integrative Ecology Group (http://ebd10.ebd.csic.es/)
Estación Biológica de Doñana (CSIC)
Avenida Américo Vespucio, 26, 41092, Sevilla, Spain
Phone: 954 46 67 00 ext. 1451

https://www.researchgate.net/profile/Ana_Benitez-Lopez

orcid.org/0000-0002-6432-1837

http://www.environmentalevidencejournal.org/

[[alternative HTML version deleted]]

```