Correlation matrix is not positive definite

[stonelight816]

Hi Sacha,

I encounter a problem when I used bootnet function. For my data, I got 37 nodes and 43 samples. Although the number of samples is not large, it still exceeds the number of nodes.

The code I'm using is as follows:
mynetwork <- estimateNetwork(raw_data, default = "EBICglasso", tuning = 0.5,corMethod="spearman")
b1<-bootnet(mynetwork,nBoots=1000,type="nonparametric",nCores=1,statistics=c("strength","betweenness", "closeness","edge"))

I got the following error message:
Note: bootnet will store only the following statistics: strength, betweenness, closeness, edge
Bootstrapping...
| | 0%Error in bootnet_correlate(data = data, corMethod = corMethod, corArgs = corArgs, :
Correlation matrix is not positive definite.
Error in bootnet_correlate(data = data, corMethod = corMethod, corArgs = corArgs, :
Correlation matrix is not positive definite.
Error in bootnet_correlate(data = data, corMethod = corMethod, corArgs = corArgs, :
Correlation matrix is not positive definite.
Error in bootnet_correlate(data = data, corMethod = corMethod, corArgs = corArgs, :
Correlation matrix is not positive definite.
Error in bootnet_correlate(data = data, corMethod = corMethod, corArgs = corArgs, :
Correlation matrix is not positive definite.
Error in bootnet_correlate(data = data, corMethod = corMethod, corArgs = corArgs, :
Correlation matrix is not positive definite.
Error in bootnet_correlate(data = data, corMethod = corMethod, corArgs = corArgs, :
Correlation matrix is not positive definite.
Error in bootnet_correlate(data = data, corMethod = corMethod, corArgs = corArgs, :
Correlation matrix is not positive definite.
Error in bootnet_correlate(data = data, corMethod = corMethod, corArgs = corArgs, :
Correlation matrix is not positive definite.
Error in bootnet_correlate(data = data, corMethod = corMethod, corArgs = corArgs, :
Correlation matrix is not positive definite.
Error in bootnet_correlate(data = data, corMethod = corMethod, corArgs = corArgs, :
Correlation matrix is not positive definite.
Error in bootnet(mynetwork, nBoots = 1000, type = "nonparametric", nCores = 1, :
Maximum number of errors in bootstraps reached

Thanks for the help!

[SachaEpskamp]

While the original sample has 43 cases, the bootstrapped samples will have fewer than 43 cases leading to potentially non-positive definite correlation matrices used as input. While technically EBICglasso can still be used (you would have to overwrite this error both in qgraph and bootnet) I really do not advice you to do so. See here for more info:

#126

[stonelight816]

Hi Sacha,

thanks for your response. In this example:#126, the number of datapoints was fewer than number of nodes. In my project, number of datapoints (43) beyonds the number of nodes (37). Why would this error still happened?

[SachaEpskamp]

Even though you have more datapoints than nodes in the original data, you don't have this in the bootstrapped data as you resample cases with replacement, leading to less unique cases. See for example:

# Original data with N = 11; P = 10:
data <- matrix(rnorm(11*10),11,10)
all(eigen(cor(data))$values > 0)
# Is positive definite

# Bootstrap sample:
set.seed(42)
bootdata <- data[sample(1:nrow(data),nrow(data),TRUE),]
all(eigen(cor(bootdata))$values > 0)
# No longer positive definite