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

[Andreas Voldstad]

Dear everyone,

I have one study in my meta-analysis with a covariance matrix that is non-positive definite.

I am wondering what consequences this might have for my meta-analysis with rma.mv, and whether you have any suggestions of how to deal with the issue.

The study had four arms and effect sizes are additionally correlated over time and within dyads.

The correlations over time and dyad members used for creating the covariance matrix was based on the corresponding correlations between participants' scores, estimated from the study dataset.

Because of the four arms, some effect sizes have no overlap, leading to blocks of zeros in the covariance matrix.

The covariance matrix is reproduced below:

study_escalc <- data.frame(  StudyID = c("StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA", "StudyA"),  Role = c("Husband", "Husband", "Wife", "Wife", "Husband", "Husband", "Wife", "Wife", "Husband", "Husband", "Wife", "Wife", "Husband", "Husband", "Wife", "Wife"),  Timenum = c(2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3),  Tx = c("Tx1", "Tx1", "Tx1", "Tx1", "Tx2", "Tx2", "Tx2", "Tx2", "Tx1", "Tx1", "Tx1", "Tx1", "Tx2", "Tx2", "Tx2", "Tx2"),  Control = c("Passive", "Passive", "Passive", "Passive", "Passive", "Passive", "Passive", "Passive", "Active", "Active", "Active", "Active", "Active", "Active", "Active", "Active"),  Contrast = c("Tx1 vs Passive", "Tx1 vs Passive", "Tx1 vs Passive", "Tx1 vs Passive", "Tx2 vs Passive", "Tx2 vs Passive", "Tx2 vs Passive", "Tx2 vs Passive", "Tx1 vs Active", "Tx1 vs Active", "Tx1 vs Active", "Tx1 vs Active", "Tx2 vs Active", "Tx2 vs Active", "Tx2 vs Active", "Tx2 vs Active"),  delta = c(0.467304, 0.429311, 0.145277, 0.248136, 0.684523, 0.537425, 0.380137, 0.335112, 0.432723, 0.480095, 0.145031, 0.252715, 0.628890, 0.572478, 0.373187, 0.338829),  v = c(0.053375, 0.053154, 0.051417, 0.051710, 0.056543, 0.056865, 0.052208, 0.052756, 0.053863, 0.053454, 0.050774, 0.053052, 0.056766, 0.057132, 0.051522, 0.054108),  N_tx = c(38, 39, 39, 38, 36, 35, 39, 37, 38, 39, 39, 38, 36, 35, 39, 37),  N_Control = c(39, 38, 39, 40, 39, 38, 39, 40, 38, 38, 40, 38, 38, 38, 40, 38),  Category = c("Husband_2", "Husband_3", "Wife_2", "Wife_3", "Husband_2", "Husband_3", "Wife_2", "Wife_3", "Husband_2", "Husband_3", "Wife_2", "Wife_3", "Husband_2", "Husband_3", "Wife_2", "Wife_3"),  Effect = c("Tx1 vs Passive_Husband_2", "Tx1 vs Passive_Husband_3", "Tx1 vs Passive_Wife_2", "Tx1 vs Passive_Wife_3", "Tx2 vs Passive_Husband_2", "Tx2 vs Passive_Husband_3", "Tx2 vs Passive_Wife_2", "Tx2 vs Passive_Wife_3", "Tx1 vs Active_Husband_2", "Tx1 vs Active_Husband_3", "Tx1 vs Active_Wife_2", "Tx1 vs Active_Wife_3", "Tx2 vs Active_Husband_2", "Tx2 vs Active_Husband_3", "Tx2 vs Active_Wife_2", "Tx2 vs Active_Wife_3"))

study_cormat <- matrix(c(  1.000000, 0.781447, 0.689538, 0.639455,  0.781447, 1.000000, 0.565192, 0.653545,  0.689538, 0.565192, 1.000000, 0.820650,  0.639455, 0.653545, 0.820650, 1.000000),  nrow=4, byrow=TRUE, dimnames = list(    c("Husband_2", "Husband_3", "Wife_2", "Wife_3"),    c("Husband_2", "Husband_3", "Wife_2", "Wife_3")))

Study_Vmat <-   vcalc(vi = v,        cluster = StudyID,        obs = Category,                 grp1 = Tx,         grp2 = Control,                 w1 = N_tx,        w2 = N_Control,                rho = study_cormat,        data = study_escalc)

# Warning message: The var-cov matrix appears to be not positive definite in cluster StudyA. cov2cor(Study_Vmat)



Warm wishes,

Andreas Voldstad (he/him)
PhD student in Psychiatry
University of Oxford
Please don�t feel obliged to read or respond to my email outside your own working hours.

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