Re: Problem with MTMM simulation with higher order trait

[Alex Schoemann]

Hi Hacer,

It seems like your specification of the higher order trait is the issue. One thing to consider, you haven't explicitly specified the variances/residual variances of the latent variables. I'm guessing they're being set to 1, and this is likely the culprit for your error. I'd recommend explicitly setting those values to help with debugging (further, I'd guess that including residual covariances between all lower order latent variables isn't helping here).

Alex

On Sunday, October 28, 2018 at 3:10:08 PM UTC-4, Hacer Karamese wrote:

Hello everyone, 

I'm trying to simulate mtmm data with higher order trait. When I use the code below I get this error message : " Error in MASS::mvrnorm(n = sample.nobs[g], mu = Mu.hat[[g]], Sigma = COV,  : 'Sigma' is not positive definite "

When I remove the second order trait, the code works without problem. What is the problem with my code?

Thanks,

Hacer

Model1<-'

##traits

ListeningSpeaking=~ .49*CELDTls + .95*ELDlo+.95*ELDlt

Reading=~ .55*CELDTr+ .98*ELDwa+.97*ELDfv+.95*ELDc+.94*ELDlr

Writing=~ .60*CELDTw+ .96*ELDw+.95*ELDwc

##methods

CELDT=~.35*CELDTls +.65*CELDTr +.69*CELDTw 

ELD=~.28*ELDlo +.27*ELDlt +.16*ELDwa +.21*ELDfv +.30*ELDc +.31*ELDlr +.23*ELDw +.24*ELDwc

##higher order trait

HOT=~ .957*ListeningSpeaking+.999*Reading+.991*Writing

##trait correlations

ListeningSpeaking~~.5*Reading

ListeningSpeaking~~.5*Writing

Writing~~.5*Reading

# methods correlation

CELDT ~~.3*ELD

##zero cross covariances

ListeningSpeaking~~0*CELDT

Reading~~0*CELDT

Writing ~~0*CELDT

ListeningSpeaking~~0*ELD

Reading~~0*ELD

Writing ~~0*ELD

HOT~~0*CELDT

HOT~~0*ELD

##distribution of categories in each indicator 

CELDTls|-.70*t1+ .39*t2+ 1.16*t3+ 2.05*t4

CELDTr|-.70*t1+ .39*t2+ 1.16*t3+ 2.05*t4

CELDTw|-.70*t1+ .39*t2+ 1.16*t3+ 2.05*t4

ELDlo|-.70*t1+ .39*t2+ 1.16*t3+ 2.05*t4

ELDlt|-.70*t1+ .39*t2+ 1.16*t3+ 2.05*t4

ELDwa|-.70*t1+ .39*t2+ 1.16*t3+ 2.05*t4

ELDfv|-.70*t1+ .39*t2+ 1.16*t3+ 2.05*t4

ELDc|-.70*t1+ .39*t2+ 1.16*t3+ 2.05*t4

ELDlr|-.70*t1+ .39*t2+ 1.16*t3+ 2.05*t4

ELDw|-.70*t1+ .39*t2+ 1.16*t3+ 2.05*t4

ELDwc|-.70*t1+ .39*t2+ 1.16*t3+ 2.05*t4

'

Model<-'ListeningSpeaking=~ ELDlt+CELDTls + ELDlo

Reading=~ ELDwa+CELDTr+ ELDfv+ELDc+ELDlr

Writing=~ ELDw+CELDTw+ELDwc

CELDT=~CELDTls +CELDTr +CELDTw 

ELD=~ELDlo +ELDlt +ELDwa +ELDfv +ELDc +ELDlr +ELDw +ELDwc 

HOT=~ ListeningSpeaking+Reading+Writing

ListeningSpeaking~~0*CELDT

Reading~~0*CELDT

Writing ~~0*CELDT

ListeningSpeaking~~0*ELD

Reading~~0*ELD

Writing ~~0*ELD 

HOT~~0*CELDT

HOT~~0*ELD

'

Output1 <- sim(10,model=Model, n=500, generate=Model1, dataOnly= TRUE) #raw data only

Output2 <- sim(100,model=Model, n=1000, generate=Model1, std.lv=TRUE, model.type= "cfa", estimator= 'WLSMV')

mysample<-simulateData(Model1, model.type = "cfa", seed=1234, sample.nobs = 5000, return.type = "data.frame")

complete.fit<-cfa(Model, data=mysample,

                  ordered= c('CELDTls', 'CELDTr', 'CELDTw','ELDlo', 'ELDlt', 'ELDwa', 'ELDfv' ,'ELDc' ,'ELDlr', 'ELDw', 'ELDwc'),      

                  estimator= 'DWLS', mimic= 'Mplus', std.lv=T, std.ov=T)

[Hacer Karamese]

Hi Alex,

Thanks for your feedback. Unfortunately, fixing variances of higher and/or lower latent variables doesn't solve the problem.

Thanks,

Hacer 

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[Terrence Jorgensen]

" Error in MASS::mvrnorm(n = sample.nobs[g], mu = Mu.hat[[g]], Sigma = COV,  : 'Sigma' is not positive definite "

This means your population covariance matrix is not possible.  To see why, run this code to see what your model implies Sigma would be:

fitted(sem(Model1))

As you can see, the diagonal elements are 1, so this is a correlation matrix.  But there are several correlations > 1, which makes Sigma NPD.

Try setting the population factor variances to values < 1, and check the implied Sigma by trial and error until you find values that work.  From a practical standpoint, starting with loadings nearly == 1 does not leave you a lot of wiggle room if you are considering those to be standardized loadings, because nearly all their variance is due to that common factor (so that doesn't leave a method factor much variance to explain).

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen