Warning: covariance matrix of latent variables is not positive definite

[fotin...@gmail.com]

Hi,

I have looked on the forum and this has been covered before but I am confused with my particular situation.

I am running the following code and I receive the warning message that the covariance matrix is not positive definite.  See code and results of inspect function below.  I receive good model fit so I am not sure what to do at this stage.  Is this telling me that I have to exclude PAa from my model?  I need to keep PAa in the model so I am not sure what to do at this stage if anything at all.

Thanks!

model.Rq3eq <- '

# measurement model

ERa =~ ER1 + ER2 + a4*ER3 + a2*ER4 + a3*ER5

PAa =~ PA1 + PA2 + PAMV1

ERb =~ a4*ER6 + a2*ER7 + a3*ER8

ERc =~ a4*ER9 + a2*ER10 + a3*ER11

CaAap =~ CogAbVerbMCS3BAS + CogAbNVMCS3BASPC + AcAtMCS3

AAa =~ AcAtMCS4MSS + AcAtMCS4LSS + a1*AcAtMCS4E + a2*AcAtMCS4M + a3*AcAtMCS4S + a4*AcAtMCS4IT + a5*AcAtMCS4ADM + a6*AcAtMCS4PE

AAb =~ a1*AcAtMCS5E + a2*AcAtMCS5M + a3*AcAtMCS5S + a4*AcAtMCS5IT + a5*AcAtMCS5AD + a5*AcAtMCS5Mus + a6*AcAtMCS5PE

#Thresholds

ER3 | c1*t1 + c2*t2; ER9 | c1*t1 + c2*t2; ER6 | c1*t1 + c2*t2

ER4 | d1*t1 + d2*t2; ER10 | d1*t1 + d2*t2; ER7 | d1*t1 + d2*t2

ER5 | e1*t1 + e2*t2; ER11 | e1*t1 + e2*t2; ER8 | e1*t1 + e2*t2

AcAtMCS4E  | h1*t1 + h2*t2 + h1*t3 + h1*t4; AcAtMCS5E  | h1*t1 + h2*t2 + h1*t3 + h1*t4

AcAtMCS4M  | i1*t1 + i2*t2 + i1*t3 + i1*t4; AcAtMCS5M  | ii1*t1 + i2*t2 + i1*t3 + i1*t4

AcAtMCS4S  | j1*t1 + j2*t2 + j1*t3 + j1*t4; AcAtMCS5S  | j1*t1 + j2*t2 + j1*t3 + j1*t4

AcAtMCS4IT  | k1*t1 + k2*t2 + k1*t3 + k1*t4; AcAtMCS5IT  | k1*t1 + k2*t2 + k1*t3 + k1*t4

AcAtMCS4ADM  | l1*t1 + l2*t2 + l1*t3 + l1*t4; AcAtMCS5AD  | l1*t1 + l2*t2 + l1*t3 + l1*t4; AcAtMCS5Mus | l1*t1 + l2*t2 + l1*t3 + l1*t4

AcAtMCS4PE  | m1*t1 + m2*t2 + m1*t3 + m1*t4; AcAtMCS5PE  | mm1*t1 + m2*t2 + m1*t3 + m1*t4

# regressions

# a Path

ERa ~ a * PAa

ERc ~ d * PAa

# b path

AAa ~ b1 * ERa + b2 * CaAap

AAb ~ e1 * ERa + e2 * CaAap

#c prime path

AAa ~ cp * PAa

AAb ~ fp * PAa

#Indirect and total effects

ab := a * (b1 + b2)

total := cp + ab

de := d * (e1 + e2)

totali := fp + de'

fit.M3 <- sem(model.Rq3eq, data=imputeFMoutliersRC, std.lv = TRUE, estimator="WLSMV")

> inspect(fit.M3,"cor.lv")

             ERa    PAa    ERb    ERc    CaAap  AAa    AAb   

ERa    1.000                                          

PAa   -0.794  1.000                                   

ERb    0.303 -0.382  1.000                            

ERc    0.625 -0.788  0.301  1.000                     

CaAap  0.678 -0.854  0.407  0.673  1.000              

AAa    0.797 -0.657  0.259  0.252  0.587  1.000       

AAb    0.236 -0.649  0.229  0.925  0.491  0.335  1.000

[Terrence Jorgensen]

Is this telling me that I have to exclude PAa from my model? 

I'm not sure why you are singling out this one factor.  I don't see any Heywood cases in your latent correlation matrix, so I think the linear dependency is instead due to (multi)collinearity.  Without it being a specific parameter to test whether the CI includes acceptable values (http://journals.sagepub.com/doi/abs/10.1177/0049124112442138), it is not straight-forward to find out why it is a NPD matrix.  But if your model fits well, I would not let this warning prevent you from proceeding.

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

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

UvA web page: http://www.uva.nl/profile/t.d.jorgensen