Bivariate latent change score error: initial model-implied matrix (Sigma) is not positive definite

[Vibeke Nielsen]

Hi, I’ve a question regarding an error I got when adding ‘age at time 1’
(T1_ Age) to my model. Before I included age, the model worked perfectly. When
adding age at time 1 as covariance to prosocial behaviour and cortical thickness
at time one, in order to account for age related differences in baseline levels,
I got the following error: 

Error
in lav_model_estimate(lavmodel = lavmodel, lavpartable = lavpartable,  : lavaan ERROR: initial model-implied matrix
(Sigma) is not positive definite;check your model and/or starting parameters in
group 1.

In
addition: Warning message In lav_partable_check(lavpartable, categorical =
lavoptions$categorical,  :lavaan WARNING:
automatically added intercepts are set to zero: [T1_Age]
 

Below you will find my model. I hope someone can explain what is going
wrong and how to solve this. 

BLCS_PB_mPFC_CT<-'

T2_PB ~ 1*T1_PB 
dPB1 =~ 1*T2_PB
dPB1 ~ c(IC_dPB_b, IC_dPB_g)*1
T1_PB ~ c(IC_PB_b, IC_PB_g)*1
T2_PB ~ 0*1

T2_mPFC_CT ~ 1*T1_mPFC_CT 
dmPFC_CT1 =~ 1*T2_mPFC_CT             
T2_mPFC_CT ~ 0*1
T2_mPFC_CT ~~ 0*T2_mPFC_CT

dPB1 ~~ dPB1    
T1_PB ~~ T1_PB                    
T2_PB ~~ 0*T2_PB             

dmPFC_CT1 ~ c(IC_dCT_b, IC_dCT_g)*1  
T1_mPFC_CT ~ c(IC_CT_b, IC_CT_g)*1  
dmPFC_CT1 ~~ dmPFC_CT1 
T1_mPFC_CT ~~ T1_mPFC_CT

dmPFC_CT1 ~ c(G1_b, G1_g)* T1_PB +c(B2_b, B2_g)* T1_mPFC_CT  
dPB1 ~ c(G2_b, G2_g)* T1_mPFC_CT +c(B1_b,B1_g)* T1_PB

T1_PB ~~ T1_mPFC_CT                  
dPB1~~dmPFC_CT1                     
T1_Age ~~ T1_mPFC_CT + T1_PB


dr_PB_boys := IC_dPB_b
idr_PB_boys :=  (IC_PB_b * B1_b) + (IC_CT_b * G2_b)
t_PB_boys := IC_dPB_b + (IC_PB_b * B1_b)+ (IC_CT_b * G2_b)
dr_CT_boys := IC_dCT_b
idr_CT_boys :=  (IC_CT_b * B2_b) + (IC_PB_b * G1_b)
t_CT_boys :=  IC_dCT_b + (IC_CT_b * B2_b) + (IC_PB_b *G1_b)


dr_PB_girls := IC_dPB_g
idr_PB_girls :=  (IC_PB_g * B1_g) + (IC_CT_g * G2_g)
t_PB_girls := IC_dPB_g + (IC_PB_g * B1_g) + (IC_CT_g * G2_g)
dr_CT_girls := IC_dCT_g
idr_CT_girls :=  (IC_CT_g * B2_g) + (IC_PB_g * G1_g)
t_CT_girls :=  IC_dCT_g + (IC_CT_g * B2_g) + (IC_PB_g *G1_g)’

[Nickname]

Vibeke,
  Unfortunately, the model syntax is not sufficient to determine the model that you fit.  Depending upon the options to the function that you used to fit the model, the same syntax can fit different models.  However, I searched your syntax for T1_age and found only one instance on line 42:

T1_Age ~~ T1_mPFC_CT + T1_PB

  This could indicate a problem because if you are using fixed.x = TRUE then you should not reference the covariances of exogenous variables in your model syntax.  Conversely, if you are using fixed.x = FALSE then you may need a line to free the variance of T1_Age if you are not freeing it another way.  Fixing the variance to zero would account for your non-positive-definite implied covariance matrix. 

T1_Age ~~ T1_Age

However, other things might also account for it.  It may be that your omitted intercept which was fixed to zero also played a role.

Keith
------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/