Bivariate dual change core model - fits in Mplus but not in lavaan (ERROR: initial model-implied matrix (Sigma) is not positive definite; check your model and/or starting parameters)

[Caroline Wehner]

Hi everyone, 

I am trying to fit a bivariate dual change score model to my data. I get the lavaan ERROR: initial model-implied matrix (Sigma) is not positive definite; check your model and/or starting parameters.

I decided to fit a univariate model first to obtain useful starting values. However, here I got the same error. Then I used Mplus to see whether I might be able to obtain starting values. This indeed works but entering the values to the model I set up in R does not solve the initial problem.

This is the model specification I used in R (with already inserted starting values from the Mplus model):

udcsm_model3 <- '

#define latents

narc1 =~ 1*t1_narq_mean

narc2 =~ 1*t2_narq_mean

narc3 =~ 1*t3_narq_mean

narc4 =~ 1*t4_narq_mean

#define regression of latents

narc2~1*narc1

narc3~1*narc2

narc4~1*narc3

#define latent cs

dn2 =~ 1*narc2

dn3 =~ 1*narc3

dn4 =~ 1*narc4

#define autoproportions

dn2 ~ start(-.78)*pi_n*narc1  

dn3 ~ start(-.78)*pi_n*narc2  

dn4 ~ start(-.78)*pi_n*narc3  

#define level and slope

BL =~ 1*narc1

SL =~ 1*dn2 + 1*dn3 + 1*dn4

#define fake level and slope

BL2 =~ 1*BL

SL2 =~ 1*SL

#means/intercepts

## observed intercepts (fixed to 0)

t1_narq_mean ~ 0*1

t2_narq_mean ~ 0*1

t3_narq_mean ~ 0*1

t4_narq_mean ~ 0*1

##latents

narc1 ~ 0*1 

narc2 ~ 0*1

narc3 ~ 0*1

narc4 ~ 0*1

##cs

dn2 ~ 0*1

dn3 ~ 0*1

dn4 ~ 0*1

##Level and Slope

BL ~ 0*1

SL ~ 0*1

BL2 ~ start(2.52)*1

SL2 ~ start(2.20)*1

#variances

##latents

narc1 ~~ 0*narc1 

narc2 ~~ 0*narc2

narc3 ~~ 0*narc3

narc4 ~~ 0*narc4

##cs

dn2 ~~ 0*dn2

dn3 ~~ 0*dn3

dn4 ~~ 0*dn4

##BL and SL

BL~~0*BL

SL~~0*SL

BL2~~start(.91)*BL2

SL2~~start(.65)*SL2

#correlation among fake factors

BL~~0*SL

BL~~0*SL2

SL~~0*BL2

BL2~~NA*SL2

#setting residuals equal

t1_narq_mean ~~ sigma2_n*10*t1_narq_mean

t2_narq_mean ~~ sigma2_n*10*t1_narq_mean

t3_narq_mean ~~ sigma2_n*10*t1_narq_mean

t4_narq_mean ~~ sigma2_n*10*t1_narq_mean

'

Here the equivalent in Mplus:

MODEL:  

      !define level factors

      narc1  BY t1_narq_mean@1;

      narc2  BY t2_narq_mean@1;

      narc3  BY t3_narq_mean@1;

      narc4  BY t4_narq_mean@1;

      !define regression of level factors

      narc2  ON narc1@1;

      narc3  ON narc2@1;

      narc4  ON narc3@1;

      !define difference scores

      dnarc1  BY narc2@1;  

      dnarc2  BY narc3@1;

      dnarc3  BY narc4@1;

   

      !define auto-proportion

      dnarc1  ON narc1*0 (nauto);

      dnarc2  ON narc2*0 (nauto);

      dnarc3  ON narc3*0 (nauto);

      !define level and linear slope factors

      narcI BY narc1@1;

      narcS BY dnarc1-dnarc3@1;

      !define fake level and slope factors

      narcIa BY narcI@1;

      narcSa BY narcS@1;

      !means

      [t1_narq_mean-t4_narq_mean@0];

      [narc1-narc4@0];

      [dnarc1-dnarc3@0];

      [narcI@0 narcS@0];

      [narcIa* narcSa*];

      !variance

      narc1-narc4@0;

      dnarc1-dnarc3@0;

      narcI@0 narcS@0;

      narcIa*50 narcSa*1;

      !intercorrelation among fake factors

      narcI  WITH narcS@0;

      narcI  WITH narcSa@0;

      narcS  WITH narcIa@0;

      narcIa WITH narcSa*0;

      !specific variance set equal

      t1_narq_mean-t4_narq_mean*10 (spnarc);

This is the correlation matrix of my data:

                  T1_NARQ_      T2_NARQ_      T3_NARQ_      T4_NARQ_

                     ________      ________      ________      ________

 T1_NARQ_       1.000

 T2_NARQ_       0.702         1.000

 T3_NARQ_       0.699         0.778         1.000

 T4_NARQ_       0.657         0.771         0.800         1.000 

I would really appreciate your help or sharing your experiences with similar problems. 

Caroline

[Edward Rigdon]

Caroline--

     May I suggest that these lines are a problem:

#define autoproportions

dn2 ~ start(-.78)*pi_n*narc1  

dn3 ~ start(-.78)*pi_n*narc2  

dn4 ~ start(-.78)*pi_n*narc3  

I think these lines are a problem because they apply two modifiers ("start(-.78)" and "pi_n") together. Instead, try restating these lines as, for example:

dn2 ~ start(-.78)*narc1 + pi_n*narc1  

Similarly, you have lines in your syntax that feature multiple moderators:

#setting residuals equal

t1_narq_mean ~~ sigma2_n*10*t1_narq_mean

t2_narq_mean ~~ sigma2_n*10*t1_narq_mean

t3_narq_mean ~~ sigma2_n*10*t1_narq_mean

t4_narq_mean ~~ sigma2_n*10*t1_narq_mean

Yes, I would expect the lavaan syntax parser to complain about this, but sometimes it just gets confused. If it wouldn't be too much trouble, try rewriting these lines and see if it makes a difference.

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[Caroline Wehner]

Thank you for your suggestion, Edward. 

I did change my syntax accordingly but unfortunately it does not change anything.

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[Mauricio Garnier-Villarreal]

Caroline

I found the problem, you had misspecified the residual variances, by

t1_narq_mean ~~ sigma2_n*10*t1_narq_mean

t2_narq_mean ~~ sigma2_n*10*t1_narq_mean

t3_narq_mean ~~ sigma2_n*10*t1_narq_mean

t4_narq_mean ~~ sigma2_n*10*t1_narq_mean

You specified that time had covariances with every other variable, which should have been

t1_narq_mean ~~ sigma2_n*t1_narq_mean
t2_narq_mean ~~ sigma2_n*t2_narq_mean
t3_narq_mean ~~ sigma2_n*t3_narq_mean
t4_narq_mean ~~ sigma2_n*t4_narq_mean

I assume you copy and paste the section and missed to change the variable name for the right side of the covariances, simple fix. This worked for me when I corrected it

[Caroline Wehner]

You were right. Thank you so much and sorry for taking your time with this silly error!

[Mauricio Garnier-Villarreal]

No problem, good it was an easy fix