lavaan error: covariance matrix of the residuals of the observed variables is not positive definite

[Emma Mills]

Hi 

I am carry out a mediation structural model and have received the below warning. What does this mean and how can I correct this? Full syntax is attached.

Thanks very much!

> SCTModel2 <- '

+ RBehF1=~BF1_RAV+BF2_RAV+BF3_RAV+BF4_RAV+BF6_RAV+BF7_RAV

+ RJobSat=~RaterJobSat

+ RReward=~RaterReward

+ # direct effect

+ RaterJobSat ~ c*RBehF1

+ # mediator

+ RaterReward ~ a*RBehF1

+ RaterJobSat ~ b*RaterReward

+ # indirect effect (a*b)

+ indirect := a*b

+ # total effect

+ total := c + (a*b)

+ RBehF1~~RaterJobSat

+ RBehF1~~RaterReward

+ RaterReward~~RaterJobSat

+ '

>

> SCT1fit2<-sem(SCTModel2, data = SMBI_Alldata, test = "bollen.stine",  se="boot", bootstrap = 5000)

Warning message:

In lav_object_post_check(lavobject) :

  lavaan WARNING: the covariance matrix of the residuals of the observed

                variables (theta) is not positive definite;

                use inspect(fit,"theta") to investigate.

 

 

inspect(SCT1fit2,"theta") 

            BF1_RA BF2_RA BF3_RA BF4_RA BF6_RA BF7_RA RtrJbS RtrRwr

BF1_RAV     0.038                                                  

BF2_RAV     0.000  0.029                                           

BF3_RAV     0.000  0.000  0.030                                    

BF4_RAV     0.000  0.000  0.000  0.041                             

BF6_RAV     0.000  0.000  0.000  0.000  0.026                      

BF7_RAV     0.000  0.000  0.000  0.000  0.000  0.040               

RaterJobSat 0.000  0.000  0.000  0.000  0.000  0.000  0.000        

RaterReward 0.000  0.000  0.000  0.000  0.000  0.000  0.117  0.000 

 

 

[Terrence Jorgensen]

What does this mean and how can I correct this?

You can find out what an NPD matrix is with a quick Google search.  Here is a quite informative page:

http://www2.gsu.edu/~mkteer/npdmatri.html

It doesn't necessarily need "correction", if sampling variability is a better explanation than model misspecification.  Concluding so requires (a) your model fits well and (b) the 95% CI for the Heywood case includes plausible values. Here is an article on the topic:

https://uncch.pure.elsevier.com/en/publications/testing-negative-error-variances-is-a-heywood-case-a-symptom-of-m

But in your specific case, I would guess the problem is that you are modeling the relationship between RaterJobSat and RaterReward twice (as a regression path "b" and as a residual covariance), which is a particularly odd choice because you are using them as single indicators of latent constructs:

RJobSat=~RaterJobSat

RReward=~RaterReward

RaterJobSat ~ b*RaterReward

RaterReward~~RaterJobSat

I'm surprised lavaan even converged on a solution, because this model is not identified.  Regardless, your theta matrix is NPD because it is impossible for two variables (here, "residuals" of RaterJobSat and RaterReward) to covary (i.e., to vary together) when they don't even vary.

            RtrJbS RtrRwr

RaterJobSat  0.000        

RaterReward  0.117  0.000 

If there is a regression between those variables, then there is no need to additionally estimate a correlation between their residuals (likewise for both of those with RBehF1).  And if you are using them as single indicators, then you should estimate the regression path between the latent variables, not between the indicators.

SCTModel2 <- '

  RBehF1 =~ BF1_RAV + BF2_RAV + BF3_RAV + BF4_RAV + BF6_RAV + BF7_RAV

  RJobSat =~ RaterJobSat

  RReward =~ RaterReward

# direct effect

  RJobSat ~ c*RBehF1

# mediator

  RReward ~ a*RBehF1

  RJobSat ~ b*RReward 

# indirect effect (a*b)

  indirect := a*b

# total effect

  total := c + (a*b)

'

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

[Camille Williams]

Hi Terrence Jorgensen,

How do we determine "(b) the 95% CI for the Heywood case includes plausible values."? Is it located in the summary of our model ?

Best, 

Camille Williams 

[Terrence Jorgensen]

How do we determine "(b) the 95% CI for the Heywood case includes plausible values."? Is it located in the summary of our model ?

yes, that is an option

summary(fit, ci=TRUE)

Or you can use the parameterEstimates() function.

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