Warning message when using estimator="WLSMV"

[Theuns]

Dear lavaan community,

I am new to lavaan and would appreciate your guidance on the following issue.

When I try to test the simple two-factor CFA model shown below using the WLSMV option in lavaan in a large dataset (n = 1 523) with no missing values, I get the warning message shown in red below.


> CFAmodel2 <- '
 
     SQ_SAT =~ Q3_1 + Q3_2 + Q3_3 + Q3_4 + Q3_5 + Q3_6
     Loyalty =~ Q5_1 + Q5_2 + Q5_3 + Q5_4
 
 '

> fit <- cfa(CFAmodel2, data=my_data, estimator="WLSMV", ordered = c("Q3_1", "Q3_2", "Q3_3", "Q3_4", "Q3_5", "Q3_6", "Q5_1", "Q5_2", "Q5_3", "Q5_4"))

Warning message:
In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats,  :
  lavaan WARNING:
    The variance-covariance matrix of the estimated parameters (vcov)
    does not appear to be positive definite! The smallest eigenvalue
    (= 9.027647e-18) is close to zero. This may be a symptom that the
    model is not identified.

> summary(fit, fit.measures = TRUE, estimates=TRUE, standardized = TRUE, rsquare = TRUE, nd=5)


I have the following questions:

1. Can I ignore this warning message and use the model estimates produced by lavaan?

2. If not, which alternative estimator should I rather use given that the manifest variables were all measured with 5-point Likert scales? The responses on these scales all have a strong "ceiling effect" with more than 90% of respondents having selected either a 4 or a 5 on the 5-point scale in all cases.

3. Is there some other way to resolve the issue causing warning message?

Thank you for your inputs.

Kind regards,

Theuns 

[Terrence Jorgensen]

1. Can I ignore this warning message and use the model estimates produced by lavaan?

Your model is identified, so I think you can.

 

The responses on these scales all have a strong "ceiling effect" with more than 90% of respondents having selected either a 4 or a 5 on the 5-point scale in all cases.

So < 150 responded to one of the 3 lowest categories?  If the extreme categories are quite low N, then those estimates could be quite unstable, and probably causing the warning (which is caused by near-redundancy among some parameter estimates). 

3. Is there some other way to resolve the issue causing warning message?

Consider collapsing the 2 lowest categories if N is so low that the threshold estimate is unstable.  But if your model converged and you have SEs, I wouldn't worry about it.

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

[Theuns Kotze]

Dear Terrence,

Thank you for your insightful reply. It is most helpful.

Best regards,

Theuns

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Theuns Kotzé
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