Covariance between latent factors = greater than 1 : can I constrain it to 1?

[Hannah C]

Hi

I have a model with two latent variables, loading onto five indicators each.

 

Model <- 'VAR1 =~ x1 + x2 + x3 + x4 + x5              

               VAR2 =~ x6 + x7 + x8 + x9 + x10'

 

 

When I run the model, I get a message from Lavaan saying that the covariance matrix of latent variables is not positive definite. The standardized covariance between the two latent factors is 1.02. Is the model still permissible like this? i.e. could this be a result of a very high correlation between the two factors that fluctuates just below and above 1 ? In that case, would it be appropriate for me to constrain the covariance between them to be set at 1 (or.99) ? 

Thanks in advance !

Hannah

[Terrence Jorgensen]

The standardized covariance between the two latent factors is 1.02. Is the model still permissible like this?

Fit a model where those indicators load on a single factor instead of 2, and use anova() to compare them.  This is a test of redundancy.

i.e. could this be a result of a very high correlation between the two factors that fluctuates just below and above 1 ?

Yes, sampling error could be the explanation.  If you set std.lv = TRUE, then the estimated covariance is already a correlation, so you can look at the 95% CI to test the H0 that the population correlation < 1 (i.e., does the CI include values < 1?).

Kolenikov, S., & Bollen, K. A. (2012). Testing negative error variances: Is a Heywood case a symptom of misspecification?. Sociological Methods & Research, 41(1), 124-167.

In that case, would it be appropriate for me to constrain the covariance between them to be set at 1 (or.99) ? 

I would not recommend it.

Savalei, V., & Kolenikov, S. (2008). Constrained versus unconstrained estimation in structural equation modeling. Psychological Methods, 13(2), 150.

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

[Hannah C]

Hi Terrence

Thanks for your reply. Regarding your second point, the CI's do include values < 1 (range from 0.766 to 1.271) - Thank you for that Heywood reference. 

Hannah