CFA using DWLS based on polychoric correlations or full weight matrix?

[J P]

Dear all, 

After searching in the forum and online, I am still somewhat confused based on which correlation or weight matrix lavaan bases its results in CFA for ordinal data, i.e., when ordered = TRUE. 

In the manual I found that when the lavaan R comment on setting ordered = TRUE, then "It will use DWLS to estimate model parameters, but it will use the full weight matrix to compute robust standard errors and a mean and variance adjusted test statistic”. 

However, in this forum I have found that it uses polychoric correlations when ordered = TRUE in combination with DWLS. 

Any help to clarify this will be appreciated! 

Context: I developed a questionnaire (17 items, 7-point Likert scale, 2 factors), completed all EFAs and will now conduct CFA with a new sample of N=423. 

Cheers

[Rick Hass]

There are simulation results that suggest that you don't necessarily need to run an ordinal / categorical model with a 7-point scale on your indicators. However, this depends on the symmetry of the distribution. 

I believe that Weighted Least Squares estimation always uses polychoric correlations for the sample covariance matrix, by the way. That's how the parameters are estimated. Using the full weight matrix (instead of just the diagonal) for standard errors and adjusting the test statistic is done after parameters are estimated (since one needs estimates to compute a fit function). 

[Terrence Jorgensen]

when the lavaan R comment on setting ordered = TRUE, then "It will use DWLS to estimate model parameters, but it will use the full weight matrix to compute robust standard errors and a mean and variance adjusted test statistic”. 

However, in this forum I have found that it uses polychoric correlations when ordered = TRUE in combination with DWLS. 

Estimating polychorics is the precursor to fitting an SEM to reproduce them.  

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3162326/

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