I'm comparing the fit of several nested CFA models of a 6-item scale composed of a mixture of ordinal and dichotomous responses (n=231) - am therefore declaring all the variables catgorical and using WLS to generate models then conducting chi-square difference tests. I have then re-run the final best fitting model using WLSMV (see below) and plan on reporting the loadings etc of this final model. I'm in the process of writing up the results and have 3 questions:
1)Is there a reference for the process of using WLS to conduct chi-square different tests and then using WLSMV on the 'final' best fitting model to provide assessments of model fit, loadings etc? I read through the posts on this discussion board to find this method and was thinking that I could at least reference Linda's posting (i.e. WLSMV doesn't support chi-square diff tests).
2)My results for the final model seem almost too good to be true - are the following within the normal possible range?
The model statement with starting values is f1 BY v2 v4*-.91 v6*.55 v7*.70 ; f2 BY v3 v4*-.91 v5*-.51 ; f1 WITH f2
(this model was taken directly from the lit and is not the product of post-hoc modification)
Chi-Square Test of Model Fit 5.172* (DF =6), p=0.52, CFI = 1.000, TLI =1.005, RMSEA=0.000
3) Lastly, is there a way I can produce and save the asymptotic covariance matrix?
Thanks for your assisstance and for producing such a user friendly software package!
1. No reference for this. 2. This can happen if the correlations among the items are very low or if the sample size is very small. Or, if the theory and the measurements are very strong. 3. Mplus does not save the asymptotic covariance matrix.
WLS requires the weight matrix to be positive definite because the weight matrix is inverted as part of the estimation procedure. WLSMV does not require the weight matrix to be positive definite because it is not inverted as part of the estimation procedure. So in the situation that WLS does not get results and WLSMV does, you do not have an option for difference testing. In Version 3, WLSMV difference testing will be included as a two step procedure.
A small sample with variables with floor or ceiling effects is usually the reason for the weight matrix not being positive definite. WLSMV has been studied with samples as low as 200 for variables with floor or ceiling effects and has performed well. I don't know what your situation is.
In simulation studies, the WLSMV chi-square has performed better than the WLS chi-square. So we suggest reporting that for the final model.
Rich Jones posted on Friday, April 21, 2006 - 10:39 am
With early versions of Mplus, I used to estimate interim models with WLS, perform model building by examining derivatives (later modification indices). I would estimate a final, fitted model with WLSMV.
1) Now that Mplus (v3+) produces modification indices under WLSMV, is this approach still needed/recommended?
2) If no...since I am getting that WLSMV is the preferred estimator based on simulations, when using modification indices to build models, would it be recommended to assess model modifications using the DIFTEST option/procedure?
3) Maybe what I'm asking is: is the value for a modification index under WLSMV equal or similar to what I would get doing a chi-square difference test using DIFTEST procedure?