I'm running a series of CFA models using dichotomous indicators. I've noticed what appears to be a discrepancy in the computation of df & wondered if someone might spot an error in my reasoning.
Consider a cross-sectional 2 factor model with 13 dichotomous indicators. The tetrachoric corr matrix has 78 unique pieces of info [=13(12)/2]. If I estimate 11 factor loadings (2 items have factor loadings fixed to 1.0 for identification of the 2 latent variables), 2 latent variances & their covariance - 14 total params are estimated leaving model df = 64. This is exactly what I get in my output file (note: Mplus doesn't explicity estimate params for residuals, that's why they're not considered when counting dfs).
Now consider a longitudinal CFA of the same 13 items (2 factors at 2 points in time). I now have 26 indicators which yield 325 unique pieces of info [=26(25)/2]. 22 factor loadings are estimated. Furthermore with 4 latent variables a total of 10 (co)variances are estimated (all factors are inter-correlated). In total 32 params are esimated which should leave 293 df (325-32). However my output file evaluates the chi sq @ 306 df.
Finally when I specify another model that imposes equality constraints for each factor loading at 2 points in time (that is 11 factor loadings are estimated instead of 22), the resulting df is 318 instead of 306. Had 306 df been correct, shouldn't the resulting model be eval at 317 df (306+11)?
I'm assuming that WLSM doesn't adjust df (unlike WLSMV). Furthermore, I'm assuming that my imposing equal thresholds for items involved in the longitudinal model is in no way associated with computing df.
Does anyone see an error in my rationale? Further, has anyone else doing longitudinal CFA on dichtomous items noted a problem in computing df?
The difference in the degrees of freedom you expect and the degrees of freedom that you get is 293 versus 306 or a difference of 13. You imply that you have thresholds in the model and that you hold them equal across time. In such a model, thresholds do influence the degrees of freedom. There are 26 thresholds and 13 thresholds parameters estimated which I think explains the difference of 13.
I am doing a series of CFAs with ordinal variables using Mplus 2.12. Everything looks fine except I am not sure I understand clearly the warning "* The chi-square value for MLM, MLR, MLMV, WLSM and WLSMV cannot be used for chi-square difference tests. MLM and MLR chi-square difference testing is described on page 360 in the Mplus User's Guide."
I read the chapter decribing these features but I found it too sophisticated for me. So here are my questions:
1) Is it possible to compare model fit indices (chi. sqs) involving categorical outcome variables estimated with WLSMV?
2) If yes, which statistic can be used or how are these statistic obtained?
It is not possible to do nested model difference testing using WLSMV. There is no correction factor yet available. We recommend using WLS for difference testing and then using WLSMV for the final model.
Hello, I would like to understand how dfs are obtained when analyzing a CFA model with categorical indicators when using WLSMV. For instance, with 2 correlated factors each predicting 3 variables, I would expect 6*7/2-13=8 dfs, but the output gives 7 dfs. Apparently, the reference to p. 360 of the Mplus manual is obsolete. I have the manual for version 3. I was also unable to find something relevant in the technical appendices online. Thanks in advance for your help.
The technical appendices can be found on the website. The Version 3 Mplus User's Guide does not contain the technical appendices. You must be using an old version of the program. Degrees of freedom are calculated differently using WLSMV. If you want to see degrees of freedom the way you expect, use WLS or WLSM.
Thank you Linda. May I insist? The output given by Mplus 3.11 is "The degrees of freedom for MLMV and WLSMV are estimated according to a formula given in the Mplus Technical Appendices at www.statmodel.com. See degrees of freedom in the index of the Mplus User's Guide". Could you give me the number of the equation in the Mplus Tech App on line? I have Version 3 of the manual, and there is no entry "Degree of freedom" in the index.
bmuthen posted on Sunday, January 23, 2005 - 3:36 pm
The Version 3 User's Guide does not have Technical appendices. Technical appendices are on the Mplus web site. The WLSMV df discussion is in the appendix section on estimators and tests.
Anonymous posted on Thursday, April 28, 2005 - 7:24 am
I just wanted to ask if the technical appendices for version 3 of M-Plus are out. In case they are, where are them? In the technical appendices section of the web I just can find the version 2 ones.
Linda, Your response on Jan 20 2006 was helpful in translating how df is estimated using the wlsmv estimator. Could you elaborate on what criterion is used to define a "correct p-value"? I am referencing this quotation from your posting on Jan 20 2006 2:03pm. I have been asked by a journal editor to explain the df calculation in non-technical terms for my manuscript submission involving wlsmv estimator analyses. Although I am not the anonymous posting author that you responded to on Jan 20 2006, this additional clarification would be very helpful to my explanation to the editor.
There are some things in life that do not lend themselves well to non-technical terms. Let me try one more approach. A test statistic and its degrees of freedom are estimated as shown in formulas (108)-(110) in our technical appendices. The test statistic and the degrees of freedom refer to a chi-square distribution for which a p value is obtained. The p-value is the probability that the null hypothesis is true. With WLSMV, the only quantity interpretable in the usual way is this p-value.
can someone tell me how to calculate the df for the models below, when i am using wlsm estimator?
mgfa with 2 groups 3 factor model with 35 dichotomous indicators and the factor loadings and thresholds are free to be estimated across groups and the residual variances @1 for both groups and factor means @0 for both groups.
using the calculations from a previous discussion above: 35(34)/2 = 595 X 2 groups = 1190 (i know i only need to do 35(34))
factor loadings (3 items have factor loadings fixed to 1.0 for identification) 35-3=32 X 2 groups = 64
3 latent variances + 3 their covariance = 6 X 2 groups = 12
= 1114 but the output has 1113 df.
using the same model but this time the factors and thresholds are constrained to equal across the 2 groups and the residual variances @1 in both groups but the factor means @0 for one group but freed in the other. -- i have no idea how to calculate the df for this one. the output indicates df= 1174.
This is a research question that has not yet been answered. I would use WLSM and use the average chi-square value and the degrees of freedom from WLSM. This should work pretty well as long as you don't have a huge amount of missing data.