Tor Neilands posted on Wednesday, November 03, 2004 - 2:19 pm
I am fitting the following model in Mplus:
MODEL: Positive BY ppo rps ; Negative BY npo ics as ;
PsyHlth BY avgsps bdisum1 pss1 psomsum1 ;
PsyHlth ON Positive Negative ; Adhlt90 ON PsyHlth ;
All observed variables and latent variabls are continuous, with the exception of the distal outcome Adhlt90, which is dichotomous. I am using the WLSMV estimator and theta parameterization to estimate this model.
I am curious as to what the interpretation of the r-square value reported for Adhtl90 is? And, does that interpretation change if I were to use ML estimation or delta parameterization? What if Adhlt90 were a count or zero-inflated count outcome?
Thanks so much for your insights,
bmuthen posted on Wednesday, November 03, 2004 - 6:03 pm
With WLSMV you get a probit regression for Adhlt90. With ML you get logit. In both cases does the R-square refer to explained variance proportion in an underlying continuous latent response variable. For probit this response variable has a conditionally normal density with unit variance given covariates, while for logit it has a conditionally logistic density with variance pi^2/3. For probit, see Tech App 1 on our web site. This kind of R-square was discussed in Amemiya, and also in McKelvey & Zavoina (I think a 1985 Math Soc article) - it is also discussed in the Snijders-Bosker's multilevel book. I don't know what to say about the count question - do we give an R-square here?
Tor Neilands posted on Thursday, November 04, 2004 - 10:24 am
Thank you, Bengt. I will check out those references. I have Snijers & Bosker. Can you post the full citation for the Amemiya reference? I noticed two Amemiya citations in the Mplus appendices. One is an article; the other a full textbook.
Regarding the R-square for count outcomes, Mplus does not produce an R-square on the output for count outcomes.
With best wishes,
bmuthen posted on Thursday, November 04, 2004 - 10:26 am
That's Amemiya (1981) - a good overview.
Tor Neilands posted on Thursday, November 04, 2004 - 12:30 pm
Thank you, Bengt. I will get a copy.
Lois Downey posted on Tuesday, March 25, 2008 - 3:55 pm
I'm running a path model with ordinal outcomes, using WLSMV. My understanding is that the R-squares provided in the output represent the estimated proportion of the assumed underlying Y*s explained by the model. There is a column in the R-square table labeled "Scale Factors." What is the interpretation of those numbers?
You are correct about R-square. A scale factor is one divided by the standard deviation of the underlying latent response variable.
Heike B. posted on Friday, January 20, 2012 - 4:32 am
I have a path model containing an observed categorical mediator and observed categorical outcome variables. I see some indirect effects that are small but significant. However I worry about the R-squared of the mediator as it is very small.
1. Does the small R-Squared somehow puts in question the exsitence of my indirect paths?
2. Can I test the significance of the mediator's R-Squared using an F-Test? (The data had been non-normal, and I used WLSMV)