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Tor Neilands posted on Wednesday, November 03, 2004  2:19 pm



Greetings, 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 rsquare 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 zeroinflated count outcome? Thanks so much for your insights, Tor Neilands 

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 Rsquare 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 Rsquare was discussed in Amemiya, and also in McKelvey & Zavoina (I think a 1985 Math Soc article)  it is also discussed in the SnijdersBosker's multilevel book. I don't know what to say about the count question  do we give an Rsquare 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 Rsquare for count outcomes, Mplus does not produce an Rsquare on the output for count outcomes. With best wishes, Tor 

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 Rsquares provided in the output represent the estimated proportion of the assumed underlying Y*s explained by the model. There is a column in the Rsquare table labeled "Scale Factors." What is the interpretation of those numbers? 


You are correct about Rsquare. 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 Rsquared of the mediator as it is very small. 1. Does the small RSquared somehow puts in question the exsitence of my indirect paths? 2. Can I test the significance of the mediator's RSquared using an FTest? (The data had been nonnormal, and I used WLSMV) Thanks a lot in advance. 


I would look at significance of the indirect effect and not be concerned with Rsquare. 

Heike B. posted on Friday, January 20, 2012  2:19 pm



Thank you, Linda for the good news. Heike 


Dear Dr. Muthen, I want to compare an effect of a indep. variable on a continious and a dichtomous dep. Variable. (two different models) Model 1: Y on x; Model 2: categorical = y; y On x; Is it possible to compare the R squared? Is there a transformation to make the R squared for probit and ML (OLS) compareable? Thanks Christoph Weber 


You should not compare the Rsquare values from a continuous and a categorical dependent variable. There is no such transformation. 

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