Interpretation of R-square in categor... PreviousNext
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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 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,

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 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,

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 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?
 Linda K. Muthen posted on Tuesday, March 25, 2008 - 4:16 pm
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)

Thanks a lot in advance.
 Linda K. Muthen posted on Friday, January 20, 2012 - 9:10 am
I would look at significance of the indirect effect and not be concerned with R-square.
 Heike B. posted on Friday, January 20, 2012 - 2:19 pm
Thank you, Linda for the good news.

Heike
 Christoph Weber posted on Wednesday, April 25, 2012 - 5:11 am
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
 Linda K. Muthen posted on Wednesday, April 25, 2012 - 11:08 am
You should not compare the R-square values from a continuous and a categorical dependent variable. There is no such transformation.
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