Poisson R-Square estimate possible? PreviousNext
Mplus Discussion > Categorical Data Modeling >
 Ben Chapman posted on Saturday, March 24, 2007 - 7:43 am
Hi--I have just purchased Mplus and fit a few path models in which observed outcomes are variously continuous, ordered categorical, and poisson. Estimator is MLR. While there is an R-square for the ordered categorical outcome (the source of which I see referenced on the board here), none is generated for the poisson outcome. Is it possible to obtain some sort of (pseduo?)R-square estimate for the poisson outcome?
 Bengt O. Muthen posted on Monday, March 26, 2007 - 9:41 am
I haven't seen this done and I cannot think of a natural way to do this. Other readers?
 Ben Chapman posted on Monday, March 26, 2007 - 12:15 pm
Thanks for the quick reply. I was just curious, having seen seen deviance-based R-square measures for poisson models, i.e. Waldhör et al 1998, but maybe it's not applicable here or wouldn't be a good idea. Thanks again.
 Bengt O. Muthen posted on Monday, March 26, 2007 - 7:08 pm
That's a possible approach.
 Jon Elhai posted on Wednesday, March 28, 2007 - 6:42 pm
In answer to Ben Chapman's question about generating pseudo R-squared values for poisson regression... If you have access to a general purpose stats software program like Stata, for estimating regression (albeit, not for a path model), you can generate pseudo r-squared values for poisson, as well as negative binomial regression, and zero-inflated and zero-truncated versions of these models. If you have access to Stata, this is accomplished by using the "fitstat" ado user-written supplemental file. Again, this is for regression - not for path models.
 S.Arunachalam posted on Monday, September 09, 2013 - 8:07 am
Dear Prof. Muthen,

I am running a zero-inflated negative binomial model. The model fits very well. Reviewers are asking for pseudo-R-sqr to be reported.

May I kindly request you to guide me to the formula which I can use to calculate pseudo-Rsqr from the output values produced by MPlus please. As I am not familiar with other software like STATA it would be great if you would advice to calculate this value within the MPlus environment itself. Thanking you so very much in advance.
Respectfully, Arun.
 Bengt O. Muthen posted on Monday, September 09, 2013 - 9:18 am
The negbin book by Hilbe (2011, 2nd ed.) gives the pseudo-R2 statistic on page 65. This is easily obtained by Mplus by doing two runs (see also Hilbe, pp. 65-66), one without the covariates (intercept-only model) and one with the covariates. Then

R2 = 1 - LLF/LLI,

where LLF is the loglikelihood value for the model with covariates and LLI is the loglikelihood value for the intercept-only model. This type of R2 is also used with binary outcomes and called the McFadden R2.
 S.Arunachalam posted on Monday, September 09, 2013 - 9:28 am
Respected Prof Muthen,
Thank you so very much for your quick reply. My sincere gratitude to you.
Respectfully, Arun.
 Dennis Reidy posted on Tuesday, April 28, 2015 - 12:56 pm
Professor Muthen,

In attempting to calculate the McFadden R2 for negbin how do I request an intercept only model? I thought this would be done by simply running without any covariates but my loglilihood for this model with only the count outcome is larger than my full model. This seems incorrect to me and thus I suspect I am not correctly running the intercept only model. I greatly appreciate any clarification you can offer.
 Bengt O. Muthen posted on Tuesday, April 28, 2015 - 5:31 pm
Run the model with all the covariates, but fix their slopes at zero.
 Dennis Reidy posted on Wednesday, April 29, 2015 - 10:37 am
Thank you.
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