

PseudoR^2 for Models with an Ordinal... 

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The background: In the context of some work I did comparing pseudoRsquared measures for ordinal response models (e.g., ordinal logit or probit), a reviewer mentioned casually that an alternative to the existing measures could easily be implemented by using polychoric correlations and WLS in an SEM framework, and then *somehow* obtaining some kind of RSquared. I'm wondering how to get such an Rsquared. Here's more detail: I have data available for a manifest ordinal variable Y, along with a covariate vector of manifest Xs, all continuous or dummies. Assuming that this Y is a categorized version of a latent continuous Y*, I want to use an SEM approach to generate a pseudo Rsquared measure that would estimate the "true" Rsquared that would occur if Y* were regressed on the X vector. I'm not even sure here whether what I want is best conceptualized as the Rsquared for the latent Y* regressed on the manifest X vector, or, more in line with the nature of polychoric correlations, the Rsquared for the latent Y* regressed on the vector of latent Xs underlying my manifest Xs. Since I am doing this for a methodological invesigation, I in fact have the actual data for the continuous Y* and the associated Xs, so I know the true Rsquared for the model with the underlying Y*. I have categorized Y* into various ordinal Ys, and now wish to compare an SEM based Rsquared to those true values, as well as to the various other existing pseudoRsquared measures for nonSEM ordinal response models. Is getting some kind of pseudoRsquared like this possible in Mplus and/or other SEM implementations, and how might I do it? Regards, Mike Lacy 

bmuthen posted on Friday, September 02, 2005  9:43 am



With an ordered categorical dependent variable Mplus gives you the Rsquare for the y*, using either a logit (with ML) or probit (with WLSMV) regression link. Note that Mplus does not force you to work with polychorics assuming underlying normal x* variables behind the x's  that would add unnessarily strict assumptions. 


This sounds very interesting. Since it seems many other SEM program don't produce an R^2 for this kind of situation, let alone one based on reasonable assumptions, I'll be curious to understand how it is done. Can you point to where I should look in the documentation, or to a published source where I might get a better idea of how the R^2 is being done? 

BMuthen posted on Monday, September 05, 2005  2:56 pm



You can look at the technical appendices on the website specifically Appendix 1. Also, see the McKelvey and Zavoina article from 1975 in Mathematical Sociology or the Snijder and Boskers multilevel book. 


Hello, my SEM contains two binary dependent variables and the output highlights related Rsquares (WLSVM estimator). Would you please so kind two explain what kinds of Rsquare Mplus produces? Is it McFadden's Adj R2,Cragg & Uhler's R2, Efron's R2 or other? I tried to find explanations in the appendix on your website but failed. Simply having an Rsquarename in my paper would definitily be a plus in the review process. Thank you very much for your help. stephan 


For categorical outcomes, we use the underlying continuous latent response variable approach, also discussed in McKelvey & Zavoina (1975) in J of Math'l Soc. You also find this discussed in the Snijders & Bosker multilevel book. See also Formula 15 in Technical Appendix 1 and the reference given there. 

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