

R2 for categorical DV (Snijders & Bos... 

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Dear Drs. Muthen, Complying with a reviewer comment, I am trying to calculate explained variance (R2) for a twolevel model with an ordered categorical dependent variable following the recommendations of Snijders & Bosker (1999: 225234 (available at http://faculty1.ucmerced.edu/sdepaoli/docs/SnijdersBosker%20Intro%20to%20HLM.pdf). Now I'm having trouble understanding how to obtain the variance for the linear predictor (or fixed part) for Y as well as the intercept variance (both referenced on p. 225) from the MPlus output, which are needed to calculate their R2 in equation 14.21. Do you have any suggestions? Thanks in advance for your help! 


Mplus calculates R2 in line with this reference. You should find this when requesting standardized solution. As the reference says, the residual variance on level 1 is 3.29 for logit and 1 for probit. 

Jorge Walter posted on Wednesday, August 28, 2013  10:21 am



Thanks for your answer. The reason I was trying to calculate this myself is that, in a different multilevel regression with a 17 Likerttype dependent variable, the Level1 R2 I got from MPlus is substantially higher (.61 compared to .36) than the one I got from manually calculating the Level1 R2 = (unrestricted level1 error term – restricted level1 error term) / unrestricted level1 error term, with the unrestricted model containing only the dependent variable and level1 random intercept, and the restricted model containing all level1 and level2 variables (Kreft and De Leeuw 1998). Do you have any thoughts on why this discrepancy might exist? Unfortunately, the formula above does not seem work for a categorical DV; when I try to run the unrestricted model, I get the following error message: "Variances for categorical outcomes are not allowed on the within level." Thanks in advance for your help! 


On a related note, which literature reference (and calculations) could I provide reviewers for MPlus's R2 calculations for multilevel models with ordinal/interval/ratioscale DVs? Thanks and best, Jorge 


Mplus computes R2 for each level using the same principle as with simple regression: R2 = 1  standardized residual variance, Here, the standardized residual variance is the residual variance for the particular level, divided by that level's DV variance. There is a good discussion of this in the 2nd edition of the SnijdersBosker multilevel book of 2012, see chapter 7. 

Jorge Walter posted on Wednesday, September 04, 2013  7:03 am



Thanks, Bengt, much appreciated! 

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