

How to get Rsquared out of type=twol... 

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Qi posted on Thursday, October 16, 2008  10:55 pm



I ran several models using type=twolevel random, and requested "standardized" in the output command in order to get Rsquared value, no latent variables in the model and it's just simple multiple regression with one DV, and IV at either the between or within levels. After I run the models, I got the following warning: *** WARNING in OUTPUT command STANDARDIZED (STD, STDY, STDYX) options are not available for TYPE=RANDOM. Request for STANDARDIZED (STD, STDY, STDYX) is ignored. 1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS Does it mean that Mplus don't provide R2 for this type of model? How can I report any measure of fit for this type of model? Thanks a lot! 

Qi posted on Thursday, October 16, 2008  11:35 pm



I wonder whether this method is correct: I used "1residual variance of the DV" at the level the predictor was entered. For instance, the residual variance for DV is 0.046 at the between level, then the R2 for DV at the between level is 10.046=0.954. and if in the same model, the residual variance for DV is .85 at the within level, then the R2 for DV at the within level is 1.85=.15. I can only get R2 for each level, not a R2 for the whole model, right? Thanks! 


When slopes are random, the variance of y given x varies as a function of x. It is not clear how Rsquare would be computed. 

Dan Feaster posted on Wednesday, October 22, 2008  10:53 am



There is a measure (not what you did) called pseudoR2 (see Singer about 1998 in JEBS). It forms the change in a variance component when you add a covariate divided by the variance component as estimated without the variable. Thus there are as many pseudo R2 as there are variance components. There are problems with this measure, but it may be informative. You should realize that the pseudoR2 does not necessarily increase when you add an additional predictor and that the pseudoR2 can be negative. Also, just because a variable is entered at a particular level does not mean that adding that variable won't affect variance components from other levels of the model. As Linda points out in the next post, there are theoretical reasons that a true R2 is not a welldefined quantity in multilevel modeling because of the heteroskedasticity. 

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