How to get R-squared out of type=twol...
Message/Author
 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 R-squared 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 "1-residual 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 1-0.046=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!
 Linda K. Muthen posted on Friday, October 17, 2008 - 8:46 am
When slopes are random, the variance of y given x varies as a function of x. It is not clear how R-square would be computed.
 Dan Feaster posted on Wednesday, October 22, 2008 - 10:53 am
There is a measure (not what you did) called pseudo-R2 (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 pseudo-R2 does not necessarily increase when you add an additional predictor and that the pseudo-R2 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 well-defined quantity in multi-level modeling because of the heteroskedasticity.