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In a twolevel model predicting level 1 outcome y, the standardized output returns an rsquared within and rsquared between. My question is whether the rsquared between tells me the proportion of variance on y that is explained by the level 2 predictor and thus whether the rsquared for the complete multilevel model is the sum of the two rsquared outputs (total explained variance of y is rsquared from the within variables plus the rsquared from the between variables)? Thank you. 


The sum of Rsquares is not what you want because Rsquare(W) = withinexplained/(withintotal), Rsqauare(B) = betweenexplained/(betweentotal), where for each level total = explained plus residual. If you want the total rsquare for y, I think you want the numerator to be withinexplained + betweenexplained and for the denominator you add the two residual terms. You can get all these quantities from the output. 


Thank you for this explanation. If I understand correctly, you are suggesting that I would add the estimates for the between and within Rsquares for the numerator, and add together the between and within standardized estimates for the residuals? My within Rsquare is .39 and my between is 0.148 (sum .538). The standardized residual estimate (STDYX) for within = .609 and between=.852. I estimate a total Rsquare for the y = (.538/1.461) .368. Correct? If that is correct, why would my total explained variance be less than the model rsquare when I only have level 1 predictors? If that is not correct, what should I have done instead? Thanks. 


No, that's not what I suggested. Your within Rsquare is for instance R_W = a/(a+b), and your between is R_B = c/(c+d). Then your total Rsquare would be R_T = (a+c)/(a+c+b+d). 

Tammy Kochel posted on Wednesday, February 13, 2013  12:43 pm



Thanks, so do I used the standardized or unstandardized residual estimate for d and b? 


Unstandardized everywhere. 

fangfang posted on Saturday, September 19, 2015  1:03 am



Dear Dr.Muthen, I have another question on a multilevel model with random slope. How can I get an Rsquare (R_w and R_b) for this model? The output did not provide the R2 results. Thank you very much for your help! 

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