In a two-level model predicting level 1 outcome y, the standardized output returns an r-squared within and r-squared between.
My question is whether the r-squared between tells me the proportion of variance on y that is explained by the level 2 predictor and thus whether the r-squared for the complete multi-level model is the sum of the two r-squared outputs (total explained variance of y is r-squared from the within variables plus the r-squared from the between variables)?
Thank you for this explanation. If I understand correctly, you are suggesting that I would add the estimates for the between and within R-squares for the numerator, and add together the between and within standardized estimates for the residuals?
My within R-square 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 R-square for the y = (.538/1.461) .368. Correct?
If that is correct, why would my total explained variance be less than the model r-square when I only have level 1 predictors? If that is not correct, what should I have done instead?