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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. |
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The sum of R-squares is not what you want because R-square(W) = within-explained/(within-total), R-sqauare(B) = between-explained/(between-total), where for each level total = explained plus residual. If you want the total r-square for y, I think you want the numerator to be within-explained + between-explained and for the denominator you add the two residual terms. You can get all these quantities from the output. |
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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? Thanks. |
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No, that's not what I suggested. Your within R-square is for instance R_W = a/(a+b), and your between is R_B = c/(c+d). Then your total R-square would be R_T = (a+c)/(a+c+b+d). |
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Tammy Kochel posted on Wednesday, February 13, 2013 - 12:43 pm
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Thanks, so do I used the standardized or unstandardized residual estimate for d and b? |
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Unstandardized everywhere. |
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fangfang posted on Saturday, September 19, 2015 - 1:03 am
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Dear Dr.Muthen, I have another question on a multilevel model with random slope. How can I get an R-square (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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