 R-squared    Message/Author  Tammy Kochel posted on Monday, February 11, 2013 - 8:31 pm
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.  Bengt O. Muthen posted on Monday, February 11, 2013 - 11:46 pm
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.  Tammy Kochel posted on Tuesday, February 12, 2013 - 7:20 pm
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.  Bengt O. Muthen posted on Tuesday, February 12, 2013 - 9:57 pm
No, that's not what I suggested.

Your within R-square is for instance

R_W = a/(a+b),

R_B = c/(c+d).

Then your total R-square 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?  Bengt O. Muthen posted on Wednesday, February 13, 2013 - 8:32 pm
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 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!    Topics | Tree View | Search | Help/Instructions | Program Credits Administration