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Hello,
I have tried to do the prediction of the residuals at level two for intercept and slope (i.e. u0j and u1j):

Yij = b0j + b1j xij + ei
b0j= b0 + u0j
b1j= b1 + u1j

and after I have calculated cov(u0j; u1j) and var(u0j) on the predicted values. They result different from the corresponding covariance and variance obtained by the multilevel estimation. Can you help me to find why they differ?

Thanks in advance.

Hi Econsic1976,
This is because the residuals are shrunken residuals - I think the answer might be quite technical and available in Harvey Goldstein's book or you could email him.
Regards,
Bill.