The correlations of estimates matrix is NOT the absolute value of the corr(beta-hat) matrix. Here's an example to demonstrate. Note I have added a column of 1's for the intercept term. X = [1 0.53 -1 -1 -0.53 -0.53 1, 1 1 1 1 1 1 1, 1 -1 1 -1 -1 1 -1, 1 -1 -1 1 1 -1 -1, 1 1 1 -1 1 -1 -1, 1 -1 1 1 -1 -1 1, 1 1 -1 1 -1 1 -1]; The "color map on correlations" does not include the column of intercepts, but this is immaterial since corrleations are pairwise. Anyhow, if you put the above design into the DOE platform (less the column of 1's), or do the same and use the multivariate --> correlations option, you get the following correlations matrix among the columns of the X matrix: [1 -0.0926 -0.0926 0.2819 0.2819 0.0926, -0.0926 1 -0.1667 0.0926 0.0926 0.1667, -0.0926 -0.1667 1 0.0926 0.0926 0.1667, 0.2819 0.0926 0.0926 1 -0.2819 -0.0926, 0.2819 0.0926 0.0926 -0.2819 1 -0.0926, 0.0926 0.1667 0.1667 -0.0926 -0.0926 1] If you look into the JMP documentation regarding the correlations of estimates, you'll find that it's defined as corr(beta-hat) := V_inv*(X’X)_inv*V_inv where V:=sqrt(diag(X’X)_inv) Using the X matrix as above, this gives X_t = Transpose(X); V = sqrt(diag(Inverse(X_t*X))); corr_beta_hat = Round(Inv(V)*Inverse(X_t*X)*Inv(V),4); [1 -0.3101 -0.3154 -0.3154 0.3101 0.3101 0.3154, -0.3101 1 0.3101 0.3101 -0.5 -0.5 -0.3101, -0.3154 0.3101 1 0.3154 -0.3101 -0.3101 -0.3154, -0.3154 0.3101 0.3154 1 -0.3101 -0.3101 -0.3154, 0.3101 -0.5 -0.3101 -0.3101 1 0.5 0.3101, 0.3101 -0.5 -0.3101 -0.3101 0.5 1 0.3101, 0.3154 -0.3101 -0.3154 -0.3154 0.3101 0.3101 1] Which is exactly what you get when you use the "fit model" command in JMP. Note that the values in this matrix are not dependent on the values of either the response or the MSE. So my question is this: if one were trying to decide if the amount of confounding among model terms (or estimates) was acceptable, should one review the correlations among the columns of the design matrix or should one review the correlations among the beta-hats? Why might one be better than the other? Is there an intuitive explanation describing the relationship between the two?
... View more