Hi: I've been reading "Computational Methods for Multilevel Modeling" by Pinheiro and Bates, the idea of embedding the technique in my own c-level code. The basic idea is to rewrite the joint density in a form to mimic a single least squares problem conditional upon the variance parameters. The paper is fairly clear except that some important level of detail is missing. For instance, when we first meet Q_(i):
/ \ / \ | Z_i X_i y_i | | R_11(i) R_10(i) c_1(i) | | | = Q_(i) | | | Delta 0 0 | | 0 R_00(i) c_0(i) | \ / \ / the text indicates that the Q-R factorization is limited to the first q columns of the augmented matrix on the left. If one plunks the first q columns of the augmented matrix on the left into a qr factorization, one obtains an orthogonal matrix Q that is (n_i + q) x q and a nonsingular upper triangular matrix R that is q x q. While the text describes R as a nonsingular upper triangular q x q, the matrix Q_(i) is described as a square (n_i + q) x (n_i + q) orthogonal matrix. The remaining columns in the matrix to the right are defined by applying transpose(Q_(i)) to both sides. The question is how to augment my Q which is orthogonal (n_i + q) x q with the missing (n_i + q) x n_i portion producing the orthogonal square matrix mentioned in the text? I tried appending the n_i x n_i identity matrix to the block diagonal, but this doesn't work as the resulting likelihood is insensitive to the variance parameters. Grant Izmirlian NCI ______________________________________________ [EMAIL PROTECTED] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
