every entry is 0 except for a single entry of 1. Because of the nature of the design matrix X, must equal . Since each of the rows in contains cells equal to 1 and the rest 0, we must t b have and using we obtain This is a matrix with diagonal elements equal to and off-diagonal elements . The last term to evaluate is partly resolved we know : it consists of rows, each having t b cells equal to and cells all equal to . The positions of these cells are dictated by the t(b-1) design matrix however when is post-multiplied by the row results in the X, y, ith ith treatment mean as well as the grand mean . We need to introduce the vector of data means which we’ll denote as . Then Combining the two terms and replacing terms like by leads to
every entry is 0 except for a single entry of 1. Because of the nature of the design matrix X, must equal . Since each of the t rows in contains b cells equal to 1 and the rest 0, we must have and using we obtain This is a matrix with diagonal elements equal to and off-diagonal elements . The last term to evaluate is partly resolved we know : it consists of t rows, each having b cells equal to and t(b-1) cells all equal to . The positions of these cells are dictated by the design matrix X, however when is post-multiplied by y, the ith row results in the ith treatment mean as well as the grand mean . We need to introduce the vector of data means which we’ll denote as . Then Combining the two terms and replacing terms like by leads to
An%20introduction%20to%20REML.docx