Computational Method

The GLM Procedure

Computational Method

Let X represent the n ×p design matrix and Y the n ×1 vector of dependent variables. (See the section "Parameterization of PROC GLM Models" for information on how X is formed from your model specification.)

The normal equations ${X^'X \beta}={X^'Y}$ are solved using a modified sweep routine that produces a generalized (g2) inverse (X'X)^- and a solution b = (X'X)^-X'y (Pringle and Raynor 1971).

For each effect in the model, a matrix L is computed such that the rows of L are estimable. Tests of the hypothesis ${L \beta}=0$ are then made by first computing

${SS}({L \beta} = 0) = ({Lb})^' (L({X^'X})^{-}L^')^{-1}({Lb})$

and then computing the associated F value using the mean squared error.

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