FPROJECTIONMATRIX procedure

Forms a projection matrix for a set of model terms (R.W. Payne).

No options

Parameters

TERMS = formula

Model terms corresponding to the design matrix for which the projection matrix is required

PROJECTION = symmetric matrix

Projection matrix

Description

This procedure forms the projection matrix for the design matrix of a set of model terms. The terms are specified in a model formula using the TERMS parameter, and the projection matrix is saved (as a symmetric matrix) by the PROJECTION paremeter.

Options: none.

Parameters: TERMS, PROJECTION.

Method

The projection matrix is

X *+ Generalized-inverse( TRANSPOSE(X) *+ X ) *+ TRANSPOSE(X)

The design matrix X is formed using the TERMS directive, and the generalized inverse is formed using the GINVERSE procedure.

Action with RESTRICT

The factors must not be restricted, nor may they contain missing values.