Forms a projection matrix for a set of model terms (R.W. Payne).
No options
Parameters
TERMS = formula structures |
Defines the model terms corresponding to the design matrices whose projection matrices are required |
|---|---|
PROJECTION = symmetric matrices |
Saves the projection matrix for each formula structure |
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 parameter.
Options: none.
Parameters: TERMS, PROJECTION.
Method
The projection matrix is
X *+ GINVERSE( 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.
See also
Procedures: ASWEEP, FRTPRODUCTDESIGNMATRIX.
Commands for: Analysis of variance, Calculations and manipulation.
Example
CAPTION 'FPROJECTIONMATRIX example'; STYLE=meta FACTOR [NVALUES=9; LEVELS=3] A,B GENERATE A,B FPROJECTION !f(A),!f(A+B),!f(A*B); PROJECTION=PA,PAplusB,PAstarB PRINT [SERIAL=yes] PA,PAplusB,PAstarB; FIELD=8