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Appendix 9: Indicator Method
The indicator method is used in the GENLOG and the GLM procedures to generate
the design matrix corresponding to the design specified. Under this method, each
parameter (either non-redundant or redundant) in the model corresponds uniquely
to a column in the design matrix. Therefore, the terms parameter and design matrix
column are often used interchangeably without ambiguity.
Notation
The following notation is used throughout this appendix unless otherwise stated:
n Number of valid observations
p Number of parameters
X n
p
× design matrix (also known as model matrix)
xij Elements of X
Design Matrix
Row Dimension
The design matrix has as many rows as the number of valid observations. In the
GLM procedure, an observation is a case in the data file. In the GENLOG
procedure, an observation is a cell. In both procedures, the observations are
uniquely identified by the factor-level combination. Therefore, rows of the design
matrix are also uniquely identified by the factor-level combination.
Column Dimension
The design matrix has as many columns as the number of parameters in the model.
Columns of the design matrix are uniquely indexed by the parameters, which are in
turn related to factor-level combinations.
