KMATRIX Subcommand (GLM: Univariate command)

The KMATRIX subcommand allows you to customize your hypothesis tests by specifying the K matrix (contrast results matrix) in the general form of the linear hypothesis LB = K. The vector B is the parameter vector in the linear model.

  • The default K matrix is a zero matrix; that is, LB = 0 is assumed.
  • For the KMATRIX subcommand to be valid, at least one of the following subcommands must be specified: the LMATRIX subcommand or the INTERCEPT = INCLUDE subcommand.
  • If KMATRIX is specified but LMATRIX is not specified, the LMATRIX is assumed to take the row vector corresponding to the intercept in the estimable function, provided that the subcommand INTERCEPT = INCLUDE is specified. In this case, the K matrix can be only a scalar matrix.
  • If KMATRIX and LMATRIX are specified, the number of rows in the requested K and L matrices must be equal. If there are multiple LMATRIX subcommands, all requested L matrices must have the same number of rows, and K must have the same number of rows as these L matrices.
  • A semicolon (;) can be used to indicate the end of a row in the K matrix.
  • If more than one KMATRIX subcommand is specified, only the last subcommand is in effect.

Example

GLM DEP BY A B
  /LMATRIX = “Effect A”
              A 1  0 -1; A 1 -1  0 
  /LMATRIX = “Effect B”
              B 1  0 -1; B 1 -1  0
  /KMATRIX = 0; 0
  /DESIGN = A B.

In this example, assume that factors A and B each have three levels.

  • There are two LMATRIX subcommands; both subcommands have two rows.
  • The first LMATRIX subcommand tests whether the effect of A is 0, while the second LMATRIX subcommand tests whether the effect of B is 0.
  • The KMATRIX subcommand specifies that the K matrix also has two rows, each row with value 0.