TEST Subcommand (MIXED command)

The TEST subcommand allows you to customize your hypotheses tests by directly specifying null hypotheses as linear combinations of parameters.

  • Multiple TEST subcommands are allowed. Each is handled independently.
  • The basic format for the TEST subcommand is an optional list of values enclosed in a pair of parentheses, an optional label in quotes, an effect name or the keyword ALL, and a list of values.
  • When multiple linear combinations are specified within the same TEST subcommand, a semicolon (;) terminates each linear combination except the last one.
  • At the end of a contrast coefficients row, you can use the option DIVISOR=value to specify a denominator for coefficients in that row. When specified, the contrast coefficients in that row will be divided by the given value. Note that the equals sign is required.
  • The value list preceding the first effect or the keyword ALL contains the constants, to which the linear combinations are equated under the null hypotheses. If this value list is omitted, the constants are assumed to be zeros.
  • The optional label is a string with a maximum length of 255 bytes. Only one label per TEST subcommand can be specified.
  • The effect list is divided into two parts. The first part is for the fixed effects, and the second part is for the random effects. Both parts have the same syntax structure.
  • Effects specified in the fixed-effect list should have already been specified or implied on the FIXED subcommand.
  • Effects specified in the random-effect list should have already been specified on the RANDOM subcommand.
  • To specify the coefficient for the intercept, use the keyword INTERCEPT. Only one value is expected to follow INTERCEPT.
  • The number of values following an effect name must be equal to the number of parameters (including the redundant ones) corresponding to that effect. For example, if the effect A*B takes up to six parameters, then exactly six values must follow A*B.
  • A number can be specified as a fraction with a positive denominator. For example, 1/3 or –1/3 are valid, but 1/–3 is invalid.
  • When ALL is specified, only a list of values can follow. The number of values must be equal to the number of parameters (including the redundant ones) in the model.
  • Effects appearing or implied on the FIXED and RANDOM subcommands but not specified on TEST are assumed to take the value 0 for all of their parameters.
  • If ALL is specified for the first row in a TEST matrix, then all subsequent rows should begin with the ALL keyword.
  • If effects are specified for the first row in a TEST matrix, then all subsequent rows should use the effect name (thus ALL is not allowed).
  • When SUBJECT( ) is specified on a RANDOM subcommand, the coefficients given in the TEST subcommand will be divided by the number of subjects of that random effect automatically.

Example

MIXED Y BY A B C
  /FIX = A
  /RANDOM = B C
  /TEST = 'Contrasts of A' A 1/3 1/3 1/3; A 1 -1 0; A 1 -1/2 -1/2
  /TEST(1) = 'Contrast of B' | B 1 -1 
  /TEST = 'BLUP at First Level of A'
          ALL 0 1 0 0 | 1 0 1 0;
          ALL         | 1 0 0 1;
          ALL 0 1 0 0;
          ALL 0 1 0 0 | 0 1 0 1.

Suppose that factor A has three levels and factors B and C each have two levels.

  • The first TEST is labeled Contrasts of A. It performs three contrasts among levels of A. The first is technically not a contrast but the mean of level 1, level 2, and level 3 of A, the second is between level 1 and level 2 of A, and the third is between level 1 and the mean of level 2 and level 3 of A.
  • The second TEST is labeled Contrast of B. Coefficients for B are preceded by the vertical bar (|) because B is a random effect. This contrast computes the difference between level 1 and level 2 of B, and tests if the difference equals 1.
  • The third TEST is labeled BLUP at First Level of A. There are four parameters for the fixed effects (intercept and A), and there are four parameters for the random effects (B and C). Coefficients for the fixed-effect parameters are separated from those for the random-effect parameters by the vertical bar (|). The coefficients correspond to the parameter estimates in the order in which the parameter estimates are listed in the output.

Example

Suppose that factor A has three levels and factor B has four levels.

MIXED Y BY A B
  /FIXED = A B
  /TEST = 'test example' A 1 -1 0 DIVISOR=3;
                  B 0 0 1 -1 DIVISOR=4.
  • For effect A, all contrast coefficients will be divided by 3; therefore, the actual coefficients are (1/3,–1/3,0).
  • For effect B, all contrast coefficients will be divided by 4; therefore, the actual coefficients are (0,0,1/4,–1/4).