DESIGN Subcommand (LOGLINEAR command)

DESIGN specifies the model or models to be fit. If DESIGN is omitted or used with no specifications, the saturated model is produced. The saturated model fits all main effects and all interaction effects.

  • To specify more than one model, use more than one DESIGN subcommand. Each DESIGN specifies one model.
  • To obtain main-effects models, name all the variables listed on the variables specification.
  • To obtain interactions, use the keyword BY to specify each interaction, as in A BY B and C BY D. To obtain the single-degree-of-freedom partition of a specified contrast, specify the partition in parentheses following the factor (see the example below).
  • To include cell covariates in the model, first identify them on the variable list by naming them after the keyword WITH, and then specify the variable names on DESIGN.
  • To specify an equiprobability model, name a cell covariate that is actually a constant of 1.

Example

* Testing the linear effect of the dependent variable

COMPUTE X=MONTH.
LOGLINEAR MONTH (1,12) WITH X
  /DESIGN X.
  • The variable specification identifies MONTH as a categorical variable with values 1 through 12. The keyword WITH identifies X as a covariate.
  • DESIGN tests the linear effect of MONTH.

Example

* Specifying main effects models
 
LOGLINEAR A(1,4) B(1,5)
  /DESIGN=A
  /DESIGN=A,B.
  • The first design tests the homogeneity of category probabilities for B; it fits the marginal frequencies on A, but assumes that membership in any of the categories of B is equiprobable.
  • The second design tests the independence of A and B. It fits the marginals on both A and B.

Example

* Specifying interactions
 
LOGLINEAR A(1,4) B(1,5) C(1,3)
  /DESIGN=A,B,C, A BY B.
  • This design consists of the A main effect, the B main effect, the C main effect, and the interaction of A and B.

Example

* Single-degree-of-freedom partitions
 LOGLINEAR A(1,4) BY B(1,5)
  /CONTRAST(B)=POLYNOMIAL
  /DESIGN=A,A BY B(1).
  • The value 1 following B refers to the first partition of B, which is the linear effect of B; this follows from the contrast specified on the CONTRAST subcommand.

Example

* Specifying cell covariates
 
LOGLINEAR HUSED WIFED(1,4) WITH DISTANCE
   /DESIGN=HUSED WIFED DISTANCE.
  • The continuous variable DISTANCE is identified as a cell covariate by specifying it after WITH on the variable list. The cell covariate is then included in the model by naming it on DESIGN.

Example

* Equiprobability model
 
COMPUTE  X=1.
LOGLINEAR  MONTH(1,18) WITH X
  /DESIGN=X.
  • This model tests whether the frequencies in the 18-cell table are equal by using a cell covariate that is a constant of 1.