CONTRAST Subcommand (LOGLINEAR command)
CONTRAST
indicates the type of contrast desired for a factor, where a factor
is any categorical dependent or independent variable. The default
contrast is DEVIATION
for each
factor.
- The specification is
CONTRAST
, which is followed by a variable name in parentheses and the contrast-type keyword. - To specify a contrast for more than one factor, use
a separate
CONTRAST
subcommand for each specified factor. Only one contrast can be in effect for each factor on eachDESIGN
. - A contrast specification remains in effect for subsequent
designs until explicitly overridden by another
CONTRAST
subcommand. - The design matrix used for the contrasts can be displayed
by specifying the keyword
DESIGN
on thePRINT
subcommand. However, this matrix is the basis matrix that is used to determine contrasts; it is not the contrast matrix itself. -
CONTRAST
can be used for a multinomial logit model, in which the dependent variable has more than two categories. -
CONTRAST
can be used for fitting linear logit models. The keywordBASIS
is not appropriate for such models. - In a logit model,
CONTRAST
is used to transform the independent variable into a metric variable. Again, the keywordBASIS
is not appropriate.
The following contrast types are available:
DEVIATION(refcat). Deviations
from the overall effect. DEVIATION
is the default contrast if the CONTRAST
subcommand is not used. Refcat is the category for which parameter
estimates are not displayed (they are the negative of the sum of the
others). By default, refcat is the last category of the variable.
DIFFERENCE. Levels of a factor with the average effect of previous levels of a factor. Also known as reverse Helmert contrasts.
HELMERT. Levels of a factor with the average effect of subsequent levels of a factor.
SIMPLE(refcat). Each level
of a factor to the reference level. By default, LOGLINEAR
uses the last category of the
factor variable as the reference category. Optionally, any level can
be specified as the reference category enclosed in parentheses after
the keyword SIMPLE
. The sequence
of the level, not the actual value, must be specified.
REPEATED. Adjacent comparisons across levels of a factor.
POLYNOMIAL(metric). Orthogonal polynomial contrasts. The default is equal spacing. Optionally, the coefficients of the linear polynomial can be specified in parentheses, indicating the spacing between levels of the treatment measured by the given factor.
[BASIS]SPECIAL(matrix). User-defined
contrast. As many elements as the number of categories
squared must be specified. If BASIS
is specified before SPECIAL
, a basis matrix is generated for the special contrast, which makes
the coefficients of the contrast equal to the special matrix. Otherwise,
the matrix specified is transposed and then used as the basis matrix
to determine coefficients for the contrast matrix.
Example
LOGLINEAR A(1,4) BY B(1,4)
/CONTRAST(B)=POLYNOMIAL
/DESIGN=A A BY B(1)
/CONTRAST(B)=SIMPLE
/DESIGN=A A BY B(1).
- The first
CONTRAST
subcommand requests polynomial contrasts of B for the first design. - The second
CONTRAST
subcommand requests the simple contrast of B, with the last category (value 4) used as the reference category for the secondDESIGN
subcommand.
Example
* Multinomial logit model
LOGLINEAR PREF(1,5) BY RACE ORIGIN CAMP(1,2)
/CONTRAST(PREF)=SPECIAL(5*1, 1 1 1 1 -4, 3 -1 -1 -1 0,
0 1 1 -2 0, 0 1 -1 0 0).
-
LOGLINEAR
builds special contrasts among the five categories of the dependent variable PREF, which measures preference for training camps among Army recruits. For PREF, 1=stay, 2=move to north, 3=move to south, 4=move to unnamed camp, and 5=undecided. - The four contrasts are: (1) move or stay versus undecided,
(2) stay versus move, (3) named camp versus unnamed, and (4) northern
camp versus southern. Because these contrasts are orthogonal,
SPECIAL
andBASIS SPECIAL
produce equivalent results.
Example
* Contrasts for a linear logit model
LOGLINEAR RESPONSE(1,2) BY YEAR(0,20)
/PRINT=DEFAULT ESTIM
/CONTRAST(YEAR)=SPECIAL(21*1, -10, -9, -8, -7, -6, -5, -4,
-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 399*1)
/DESIGN=RESPONSE RESPONSE BY YEAR(1).
- YEAR measures years of education and ranges from 0 through 20. Therefore, allowing for the constant effect, YEAR has 20 estimable parameters associated with it.
- The
SPECIAL
contrast specifies the constant—that is, 21*1—and the linear effect of YEAR—that is, –10 to 10. The other 399 1’s fill out the 21*21 matrix.
Example
* Contrasts for a logistic regression model
LOGLINEAR RESPONSE(1,2) BY TIME(1,4)
/CONTRAST(TIME) = SPECIAL(4*1, 7 14 27 51, 8*1)
/PRINT=ALL /PLOT=DEFAULT
/DESIGN=RESPONSE, TIME(1) BY RESPONSE.
-
CONTRAST
is used to transform the independent variable into a metric variable. - TIME represents elapsed time in days. Therefore, the weights in the contrast represent the metric of the passage of time.