Specification of Effects
By default, the CATMOD procedure treats all variables as
classification variables. As a result, there is no CLASS
statement in PROC CATMOD. The values of a classification
variable can be numeric or character. PROC CATMOD builds a
set of effects-coded variables to represent the levels of
the classification variable and then uses these to fit the
model (for details, see the "Generation of the Design Matrix" section). You
can modify the default by using the DIRECT statement to
treat numeric independent continuous variables as continuous
variables. The classification variables, combinations of
classification variables, and continuous variables are then
used in fitting linear models to data.
The parameters of a linear model are generally divided into
subsets that correspond to meaningful sources of variation
in the response functions. These sources, called
effects, can be specified in the MODEL, LOGLIN, FACTORS,
REPEATED, and CONTRAST statements. Effects can be specified
in any of the following ways:
- A main effect is a single class variable (that is, it
induces classification levels): A B
C.
- A crossed effect (or interaction) is two or more
class variables joined by asterisks, for example:
A*B A*B*C.
- A nested effect is a main effect or an interaction,
followed by a parenthetical field containing a main
effect or an interaction. Multiple variables within
the parentheses are assumed to form a crossed effect
even when the asterisk is absent. Thus, the last two
effects are identical: B(A)
C(A*B)
A*B(C*D)
A*B(C D).
- A nested-by-value effect is the same as a nested effect
except that any variable in the parentheses can be
followed by an equal sign and a value:
B(A=1) C(A
B=1) C*D(A=1 B=1)
A(C='low').
- A direct effect is a variable specified in a DIRECT
statement: X Y.
- Direct effects can be crossed with other
effects: X*Y X*X*X
X*A*B(C D=1).
The variables for crossed and nested effects remain
in the order in which they are first encountered.
For example, in the model
model R=B A A*B C(A B);
the effect A*B is reported as B*A
since B appeared before A in the statement.
Also, C(A B) is interpreted as
C(A*B) and is therefore reported as
C(B*A).
Bar Notation
You can shorten the specification of multiple effects by
using bar notation. For example, two methods of writing a
full three-way factorial model are
proc catmod;
model y=a b c a*b a*c b*c a*b*c;
run;
and
proc catmod;
model y=a|b|c;
run;
When you use the bar (|) notation, the right- and left-hand sides
become effects, and the interaction between them becomes an
effect. Multiple bars are permitted. The expressions are
expanded from left to right, using rules 1 through 4 given
in Searle (1971, p. 390):
- Multiple bars are evaluated left to right.
For example, A|B|C is evaluated as follows:
| A | B | C |  | {A | B} | C |
| | | {A B A*B} | C |
| | | A B A*B
C A*C B*C
A*B*C |
- Crossed and nested groups of variables are combined.
For example, A(B) | C(D) generates A*C(B D), among other terms.
- Duplicate variables are removed. For example,
A(C) | B(C) generates
A*B(C C), among other terms, and
the extra C is removed.
- Effects are discarded if a variable occurs on both the
crossed and nested sides of an effect. For instance,
A(B) | B(D E)
generates A*B(B D E),
but this effect is deleted.
You can also specify the maximum number of variables
involved in any effect that results from bar evaluation by
specifying that maximum number, preceded by an @ sign, at
the end of the bar effect. For example, the specification
A | B | C @ 2 would result in only
those effects that contain 2 or fewer variables; in this
case, the effects A, B, A*B, C,
A*C, and B*C are generated.
Other examples of the bar notation are
| A | C(B) | is equivalent to | A C(B) A*C(B) |
| A(B) | C(B) | is equivalent to | A(B) C(B) A*C(B) |
| A(B) | B(D E) | is equivalent to | A(B) B(D E) |
| A | B(A) | C | is equivalent to | A B(A) C A*C B*C(A) |
| A | B(A) | C@2 | is equivalent to | A B(A) C A*C |
| A | B | C | D@2 | is equivalent to | A B A*B C A*C B*C D
A*D B*D C*D |
For details on how the effects specified lead to a design matrix,
see the "Generation of the Design Matrix" section.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.
