Each term in a model, called a regressor, is a variable or combination of variables. Regressors are specified in a special notation that uses variable names and operators. There are two kinds of variables: classification (CLASS) variables and continuous variables. There are two primary operators: crossing and nesting. A third operator, the bar operator, is used to simplify effect specification.
In the SAS System, classification ( CLASS) variables are declared in the CLASS
statement. (They can also be called categorical, qualitative, discrete, or nominal variables.) Classification variables can be either numeric or character. The values of a classification variable are called levels. For example, the classification variable Sex
has the levels "male" and "female."
In a model, an independent variable that is not declared in the CLASS statement is assumed to be continuous. Continuous variables, which must be numeric, are used for covariates. For example, the heights and weights of subjects are continuous variables. A response variable is a discrete count variable and must also be numeric.
Seven different types of regressors are used in the COUNTREG procedure. In the following list, assume that A
, B
, C
, D
, and E
are CLASS
variables and that X1
and X2
are continuous variables:
Regressors are specified by writing continuous variables by themselves: X1
X2
.
Polynomial regressors are specified by joining (crossing) two or more continuous variables with asterisks: X1
*X1
X1
*X2
.
Dummy regressors are specified by writing CLASS variables by themselves: A
B
C
.
Dummy interactions are specified by joining classification variables with asterisks: A
*B
B
*C
A
*B
*C
.
Nested regressors are specified by following a dummy variable or dummy interaction with a classification variable or list
of classification variables enclosed in parentheses. The dummy variable or dummy interaction is nested within the regressor
that is listed in parentheses: B
(A
) C
(B
*A
) D
*E
(C
*B
*A
). In this example, B
(A
) is read "B
nested within A
."
Continuousbyclass regressors are written by joining continuous variables and classification variables with asterisks: X1
*A
.
Continuousnestingclass regressors consist of continuous variables followed by a classification variable interaction enclosed
in parentheses: X1
(A
) X1
*X2
(A
*B
).
One example of the general form of an effect that involves several variables is
X1
*X2
*A
*B
*C
(D
*E
)
This example contains an interaction between continuous terms and classification terms that are nested within more than one classification variable. The continuous list comes first, followed by the dummy list, followed by the nesting list in parentheses. Note that asterisks can appear within the nested list but not immediately before the left parenthesis.
The MODEL
statement and several other statements use these effects. Some examples of MODEL
statements that use various kinds of effects are shown in the following table, where a
, b
, and c
represent classification variables. The variables x
and z
are continuous.
Specification 
Type of Model 

Simple regression 

Multiple regression 

Polynomial regression 

Regression with one classification variable 

Regression with multiple classification variables 

Regression with classification variables and their interactions 

Regression with classification variables and their interactions 

Regression with both continuous and classification variables 

Separateslopes regression 

Homogeneityofslopes regression 
You can shorten the specification of a large factorial model by using the bar operator. For example, two ways of writing the model for a full threeway factorial model follow:
model Y = A B C A*B A*C B*C A*B*C; model Y = ABC;
When the bar () is used, the right and left sides become effects, and the cross of them becomes an effect. Multiple bars are permitted. The expressions are expanded from left to right, using rules 2–4 given in Searle (1971, p. 390).
Multiple bars are evaluated from left to right. For instance, A
B
C
is evaluated as follows:








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 parts of an effect. For instance, A
(B
)  B
(D
E
) generates A
*B
(B
D
E
), but this effect is discarded immediately.
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 two or fewer variables: in this case, A
B
A
*B
C
A
*C
and B
*C
.
More examples of using the  and @ operators follow:

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