Shared Concepts

Polynomial Effects

EFFECT effect-name=POLYNOMIAL (var-list </ polynomial-options>);

EFFECT effect-name=POLY (var-list </ polynomial-options>);

The variables in var-list must be numeric. A design matrix column is generated for each term of the specified polynomial. By default, each of these terms is treated as a separate effect for the purpose of model building. For example, the following two PROC sevselect,upper() steps yield the identical analysis:

proc sevselect;
   loss y;
   effect MyPoly = polynomial(x1-x3/degree=2);
   scalemodel MyPoly;
run;

proc sevselect;
   loss y;
   scalemodel x1 x2 x3 x1*x1 x1*x2 x1*x3 x2*x2 x2*x3 x3*x3;
run;

You can specify the following polynomial-options after a slash (/):

DEGREE=n

specifies the degree of the polynomial, where n must be a positive integer and is typically a small integer, such as 1, 2, or 3. By default, DEGREE=1.

DETAILS

displays a table that shows the details of the specified polynomial, including the number of terms generated. If you also specify the STANDARDIZE option, then a table that shows the standardization details is also produced.

MDEGREE=n

specifies the maximum degree of any variable in a term of the polynomial, where n must be a positive integer. The default is the degree of the specified polynomial. For example, the following statement generates the terms , , , , , , and :

EFFECT MyPoly=POLYNOMIAL(x1 x2/degree=4 MDEGREE=2);

NOSEPARATE

treats the polynomial as a single effect that has multiple degrees of freedom. The effect-name that you specify is used as the constructed effect name, and the labels of the terms are used as labels of the corresponding parameters.

STANDARDIZE <(centerscale-opts)> <= standardize-opt>

standardizes the variables that define the polynomial. By default, the standardized variables receive prefix "s_" in the variable names.

You can use the following centerscale-opts to specify how the center and scale are estimated:

METHOD=MOMENTS

estimates the center by the variable mean and the scale by the standard deviation. If a weight variable is specified using a WEIGHT statement, the weights are not used in the computation of the mean and standard deviation, and observations that have invalid weights are ignored. Only observations that are used in performing the analysis are used for the standardization.

METHOD=RANGE

estimates the center by the midpoint of the variable range and the scale as half the variable range. Any observation that has a missing value for any regressor used in the model is ignored when the range of variables in a polynomial effect is computed. Observations that have valid regressor values but missing or invalid values of frequency variables, weight variables, or dependent variables are used in computing variable ranges. By default, METHOD=RANGE.

METHOD=WMOMENTS

is the same as METHOD=MOMENTS except that weighted means and weighted standard deviations are used.

PREFIX=NONE | quoted-string

specifies the prefix that is appended to standardized variables when forming the term labels. You can specify the following values:

quoted-string: specifies the prefix
NONE: does not apply a prefix

By default, PREFIX="s_".

Let

StartLayout 1st Row 1st Column n 2nd Column equals 3rd Column normal n normal u normal m normal b normal e normal r normal o normal f normal o normal b normal s normal e normal r normal v normal a normal t normal i normal o normal n normal s normal u normal s normal e normal d normal i normal n normal t normal h normal e normal a normal n normal a normal l normal y normal s normal i normal s 2nd Row 1st Column w 2nd Column equals 3rd Column normal w normal e normal i normal g normal h normal t normal v normal a normal r normal i normal a normal b normal l normal e 3rd Row 1st Column f 2nd Column equals 3rd Column normal f normal r normal e normal q normal u normal e normal n normal c normal y normal v normal a normal r normal i normal a normal b normal l normal e 4th Row 1st Column x 2nd Column equals 3rd Column normal v normal a normal r normal i normal a normal b normal l normal e normal t normal o normal b normal e normal s normal t normal a normal n normal d normal a normal r normal d normal i normal z normal e normal d 5th Row 1st Column x Subscript left-parenthesis n right-parenthesis 2nd Column equals 3rd Column Max Subscript i equals 1 Superscript n Baseline left-parenthesis x Subscript i Baseline right-parenthesis 6th Row 1st Column x Subscript left-parenthesis 1 right-parenthesis 2nd Column equals 3rd Column Min Subscript i equals 1 Superscript n Baseline left-parenthesis x Subscript i Baseline right-parenthesis 7th Row 1st Column upper F 2nd Column equals 3rd Column normal s normal u normal m normal o normal f normal f normal r normal e normal q normal u normal e normal n normal c normal i normal e normal s 8th Row 1st Column Blank 2nd Column equals 3rd Column normal upper Sigma Subscript i equals 1 Superscript n Baseline f Subscript i 9th Row 1st Column normal upper W normal upper F 2nd Column equals 3rd Column normal s normal u normal m normal o normal f normal w normal e normal i normal g normal h normal t normal e normal d normal f normal r normal e normal q normal u normal e normal n normal c normal i normal e normal s 10th Row 1st Column Blank 2nd Column equals 3rd Column normal upper Sigma Subscript i equals 1 Superscript n Baseline w Subscript i Baseline f Subscript i EndLayout

Table 4 shows how the center and scale are computed for each of the supported methods.

Table 4: Center and Scale Estimates by Method

Method	Center	Scale
RANGE
MOMENTS
WMOMENTS

You can control whether the standardization is to center, scale, or both center and scale by specifying one of the following standardize-opts:

CENTER: centers but does not scale the variables. For a variable x,
CENTERSCALE: centers and scales the variables. This is the default if you do not specify a standardization-opt. For a variable x,
NONE: performs no standardization.
SCALE: scales but does not center the variables. For a variable x,

Last updated: January 27, 2023