Shared Concepts

Constructed Effects: collection, multimember, polynomial, and spline Parameters

This section applies to actions in the following action sets: mixed, modelMatrix, phreg, pls, quantreg, regression, and varReduce.

This section uses the CASL language to display all syntax and example code.

Specifying constructed effect parameters enables you to construct special collections of columns for design matrices. These collections are called constructed effects to distinguish them from the usual model effects that are formed from continuous or classification variables, as discussed in the section GLM Parameterization of Classification Variables and Effects. For example, in the following CASL language statements, the terms A, B, and X, and the interaction between A and B induced by the BAR specification, and the interaction between A and X induced by the CROSS specification, define fixed effects of the usual type in a generalized linear model:

effects={ {vars={'A','B'}, interaction='BAR'},
          'X',{vars={'A','X'}, interaction='CROSS'} }

A constructed effect, on the other hand, is assigned by specifying special parameters. For example, the following CASL language statement defines a constructed effect named spl:

spline={name='spl', vars='X'}

The columns of spl are formed from the data set variable X as a cubic B-spline basis with three equally spaced interior knots.

Each constructed effect corresponds to a collection of columns that are referred to by the name you supply. You can specify many constructed effects, and they all must precede the model parameter.

For each constructed effect parameter, you must specify a unique name for the effect with the name subparameter, and a list of variables to be used in constructing the effect with the vars subparameter. You can specify the following constructed effect parameters:

collection: specifies a collection effect that defines one or more variables as a single effect with multiple degrees of freedom. The variables in a collection are considered as a unit for estimation and inference. For more information, see the section Collection Effects.
multimember: specifies a multimember classification effect whose levels are determined by one or more variables that appear in a class parameter. For more information, see the section Multimember Effects.
polynomial: specifies a multivariate polynomial effect in the specified numeric variables. For more information, see the section Polynomial Effects.
spline: specifies a regression spline effect whose columns are univariate spline expansions of one or more variables. A spline expansion replaces the original variable with an expanded or larger set of new variables. For more information, see the section Spline Effects.

Table 3 summarizes the subparameters available in the constructed effect parameters.

Table 3: Constructed Effect Subparameters

Subparameter	Description
Collection Effect Subparameter
`details`	Displays the constituents of the collection effect
Multimember Effect Subparameters
`details`	Displays the levels of the multimember effect
`noEffect`	Specifies that observations with all missing levels for the multimember variables should have zero values in the corresponding design matrix columns
`stdize`	Specifies the design matrix entries sum to 1
`weight`	Specifies the weight variable for the contributions of each of the classification effects
Polynomial Effect Subparameters
`degree`	Specifies the degree of the polynomial
`details`	Displays details about the polynomial effect
`labelStyle`	Specifies how to label the terms in the polynomial
`mDegree`	Specifies the maximum degree of any variable in a term of the polynomial
`noseparate`	Treats the polynomial as a single effect
`standardize`	Specifies centering and scaling subparameters for the variables that define the polynomial
Spline Effect Subparameters
`basis`	Specifies the type of basis (B-spline basis or truncated power function basis) for the spline effect
`dataBoundary`	Uses the extremes of the data as boundary knots for a B-spline basis
`degree`	Specifies the degree of the spline effect
`details`	Displays details about knots and their locations
`knotMax`	Specifies right-side equally-spaced boundary knots
`knotMethod`	Specifies how to construct the knots for the spline effect
`knotMin`	Specifies left-side equally-spaced boundary knots
`naturalCubic`	Uses a natural cubic spline basis
`separate`	Specifies splines for multiple variables are treated as separate effects
`split`	Specified each individual column of the spline effect is treated as a separate effect

The subparameters that you can specify are described in the Syntax section of the specific action chapters. The following sections provide more information about the different types of constructed effects.

Last updated: March 05, 2026