Shared Concepts

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

Actions in this book that have a model parameter support the formation of effects. An effect is an element in a linear model structure that is formed from one or more variables. At some point the statistical representations of these models involve linear structures such as

or

The model matrices and are formed according to effect-construction rules.

Actions that also have a class parameter support the rich set of effects that is discussed in this section.

Actions that also have a constructed effect parameters enable you to construct special constructed effects that are discussed in Constructed Effects: collection, multimember, polynomial, and spline Parameters.

In order to correctly interpret the results from a statistical analysis, you need to understand how construction (parameterization) rules apply to regression-type models, whether these are linear models as in the glm action or generalized linear models as in the logistic and genmod actions.

Effects are specified by a special notation that uses variable names and operators. There are two types of variables: classification (or class parameter) variables and continuous variables. Classification variables can be either numeric or character and are specified in a class parameter. For more information, see the section Levelization of Classification Variables. An independent variable that is not declared in the class parameter is assumed to be continuous. For example, the heights and weights of subjects are continuous variables.

Two primary operators (crossing and nesting) are used for combining the variables, and several additional operators are used to simplify effect specification. Operators are discussed in the section Effect Operators.

Actions in this book that have a class parameter support a general linear model (GLM) parameterization and might also support nonsingular parameterizations for the classification variables. The GLM parameterization, commonly called dummy parameterization, is the default for all actions in this book. For more information, see the sections GLM Parameterization of Classification Variables and Effects and Nonsingular Parameterization.

All syntax in this section is displayed in the CASL language. See the Syntax section for the relevant actions for other languages.