The GENMOD Procedure
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Overview
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Getting Started
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SyntaxPROC GENMOD StatementASSESS StatementBAYES StatementBY StatementCLASS StatementCODE StatementCONTRAST StatementDEVIANCE StatementEFFECTPLOT StatementESTIMATE StatementEXACT StatementEXACTOPTIONS StatementFREQ StatementFWDLINK StatementINVLINK StatementLSMEANS StatementLSMESTIMATE StatementMODEL StatementOUTPUT StatementProgramming StatementsREPEATED StatementSLICE StatementSTORE StatementSTRATA StatementVARIANCE StatementWEIGHT StatementZEROMODEL Statement
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DetailsGeneralized Linear Models TheorySpecification of EffectsParameterization Used in PROC GENMODType 1 AnalysisType 3 AnalysisConfidence Intervals for ParametersF StatisticsLagrange Multiplier StatisticsPredicted Values of the MeanResidualsMultinomial ModelsZero-Inflated ModelsTweedie Distribution For Generalized Linear ModelsGeneralized Estimating EquationsAssessment of Models Based on Aggregates of ResidualsCase Deletion Diagnostic StatisticsBayesian AnalysisExact Logistic and Exact Poisson RegressionMissing ValuesDisplayed Output for Classical AnalysisDisplayed Output for Bayesian AnalysisDisplayed Output for Exact AnalysisODS Table NamesODS Graphics
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ExamplesLogistic RegressionNormal Regression, Log Link Gamma Distribution Applied to Life DataOrdinal Model for Multinomial DataGEE for Binary Data with Logit Link FunctionLog Odds Ratios and the ALR AlgorithmLog-Linear Model for Count DataModel Assessment of Multiple Regression Using Aggregates of ResidualsAssessment of a Marginal Model for Dependent DataBayesian Analysis of a Poisson Regression ModelExact Poisson RegressionTweedie Regression
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Each term in a model is called an effect. Effects are specified in the MODEL statement. You specify effects with a special notation that uses variable names and operators. There are two types of variables, classification (or CLASS) variables and continuous variables. There are two primary types of operators, crossing and nesting. A third type, the bar operator, is used to simplify effect specification. Crossing is the type of operator most commonly used in generalized linear models.
Variables that identify classification levels are called CLASS variables
in SAS and are identified in a CLASS statement. These might also be called categorical, qualitative, discrete, or nominal variables. CLASS variables can be either character or numeric. The values of CLASS variables are called levels. For example, the CLASS variable Sex could have the levels ‘male’ and ‘female’.
In a model, an explanatory variable that is not declared in a CLASS statement is assumed to be continuous. Continuous variables must be numeric. For example, the heights and weights of subjects in an experiment are continuous variables.
The types of effects most useful in generalized linear models are shown in the following list. Assume that A, B, and C are classification variables and that X1 and X2 are continuous variables.
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Regressor effects are specified by writing continuous variables by themselves:
X1,X2. -
Polynomial effects are specified by joining two or more continuous variables with asterisks:
X1*X2. -
Main effects are specified by writing classification variables by themselves:
A,B,C. -
Crossed effects (interactions) are specified by joining two or more classification variables with asterisks:
A*B,B*C,A*B*C. -
Nested effects are specified by following a main effect or crossed effect with a classification variable or list of classification variables enclosed in parentheses:
B(A),C(BA),A*B(C). In the preceding example,B(A) is “Bnested withinA.” -
Combinations of continuous and classification variables can be specified in the same way by using the crossing and nesting operators.
The bar operator
consists of two effects joined with a vertical bar (|). It is shorthand notation for including the left-hand side, the right-hand
side, and the cross between them as effects in the model. For example, A | B is equivalent to A B A*B. The effects in the bar operator can be classification variables, continuous variables, or combinations of effects defined
using operators. Multiple bars are permitted. For example, A | B | C means A B C A*B A*C B*C A*B*C.
You can specify the maximum number of variables in any effect that results from bar evaluation by specifying the maximum number,
preceded by an @ sign. For example, A | B | C@2 results in effects that involve two or fewer variables: A B C A*B A*C B*C.