The GENMOD Procedure
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Overview
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Getting Started
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Syntax
PROC GENMOD Statement ASSESS Statement BAYES Statement BY Statement CLASS Statement CONTRAST Statement DEVIANCE Statement EFFECTPLOT Statement ESTIMATE Statement EXACT Statement EXACTOPTIONS Statement FREQ Statement FWDLINK Statement INVLINK Statement LSMEANS Statement LSMESTIMATE Statement MODEL Statement OUTPUT Statement Programming Statements REPEATED Statement SLICE Statement STORE Statement STRATA Statement VARIANCE Statement WEIGHT Statement ZEROMODEL Statement
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Details
Generalized Linear Models Theory Specification of Effects Parameterization Used in PROC GENMOD Type 1 Analysis Type 3 Analysis Confidence Intervals for Parameters F Statistics Lagrange Multiplier Statistics Predicted Values of the Mean Residuals Multinomial Models Zero-Inflated Models Generalized Estimating Equations Assessment of Models Based on Aggregates of Residuals Case Deletion Diagnostic Statistics Bayesian Analysis Exact Logistic and Exact Poisson Regression Missing Values Displayed Output for Classical Analysis Displayed Output for Bayesian Analysis Displayed Output for Exact Analysis ODS Table Names ODS Graphics
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Examples
Logistic Regression Normal Regression, Log Link Gamma Distribution Applied to Life Data Ordinal Model for Multinomial Data GEE for Binary Data with Logit Link Function Log Odds Ratios and the ALR Algorithm Log-Linear Model for Count Data Model Assessment of Multiple Regression Using Aggregates of Residuals Assessment of a Marginal Model for Dependent Data Bayesian Analysis of a Poisson Regression Model Exact Poisson Regression
- References
| Specification of Effects |
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.
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(B A), A*B(C). In the preceding example, B(A) is "B nested within A."
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.