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
| Parameterization Used in PROC GENMOD |
Design Matrix
The linear predictor part of a generalized linear model is
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where 
is an unknown parameter vector and 
is a known design matrix. By default, all models automatically contain an intercept term; that is, the first column of contains all 1s. Additional columns of are generated for classification variables, regression variables, and any interaction terms included in the model. It is important to understand the ordering of classification variable parameters when you use the ESTIMATE or CONTRAST statement. The ordering of these parameters is displayed in the "CLASS Level Information" table and in tables displaying the parameter estimates of the fitted model.
When you specify an overparameterized model with the PARAM=GLM option in the CLASS statement, some columns of can be linearly dependent on other columns. For example, when you specify a model consisting of an intercept term and a classification variable, the column corresponding to any one of the levels of the classification variable is linearly dependent on the other columns of . The columns of 
are checked in the order in which the model is specified for dependence on preceding columns. If a dependency is found, the parameter corresponding to the dependent column is set to 0 along with its standard error to indicate that it is not estimated. The order in which the levels of a classification variable are checked for dependencies can be set by the ORDER= option in the PROC GENMOD statement or by the ORDER= option in the CLASS statement. For full-rank parameterizations, the columns of the matrix are designed to be linearly independent.
You can exclude the intercept term from the model by specifying the NOINT option in the MODEL statement.
Missing Level Combinations
All levels of interaction terms involving classification variables might not be represented in the data. In that case, PROC GENMOD does not include parameters in the model for the missing levels.