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
| Zero-Inflated Models |
Count data that have an incidence of zeros greater than expected for the underlying probability distribution of counts can be modeled with a zero-inflated distribution. In GENMOD, the underlying distribution can be either Poisson or negative binomial. See Lambert (1992), Long (1997) and Cameron and Trivedi (1998) for more information about zero-inflated models. The population is considered to consist of two types of individuals. The first type gives Poisson or negative binomial distributed counts, which might contain zeros. The second type always gives a zero count. Let 
be the underlying distribution mean and 
be the probability of an individual being of the second type. The parameter is called here the zero-inflation probability, and is the probability of zero counts in excess of the frequency predicted by the underlying distribution. You can request that the zero inflation probability be displayed in an output data set with the PZERO keyword. The probability distribution of a zero-inflated Poisson random variable Y is given by
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and the probability distribution of a zero-inflated negative binomial random variable Y is given by
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where 
is the negative binomial dispersion parameter.
You can model the parameters and in GENMOD with the regression models:
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where 
is one of the binary link functions: logit, probit, or complementary log-log. The link function is the logit link by default, or the link function option specified in the ZEROMODEL statement. The link function 
is the log link function by default, or the link function specified in the MODEL statement, for both the Poisson and the negative binomial. The covariates 
for observation 
are determined by the model specified in the ZEROMODEL statement, and the covariates 
are determined by the model specified in the MODEL statement. The regression parameters 
and 
are estimated by maximum likelihood.
The mean and variance of Y for the zero-inflated Poisson are given by
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and for the zero-inflated negative binomial by
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You can request that the mean of Y be displayed for each observation in an output data set with the PRED keyword.