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
| Multinomial Models |
This type of model applies to cases where an observation can fall into one of 
categories. Binary data occur in the special case where 
. If there are 
observations in a subpopulation 
, then the probability distribution of the number falling into the categories 
can be modeled by the multinomial distribution, defined in the section Response Probability Distributions, with 
. The multinomial model is an ordinal model if the categories have a natural order.
Residuals are not available in the OBSTATS table or the output data set for multinomial models.
By default, and consistently with binomial models, the GENMOD procedure orders the response categories for ordinal multinomial models from lowest to highest and models the probabilities of the lower response levels. You can change the way PROC GENMOD orders the response levels with the RORDER= option in the PROC GENMOD statement. The order that PROC GENMOD uses is shown in the "Response Profiles" output table described in the section Response Profile.
The GENMOD procedure supports only the ordinal multinomial model. If 
are the category probabilities, the cumulative category probabilities are modeled with the same link functions used for binomial data. Let 
, 
, be the cumulative category probabilities (note that 
). The ordinal model is
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where 
are intercept terms that depend only on the categories and 
is a vector of covariates that does not include an intercept term. The logit, probit, and complementary log-log link functions 
are available. These are obtained by specifying the MODEL statement options DIST=MULTINOMIAL and LINK=CUMLOGIT (cumulative logit), LINK=CUMPROBIT (cumulative probit), or LINK=CUMCLL (cumulative complementary log-log). Alternatively,
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where 
is a cumulative distribution function for the logistic, normal, or extreme-value distribution.
PROC GENMOD estimates the intercept parameters and regression parameters 
by maximum likelihood.
The subpopulations are defined by constant values of the AGGREGATE= variable. This has no effect on the parameter estimates, but it does affect the deviance and Pearson chi-square statistics; it also affects parameter estimate standard errors if you specify the SCALE=DEVIANCE or SCALE=PEARSON option.