The GENMOD Procedure
-
Overview
-
Getting Started
-
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
-
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
-
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
| Residuals |
The GENMOD procedure computes three kinds of residuals. Residuals are available for all generalized linear models except multinomial models for ordinal response data, for which residuals are not available. Raw residuals and Pearson residuals are available for models fit with generalized estimating equations (GEEs).
The raw residual is defined as
 |
where 
is the 
th response and 
is the corresponding predicted mean. You can request raw residuals in an output data set with the keyword RESRAW in the OUTPUT statement.
The Pearson residual is the square root of the th contribution to the Pearson’s chi-square:
 |
You can request Pearson residuals in an output data set with the keyword RESCHI in the OUTPUT statement.
Finally, the deviance residual is defined as the square root of the contribution of the th observation to the deviance, with the sign of the raw residual:
 |
You can request deviance residuals in an output data set with the keyword RESDEV in the OUTPUT statement.
The adjusted Pearson, deviance, and likelihood residuals are defined by Agresti (2002), Williams (1987), and Davison and Snell (1991). These residuals are useful for outlier detection and for assessing the influence of single observations on the fitted model.
For the generalized linear model, the variance of the th individual observation is given by
 |
where 
is the dispersion parameter, 
is a user-specified prior weight (if not specified, 
), is the mean, and 
is the variance function. Let
 |
for the th observation, where 
is the derivative of the link function, evaluated at . Let 
be the diagonal matrix with 
denoting the th diagonal element. The weight matrix is used in computing the expected information matrix.
Define 
as the th diagonal element of the matrix
 |
The Pearson residuals, standardized to have unit asymptotic variance, are given by
 |
You can request standardized Pearson residuals in an output data set with the keyword STDRESCHI in the OUTPUT statement. The deviance residuals, standardized to have unit asymptotic variance, are given by
 |
where 
is the contribution to the total deviance from observation , and 
is 1 if 
is positive and 
if is negative. You can request standardized deviance residuals in an output data set with the keyword STDRESDEV in the OUTPUT statement. The likelihood residuals are defined by
 |
You can request likelihood residuals in an output data set with the keyword RESLIK in the OUTPUT statement.