The GENMOD Procedure
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Overview
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Getting Started
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SyntaxPROC GENMOD StatementASSESS StatementBAYES StatementBY StatementCLASS StatementCODE StatementCONTRAST StatementDEVIANCE StatementEFFECTPLOT StatementESTIMATE StatementEXACT StatementEXACTOPTIONS StatementFREQ StatementFWDLINK StatementINVLINK StatementLSMEANS StatementLSMESTIMATE StatementMODEL StatementOUTPUT StatementProgramming StatementsREPEATED StatementSLICE StatementSTORE StatementSTRATA StatementVARIANCE StatementWEIGHT StatementZEROMODEL Statement
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DetailsGeneralized Linear Models TheorySpecification of EffectsParameterization Used in PROC GENMODType 1 AnalysisType 3 AnalysisConfidence Intervals for ParametersF StatisticsLagrange Multiplier StatisticsPredicted Values of the MeanResidualsMultinomial ModelsZero-Inflated ModelsGeneralized Estimating EquationsAssessment of Models Based on Aggregates of ResidualsCase Deletion Diagnostic StatisticsBayesian AnalysisExact Logistic and Exact Poisson RegressionMissing ValuesDisplayed Output for Classical AnalysisDisplayed Output for Bayesian AnalysisDisplayed Output for Exact AnalysisODS Table NamesODS Graphics
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ExamplesLogistic RegressionNormal Regression, Log Link Gamma Distribution Applied to Life DataOrdinal Model for Multinomial DataGEE for Binary Data with Logit Link FunctionLog Odds Ratios and the ALR AlgorithmLog-Linear Model for Count DataModel Assessment of Multiple Regression Using Aggregates of ResidualsAssessment of a Marginal Model for Dependent DataBayesian Analysis of a Poisson Regression ModelExact Poisson Regression
- References
Lagrange Multiplier Statistics
When you select the NOINT or NOSCALE option, restrictions are placed on the intercept or scale parameters. Lagrange multiplier, or score, statistics are computed in these cases. These statistics assess the validity of the restrictions, and they are computed as
![\[ \chi ^2 = \frac{s^2}{V} \]](images/statug_genmod0336.png){kind=small} |
where s is the component of the score vector evaluated at the restricted maximum corresponding to the restricted parameter and 
. The matrix 
is the information matrix, 1 refers to the restricted parameter, and 2 refers to the rest of the parameters.
Under regularity conditions, this statistic has an asymptotic chi-square distribution with one degree of freedom, and p-values are computed based on this limiting distribution.
If you set k = 0 in a negative binomial model, s is the score statistic of Cameron and Trivedi (1998) for testing for overdispersion in a Poisson model against alternatives of the form 
.
See Rao (1973, p. 417) for more details.