The GLIMMIX Procedure
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Overview
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Getting Started
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SyntaxPROC GLIMMIX StatementBY StatementCLASS StatementCODE StatementCONTRAST StatementCOVTEST StatementEFFECT StatementESTIMATE StatementFREQ StatementID StatementLSMEANS StatementLSMESTIMATE StatementMODEL StatementNLOPTIONS StatementOUTPUT StatementPARMS StatementRANDOM StatementSLICE StatementSTORE StatementWEIGHT StatementProgramming StatementsUser-Defined Link or Variance Function
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DetailsGeneralized Linear Models TheoryGeneralized Linear Mixed Models TheoryGLM Mode or GLMM ModeStatistical Inference for Covariance ParametersDegrees of Freedom MethodsEmpirical Covariance (Sandwich) EstimatorsExploring and Comparing Covariance MatricesProcessing by SubjectsRadial Smoothing Based on Mixed ModelsOdds and Odds Ratio EstimationParameterization of Generalized Linear Mixed ModelsResponse-Level Ordering and ReferencingComparing the GLIMMIX and MIXED ProceduresSingly or Doubly Iterative FittingDefault Estimation TechniquesDefault OutputNotes on Output StatisticsODS Table NamesODS Graphics
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ExamplesBinomial Counts in Randomized BlocksMating Experiment with Crossed Random EffectsSmoothing Disease Rates; Standardized Mortality RatiosQuasi-likelihood Estimation for Proportions with Unknown DistributionJoint Modeling of Binary and Count DataRadial Smoothing of Repeated Measures DataIsotonic Contrasts for Ordered AlternativesAdjusted Covariance Matrices of Fixed EffectsTesting Equality of Covariance and Correlation MatricesMultiple Trends Correspond to Multiple Extrema in Profile LikelihoodsMaximum Likelihood in Proportional Odds Model with Random EffectsFitting a Marginal (GEE-Type) ModelResponse Surface Comparisons with Multiplicity AdjustmentsGeneralized Poisson Mixed Model for Overdispersed Count DataComparing Multiple B-SplinesDiallel Experiment with Multimember Random EffectsLinear Inference Based on Summary DataWeighted Multilevel Model for Survey Data
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The GLIMMIX procedure distinguishes two types of random effects. Depending on whether the parameters of the covariance structure
for random components in your model are contained in 
or in 
, the procedure distinguishes between “G-side” and “R-side” random effects. The associated covariance structures of and are similarly termed the G-side and R-side covariance structure, respectively. R-side effects are also called “residual” effects. Simply put, if a random effect is an element of 
, it is a G-side effect and you are modeling the G-side covariance structure; otherwise, you are modeling the R-side covariance
structure of the model. Models without G-side effects are also known as marginal (or population-averaged) models. Models fit
with the GLIMMIX procedure can have none, one, or more of each type of effect.
Note that an R-side effect in the GLIMMIX procedure is equivalent to a REPEATED effect in the MIXED procedure. The R-side covariance structure in the GLIMMIX procedure is the covariance structure that you would formulate with the REPEATED statement in the MIXED procedure. In the GLIMMIX procedure all random effects and their covariance structures are specified through the RANDOM statement. See the section Comparing the GLIMMIX and MIXED Procedures for a comparison of the GLIMMIX and MIXED procedures.
The columns of 
are constructed from effects listed on the right side in the MODEL statement. Columns of 
and the variance matrices 
and 
are constructed from the RANDOM statement.
The matrix is by default the scaled identity matrix, 
. The
scale parameter 
is set to one if the distribution does not have a scale parameter, such as in the case of the binary, binomial, Poisson,
and exponential distribution (see Table 43.20). To specify a different matrix, use the RANDOM statement with the _RESIDUAL_ keyword or the RESIDUAL option. For example, to specify that the Time effect for each patient is an R-side effect with a
first-order autoregressive covariance structure, use the RESIDUAL option:
random time / type=ar(1) subject=patient residual;
To add a multiplicative overdispersion parameter, use the _RESIDUAL_ keyword:
random _residual_;
You specify the link function 
with the LINK= option in the MODEL statement or with programming statements. You specify the variance function that controls the matrix 
with the DIST= option in the MODEL statement or with programming statements.
Unknown quantities subject to estimation are the fixed-effects parameter vector 
and the
covariance parameter vector 
that comprises all unknowns in and . The random effects are not parameters of the model in the sense that they are not estimated. The vector is a vector of random variables. The solutions for are predictors of these random variables.