The GLIMMIX Procedure
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Overview
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Getting Started
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Syntax
PROC GLIMMIX Statement BY Statement CLASS Statement CONTRAST Statement COVTEST Statement EFFECT Statement ESTIMATE Statement FREQ Statement ID Statement LSMEANS Statement LSMESTIMATE Statement MODEL Statement NLOPTIONS Statement OUTPUT Statement PARMS Statement RANDOM Statement SLICE Statement STORE Statement WEIGHT Statement Programming Statements User-Defined Link or Variance Function
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Details
Generalized Linear Models Theory Generalized Linear Mixed Models Theory GLM Mode or GLMM Mode Statistical Inference for Covariance Parameters Satterthwaite Degrees of Freedom Approximation Empirical Covariance (Sandwich) Estimators Exploring and Comparing Covariance Matrices Processing by Subjects Radial Smoothing Based on Mixed Models Odds and Odds Ratio Estimation Parameterization of Generalized Linear Mixed Models Response-Level Ordering and Referencing Comparing the GLIMMIX and MIXED Procedures Singly or Doubly Iterative Fitting Default Estimation Techniques Default Output Notes on Output Statistics ODS Table Names ODS Graphics
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Examples
Binomial Counts in Randomized Blocks Mating Experiment with Crossed Random Effects Smoothing Disease Rates; Standardized Mortality Ratios Quasi-likelihood Estimation for Proportions with Unknown Distribution Joint Modeling of Binary and Count Data Radial Smoothing of Repeated Measures Data Isotonic Contrasts for Ordered Alternatives Adjusted Covariance Matrices of Fixed Effects Testing Equality of Covariance and Correlation Matrices Multiple Trends Correspond to Multiple Extrema in Profile Likelihoods Maximum Likelihood in Proportional Odds Model with Random Effects Fitting a Marginal (GEE-Type) Model Response Surface Comparisons with Multiplicity Adjustments Generalized Poisson Mixed Model for Overdispersed Count Data Comparing Multiple B-Splines Diallel Experiment with Multimember Random Effects Linear Inference Based on Summary Data
- References
G-Side and R-Side Random Effects and Covariance Structures
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 40.15). 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.