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
Residual-Based Estimators
The GLIMMIX procedure can compute the classical sandwich estimator of the covariance matrix of the fixed effects, as well as several bias-adjusted estimators. This requires that the model is either an (overdispersed) GLM or a GLMM that can be processed by subjects (see the section Processing by Subjects).
Consider a statistical model of the form
 |
The general expression of a sandwich covariance estimator is then
 |
where 
, 
.
For a GLMM estimated by one of the pseudo-likelihood techniques that involve linearization, you can make the following substitutions: 
, 
, 
, 
. These matrices are defined in the section Pseudo-likelihood Estimation Based on Linearization.
The various estimators computed by the GLIMMIX procedure differ in the choice of the constant 
and the matrices 
and 
. You obtain the classical estimator, for example, with 
, and 
equal to the identity matrix.
The EMPIRICAL=ROOT estimator of Kauermann and Carroll (2001) is based on the approximation
 |
where 
. The EMPIRICAL=FIRORES estimator is based on the approximation
 |
of Mancl and DeRouen (2001). Finally, the EMPIRICAL=FIROEEQ estimator is based on approximating an unbiased estimating equation (Fay and Graubard 2001). For this estimator, is a diagonal matrix with entries
 |
where 
. The optional number 
is chosen to provide an upper bound on the correction factor. For 
, the classical sandwich estimator results. PROC GLIMMIX chooses as default value 
. The diagonal entries of are then no greater than 2.
Table 40.19 summarizes the components of the computation for the GLMM based on linearization, where 
denotes the number of subjects and 
is the rank of 
.
EMPIRICAL= |
|
|
|
|---|---|---|---|
CLASSICAL |
1 |
|
|
DF |
|
|
|
ROOT |
1 |
|
|
FIRORES |
1 |
|
|
FIROEEQ(r) |
1 |
|
|
Computation of an empirical variance estimator requires that the data can be processed by independent sampling units. This is always the case in GLMs. In this case, equals the sum of all frequencies. In GLMMs, the empirical estimators require that the data consist of multiple subjects. In that case, equals the number of subjects as per the "Dimensions" table. The following section discusses how the GLIMMIX procedure determines whether the data can be processed by subjects. The section GLM Mode or GLMM Mode explains how PROC GLIMMIX determines whether a model is fit in GLM mode or in GLMM mode.