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
The Basic Model
Suppose 
represents the 
vector of observed data and 
is a 
vector of random effects. Models fit by the GLIMMIX procedure assume that
 |
where 
is a differentiable monotonic link function and 
is its inverse. The matrix 
is an 
matrix of rank 
, and 
is an 
design matrix for the random effects. The random effects are assumed to be normally distributed with mean 
and variance matrix 
.
The GLMM contains a linear mixed model inside the inverse link function. This model component is referred to as the linear predictor,
 |
The variance of the observations, conditional on the random effects, is
 |
The matrix 
is a diagonal matrix and contains the variance functions of the model. The variance function expresses the variance of a response as a function of the mean. The GLIMMIX procedure determines the variance function from the DIST= option in the MODEL statement or from the user-supplied variance function (see the section Implied Variance Functions). The matrix 
is a variance matrix specified by the user through the RANDOM statement. If the conditional distribution of the data contains an additional scale parameter, it is either part of the variance functions or part of the matrix. For example, the gamma distribution with mean 
has the variance function 
and 
. If your model calls for G-side random effects only (see the next section), the procedure models 
, where 
is the identity matrix. Table 40.15 identifies the distributions for which 
.