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The GLIMMIX Procedure

• fits generalized linear mixed models by likelihood-based techniques
• conditional on normally distributed random effects, the data can have any distribution in the exponential family
• provides the following built-in link functions:
  • cumulative complementary log-log
  • cumulative logit
  • cumulative log-log
  • cumulative probit
  • complementary log-log
  • generalized logit
  • identity
  • log
  • logit
  • log-log
  • probit
  • power with exponent λ = number
  • power with exponent -2
  • reciprocal
• provides the following built-in distributions and associated variance functions:
  • beta
  • binary
  • binomial
  • exponential
  • gamma
  • normal
  • geometric
  • inverse gaussian
  • lognormal
  • negative binomial
  • Poisson
  • t
• use SAS programming statements within the procedure to compute model effects, weights, frequency, subject, group, and other variables, and to define mean and variance functions
• fits covariance structures including:
  • ANTE(1)
  • AR(1)
  • ARH(1)
  • ARMA(1,1)
  • Cholesky
  • compound symmetry
  • heterogeneous compound symmetry
  • factor analytic
  • Huynh-Feldt
  • general linear
  • P-spline
  • radial smoother
  • simple
  • exponential spatial
  • gaussian
  • Matern
  • power
  • anisitropic power
  • spherical
  • Toeplitz
  • unstructured
• permits subject and group effects that enable blocking and heterogeneity, respectively
• choice of linearization approach or integral approximation by quadrature or Laplace method for mixed models with nonlinear random effects or nonnormal distribution
• choice of linearization about expected values or expansion about current solutions of best linear unbiased predictors (BLUP)
• flexible covariance structures for random and residual random effects, including variance components, unstructured, autoregressive, and spatial structures
• produce hypothesis tests and estimable linear combinations of effects
• provides a mechanism to obtain inferences for the covariance parameters. Significance tests are based on the ratio of (residual) likelihoods or pseudo-likelihoods. Confidence limits and bounds are computed as Wald or likelihood ratio limits.
• construct special collections of columns for the design matrices in your model. These special collections, which are referred to as constructed effects can include the following:
  • COLLECTION is a collection effect defining one or more variables as a single effect with multiple degrees of freedom. The variables in a collection are considered as a unit for estimation and inference.
  • MULTIMEMBER | MM is a multimember classification effect whose levels are determined by one or more variables that appear in a CLASS statement.
  • POLYNOMIAL | POLY is a multivariate polynomial effect in the specified numeric variables.
  • SPLINE is a regression spline effect whose columns are univariate spline expansions of one or more variables. A spline expansion replaces the original variable with an expanded or larger set of new variables.
• provides the following estimation methods:
  • RSPL
  • MSPL
  • RMPL
  • MMPL
  • Laplace
  • adaptive quadrature
• exercise control over the numerical optimization. You can choose techniques, update methods, line search algorithms, convergence criteria, and more. Or, you can choose the default optimization strategies selected for the particular class of model you are fitting.
• generate variables with SAS programming statements inside of PROC GLIMMIX (except for variables listed in the CLASS statement).
• grouped data analysis
• obtain separate analyses on observations in groups
• use ODS to create a SAS data set corresponding to any table
• supports ODS Graphics

For further details see the SAS/STAT User's Guide: The GLIMMIX Procedure
( PDF | HTML )

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

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