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
Scale and Dispersion Parameters
The parameter 
in the log-likelihood functions is a scale parameter. McCullagh and Nelder (1989, p. 29) refer to it as the dispersion parameter. With the exception of the normal distribution, does not correspond to the variance of an observation, the variance of an observation in a generalized linear model is a function of and 
. In a generalized linear model (GLM mode), the GLIMMIX procedure displays the estimate of is as "Scale" in the "Parameter Estimates" table. Note that for some distributions this scale is different from that reported by the GENMOD procedure in its "Parameter Estimates" table. The scale reported by PROC GENMOD is sometimes a transformation of the dispersion parameter in the log-likelihood function. Table 40.16 displays the relationship between the "Scale" entries reported by the two procedures in terms of the (or 
) parameter in the GLIMMIX log-likelihood functions.
Distribution |
GLIMMIX Reports |
GENMOD Reports |
|---|---|---|
Beta |
|
N/A |
Gamma |
|
|
Inverse gaussian |
|
|
Negative binomial |
|
|
Normal |
|
|
Note that for normal linear models, PROC GLIMMIX by default estimates the parameters by restricted maximum likelihood, whereas PROC GENMOD estimates the parameters by maximum likelihood. As a consequence, the scale parameter in the "Parameter Estimates" table of the GLIMMIX procedure coincides for these models with the mean-squared error estimate of the GLM or REG procedures. To obtain maximum likelihood estimates in a normal linear model in the GLIMMIX procedure, specify the NOREML option in the PROC GLIMMIX statement.