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
Design-Adjusted MBN Estimator
Morel (1989) and Morel, Bokossa, and Neerchal (2003) suggested a bias correction of the classical sandwich estimator that rests on an additive correction of the residual crossproducts and a sample size correction. This estimator is available with the EMPIRICAL=MBN option in the PROC GLIMMIX statement. In the notation of the previous section, the residual-based MBN estimator can be written as
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where
or 
when you specify the EMPIRICAL=MBN(NODF) option 
is the sum of the frequencies 
equals the rank of 
if 
, otherwise 
equals the number of nonzero singular values of 
if 
and 
otherwise 
and 
are parameters supplied with the mbn-options of the EMPIRICAL=MBN(mbn-options) option. The default values are 
and 
. When the NODF option is in effect, the factor 
is set to 1.
Rearranging terms, the MBN estimator can also be written as an additive adjustment to a sample-size corrected classical sandwich estimator
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Because 
is of order 
, the additive adjustment to the classical estimator vanishes as the number of independent sampling units (subjects) increases. The parameter 
is a measure of the design effect (Morel, Bokossa, and Neerchal 2003). Besides good statistical properties in terms of Type I error rates in small-
situations, the MBN estimator also has the desirable property of recovering rank when the number of sampling units is small. If 
, the "meat" piece of the classical sandwich estimator is essentially a sum of rank one matrices. A small number of subjects relative to the rank of 
can result in a loss of rank and subsequent loss of numerator degrees of freedom in tests. The additive MBN adjustment counters the rank exhaustion. You can examine the rank of an adjusted covariance matrix with the COVB(DETAILS) option in the MODEL statement.
When the principle of the MBN estimator is applied to the likelihood-based empirical estimator, you obtain
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where 
, and 
is the second derivative of the log likelihood for the 
th sampling unit (subject) evaluated at the vector of parameter estimates, 
. Also, 
is the first derivative of the log likelihood for the th sampling unit. This estimator is computed if you request EMPIRICAL=MBN with METHOD=LAPLACE or METHOD=QUAD.
In terms of adjusting the classical likelihood-based estimator (White 1982), the likelihood MBN estimator can be written as
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The parameter is determined as
- if , otherwise equals the number of nonzero singular values of
