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 Odds Ratio Estimates Table
This table is produced by the ODDSRATIO option in the MODEL statement. It consists of estimates of odds ratios and their confidence limits. Odds ratios are produced for the following:
classification main effects, if they appear in the MODEL statement
continuous variables in the MODEL statement, unless they appear in an interaction with a classification effect
continuous variables in the MODEL statement at fixed levels of a classification effect, if the MODEL statement contains an interaction of the two.
continuous variables in the MODEL statements if they interact with other continuous variables
The Default Table
Consider the following PROC GLIMMIX statements that fit a logistic model with one classification effect, one continuous variable, and their interaction (the ODDSRATIO option in the MODEL statement requests the "Odds Ratio Estimates" table).
proc glimmix; class A; model y = A x A*x / dist=binary oddsratio; run;
By default, odds ratios are computed as follows:
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The covariate is set to its average,
, and the least squares means for the A effect are obtained. Suppose 
denotes the matrix of coefficients defining the estimable functions that produce the 
least squares means 
, and 
denotes the 
th row of . Differences of the least squares means against the last level of the A factor are computed and exponentiated: 
The differences are checked for estimability. Notice that this set of odds ratios can also be obtained with the following LSMESTIMATE statement (assuming A has five levels):
lsmestimate A 1 0 0 0 -1, 0 1 0 0 -1, 0 0 1 0 -1, 0 0 0 1 -1 / exp cl;You can also obtain the odds ratios with this LSMEANS statement (assuming the last level of A is coded as 5):
lsmeans A / diff=control('5') oddsratio cl; -
The odds ratios for the covariate must take into account that x occurs in an interaction with the A effect. A second set of least squares means are computed, where x is set to
. Denote the coefficients of the estimable functions for this set of least squares means as 
. Differences of the least squares means at a given level of factor A are then computed and exponentiated: 
The differences are checked for estimability. If the continuous covariate does not appear in an interaction with the A variable, only a single odds ratio estimate related to x would be produced, relating the odds of a one-unit shift in the regressor from
.
Suppose you fit a model that contains interactions of continuous variables, as with the following statements:
proc glimmix; class A; model y = A x x*z / dist=binary oddsratio; run;
In the computation of the A least squares means, the continuous effects are set to their means—that is, and 
. In the computation of odds ratios for x, linear predictors are computed at x = , x*z = 
and at x = , x*z = 
.
Modifying the Default Table, Customized Odds Ratios
Several suboptions of the ODDSRATIO option in the MODEL statement are available to obtain customized odds ratio estimates. For customized odds ratios that cannot be obtained with these suboptions, use the EXP option in the ESTIMATE or LSMESTIMATE statement.
The type of differences constructed when the levels of a classification factor are varied is controlled by the DIFF= suboption. By default, differences against the last level are taken. DIFF=FIRST computes differences from the first level, and DIFF=ALL computes odds ratios based on all pairwise differences.
For continuous variables in the model, you can change both the reference value (with the AT suboption) and the units of change (with the UNIT suboption). By default, a one-unit change from the mean of the covariate is assessed. For example, the following statements produce all pairwise differences for the A factor:
proc glimmix;
class A;
model y = A x A*x / dist=binary
oddsratio(diff=all
at x=4
unit x=3);
run;
The covariate x is set to the reference value 
in the computation of the least squares means for the A odds ratio estimates. The odds ratios computed for the covariate are based on differencing this set of least squares means with a set of least squares means computed at 
.