The GLIMMIX Procedure - SAS

1 SAS/STAT User s GuideThe GLIMMIX ProcedureThis document is an individual chapter fromSAS/STAT User s correct bibliographic citation for the complete manual is as follows: SAS Institute Inc. User s , NC: SAS Institute 2013, SAS Institute Inc., Cary, NC, USAAll rights reserved. Produced in the United States of a hard-copy book: No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or byany means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the publisher, SAS a web download or e-book: Your use of this publication shall be governed by the terms established by the vendor at the timeyou acquire this scanning, uploading, and distribution of this book via the Internet or any other means without the permission of the publisher isillegal and punishable by law.

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4 Other brand and product names are trademarks of their respective companies. 2013 SAS Institute Inc. All rights reserved. all that you need on your journey to knowledge and additional books and Greater Insight into Your SAS Software with SAS 43 The GLIMMIX ProcedureContentsOverview: GLIMMIX Procedure ..3080 Basic Features ..3080 Assumptions ..3081 Notation for the Generalized Linear Mixed Model ..3082 The Basic Model ..3082G-Side and R-Side Random Effects and Covariance Structures ..3083 Relationship with Generalized Linear Models ..3084 PROC GLIMMIX Contrasted with Other SAS Procedures ..3084 Getting Started: GLIMMIX Procedure ..3085 Logistic Regressions with Random Intercepts ..3085 Syntax: GLIMMIX Procedure .

5 3092 PROC GLIMMIX Statement ..3092BY Statement ..3119 CLASS Statement ..3119 CODE Statement ..3120 CONTRAST Statement ..3121 COVTEST Statement ..3125 EFFECT Statement ..3133 ESTIMATE Statement ..3133 FREQ Statement ..3139ID Statement ..3139 LSMEANS Statement ..3140 LSMESTIMATE Statement ..3153 MODEL Statement ..3160 Response Variable Options ..3162 Model Options ..3163 NLOPTIONS Statement ..3174 OUTPUT Statement ..3175 PARMS Statement ..3179 RANDOM Statement ..3184 SLICE Statement ..3204 STORE Statement ..3204 WEIGHT Statement ..3204 Programming Statements ..3205 User-Defined Link or Variance Function ..3206 Implied Variance Functions ..32063078 FChapter 43: The GLIMMIX ProcedureAutomatic Variables.

6 3207 Details: GLIMMIX Procedure ..3210 Generalized Linear Models Theory ..3210 Maximum Likelihood ..3210 Scale and Dispersion Parameters ..3213 Quasi-likelihood for Independent Data ..3214 Effects of Adding Overdispersion ..3215 Generalized Linear Mixed Models Theory ..3215 Model or Integral Approximation ..3215 Pseudo-likelihood Estimation Based on Linearization ..3217 Maximum Likelihood Estimation Based on Laplace Approximation ..3222 Maximum Likelihood Estimation Based on Adaptive Quadrature ..3225 Aspects Common to Adaptive Quadrature and Laplace Approximation ..3227 Notes on Bias of Estimators ..3229 Pseudo-likelihood Estimation for Weighted Multilevel Models ..3230 GLM Mode or GLMM Mode ..3233 Statistical Inference for Covariance Parameters.

7 3234 The Likelihood Ratio Test ..3234 One- and Two-Sided Testing, Mixture Distributions ..3235 Handling the Degenerate Distribution ..3236 Wald Versus Likelihood Ratio Tests ..3237 Confidence Bounds Based on Likelihoods ..3237 Degrees of Freedom Methods ..3241 Between-Within Degrees of Freedom Approximation ..3241 Containment Degrees of Freedom Approximation ..3241 Satterthwaite Degrees of Freedom Approximation ..3241 Kenward-Roger Degrees of Freedom Approximation ..3243 Empirical Covariance ( Sandwich ) Estimators ..3244 Residual-Based Estimators ..3244 Design-Adjusted MBN Estimator ..3245 Exploring and Comparing Covariance Matrices ..3246 Processing by Subjects ..3248 Radial Smoothing Based on Mixed Models ..3250 From Penalized Splines to Mixed Models.

8 3250 Knot Selection ..3251 Odds and Odds Ratio Estimation ..3256 The Odds Ratio Estimates Table ..3257 Odds or Odds Ratio ..3260 Odds Ratios in Multinomial Models ..3260 Parameterization of Generalized Linear Mixed Models ..3261 Intercept ..3261 Interaction Effects ..3261 Nested Effects ..3261 Implications of the Non-Full-Rank Parameterization ..3262 The GLIMMIX ProcedureF3079 Missing Level Combinations ..3262 Notes on the EFFECT Statement ..3262 Positional and Nonpositional Syntax for Contrast Coefficients ..3263 Response-Level Ordering and Referencing ..3266 Comparing the GLIMMIX and MIXED Procedures ..3267 Singly or Doubly Iterative Fitting ..3270 Default Estimation Techniques ..3272 Default Output.

9 3273 Model Information ..3273 Class Level Information ..3273 Number of Observations ..3273 Response Profile ..3273 Dimensions ..3274 Optimization Information ..3274 Iteration History ..3274 Convergence Status ..3275 Fit Statistics ..3275 Covariance Parameter Estimates ..3276 Type III Tests of Fixed Effects ..3277 Notes on Output Statistics ..3277 ODS Table Names ..3278 ODS Graphics ..3281 ODS Graph Names ..3281 Diagnostic Plots ..3283 Graphics for LS-Mean Comparisons ..3288 Examples: GLIMMIX Procedure ..3301 Example : Binomial Counts in Randomized Blocks ..3301 Example : Mating Experiment with Crossed Random Effects ..3312 Example : Smoothing Disease Rates; Standardized Mortality Ratios ..3320 Example : Quasi-likelihood Estimation for Proportions with Unknown Distribution 3330 Example : Joint Modeling of Binary and Count Data.

10 3338 Example : Radial Smoothing of Repeated Measures Data ..3345 Example : Isotonic Contrasts for Ordered Alternatives ..3357 Example : Adjusted Covariance Matrices of Fixed Effects ..3358 Example : Testing Equality of Covariance and Correlation Matrices ..3364 Example : Multiple Trends Correspond to Multiple Extrema in Profile Likelihoods 3371 Example : Maximum Likelihood in Proportional Odds Model with Random Effects 3378 Example : Fitting a Marginal (GEE-Type) Model ..3384 Example : Response Surface Comparisons with Multiplicity Adjustments ..3390 Example : Generalized Poisson Mixed Model for Overdispersed Count Data ..3398 Example : Comparing Multiple B-Splines ..3406 Example : Diallel Experiment with Multimember Random Effects.