Random Effects Logistic Regression Model for Odds of Amenorrhea
Clinical Trial of Contracepting Women

The GLIMMIX Procedure

Model Information
Data Set WORK.AMEN
Response Variable y
Response Distribution Binomial
Link Function Logit
Variance Function Default
Variance Matrix Blocked By id
Estimation Technique Maximum Likelihood
Likelihood Approximation Gauss-Hermite Quadrature
Degrees of Freedom Method Containment

Number of Observations Read 4604
Number of Observations Used 3616

Dimensions
G-side Cov. Parameters 1
Columns in X 5
Columns in Z per Subject 1
Subjects (Blocks in V) 1151
Max Obs per Subject 4

Optimization Information
Optimization Technique Dual Quasi-Newton
Parameters in Optimization 6
Lower Boundaries 1
Upper Boundaries 0
Fixed Effects Not Profiled
Starting From GLM estimates
Quadrature Points 50

Iteration History
Iteration Restarts Evaluations Objective
Function
Change Max
Gradient
0 0 4 3962.7364136 . 751.6664
1 0 4 3956.1434481 6.59296549 170.9975
2 0 2 3946.6562429 9.48720521 594.7693
3 0 3 3921.2647391 25.39150377 212.3625
4 0 2 3897.0620727 24.20266644 37.14434
5 0 4 3880.0445788 17.01749382 122.1483
6 0 3 3869.708903 10.33567581 114.3655
7 0 3 3868.9862599 0.72264312 36.80192
8 0 3 3868.9317498 0.05451015 2.388693
9 0 3 3868.9300356 0.00171413 1.535736
10 0 3 3868.9299681 0.00006752 0.124257
11 0 3 3868.9299668 0.00000130 0.046076
12 0 2 3868.9299658 0.00000097 0.040627
13 0 3 3868.9299656 0.00000029 0.003542
14 0 3 3868.9299655 0.00000001 0.000232
15 0 2 3868.9299655 0.00000000 0.000232

Convergence criterion (GCONV=1E-12) satisfied.

Fit Statistics
-2 Log Likelihood 3868.93
AIC (smaller is better) 3880.93
AICC (smaller is better) 3880.95
BIC (smaller is better) 3911.22
CAIC (smaller is better) 3917.22
HQIC (smaller is better) 3892.36

Fit Statistics for Conditional Distribution
-2 log L(y | r. effects) 2173.41
Pearson Chi-Square 1746.28
Pearson Chi-Square / DF 0.48

Estimated G Matrix
Effect Row Col1
Intercept 1 5.0646

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error
Intercept id 5.0646 0.5840

Solutions for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t|
Intercept -3.8057 0.3050 1150 -12.48 <.0001
time 1.1332 0.2682 2461 4.22 <.0001
time2 -0.04192 0.05481 2461 -0.76 0.4444
time*trt 0.5644 0.1922 2461 2.94 0.0034
time2*trt -0.1096 0.04961 2461 -2.21 0.0273

Type III Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
time 1 2461 17.85 <.0001
time2 1 2461 0.59 0.4444
time*trt 1 2461 8.62 0.0034
time2*trt 1 2461 4.88 0.0273

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
2 df Test of Trt X Time Interaction 2 2461 12.40 6.20 0.0020 0.0021