| Random effects proportional odds regression model for global impression scale |
| Arthritis Clinical Trial |
| Model Information | |
|---|---|
| Data Set | WORK.ARTHRITIS |
| Response Variable | y |
| Response Distribution | Multinomial (ordered) |
| Link Function | Cumulative 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 | 1194 |
|---|---|
| Number of Observations Used | 1194 |
| Response Profile | ||
|---|---|---|
| Ordered Value |
y | Total Frequency |
| 1 | 1 | 86 |
| 2 | 2 | 332 |
| 3 | 3 | 478 |
| 4 | 4 | 240 |
| 5 | 5 | 58 |
| The GLIMMIX procedure is modeling the probabilities of levels of y having lower Ordered Values in the Response Profile table. | ||
| Dimensions | |
|---|---|
| G-side Cov. Parameters | 3 |
| Columns in X | 7 |
| Columns in Z per Subject | 2 |
| Subjects (Blocks in V) | 303 |
| Max Obs per Subject | 4 |
| Optimization Information | |
|---|---|
| Optimization Technique | Dual Quasi-Newton |
| Parameters in Optimization | 10 |
| Lower Boundaries | 2 |
| Upper Boundaries | 0 |
| Fixed Effects | Not Profiled |
| Starting From | GLM estimates |
| Quadrature Points | 30 |
| Iteration History | |||||
|---|---|---|---|---|---|
| Iteration | Restarts | Evaluations | Objective Function |
Change | Max Gradient |
| 0 | 0 | 4 | 3047.1334157 | . | 147.364 |
| 1 | 0 | 5 | 3042.023412 | 5.11000369 | 138.0259 |
| 2 | 0 | 5 | 3035.8819458 | 6.14146622 | 137.0961 |
| 3 | 0 | 5 | 3033.8780696 | 2.00387618 | 138.7859 |
| 4 | 0 | 5 | 3031.509098 | 2.36897166 | 137.5461 |
| 5 | 0 | 5 | 3028.2238329 | 3.28526508 | 133.6531 |
| 6 | 0 | 5 | 3026.5473423 | 1.67649054 | 132.9108 |
| 7 | 0 | 5 | 3023.8437136 | 2.70362870 | 131.3992 |
| 8 | 0 | 5 | 3022.2062355 | 1.63747816 | 130.5198 |
| 9 | 0 | 5 | 3019.6676259 | 2.53860956 | 128.8923 |
| 10 | 0 | 5 | 3017.2990126 | 2.36861331 | 127.5443 |
| 11 | 0 | 13 | 3016.3496584 | 0.94935421 | 127.0196 |
| 12 | 0 | 17 | 3016.2521494 | 0.09750897 | 126.9578 |
| 13 | 0 | 17 | 3016.2402195 | 0.01192987 | 126.951 |
| 14 | 0 | 25 | 3016.2400969 | 0.00012262 | 126.9509 |
| 15 | 0 | 17 | 3016.2400527 | 0.00004418 | 126.9509 |
| 16 | 0 | 21 | 3016.2400523 | 0.00000045 | 126.9509 |
| 17 | 0 | 15 | 3016.2400365 | 0.00001579 | 126.9509 |
| 18 | 0 | 15 | 3016.2400332 | 0.00000331 | 126.9509 |
| 19 | 1 | 51 | 3016.2400332 | 0.00000001 | 126.9509 |
| 20 | 1 | 15 | 3016.2399718 | 0.00006144 | 126.9507 |
| 21 | 1 | 3 | 2966.6540393 | 49.58593248 | 82.45886 |
| 22 | 1 | 2 | 2921.8282867 | 44.82575257 | 156.6188 |
| 23 | 1 | 3 | 2915.5877034 | 6.24058329 | 138.8605 |
| 24 | 1 | 2 | 2897.3110791 | 18.27662431 | 92.39018 |
| 25 | 1 | 2 | 2883.0272388 | 14.28384035 | 47.78544 |
| 26 | 1 | 3 | 2874.5617221 | 8.46551668 | 46.67652 |
| 27 | 1 | 3 | 2873.5118953 | 1.04982677 | 47.13933 |
| 28 | 1 | 3 | 2873.2541993 | 0.25769605 | 46.47516 |
| 29 | 1 | 2 | 2872.8280388 | 0.42616050 | 43.59488 |
| 30 | 1 | 3 | 2872.7270072 | 0.10103152 | 41.22958 |
| 31 | 1 | 3 | 2872.6910649 | 0.03594237 | 41.83902 |
| 32 | 1 | 4 | 2872.5589275 | 0.13213735 | 38.01682 |
| 33 | 1 | 4 | 2871.2643768 | 1.29455073 | 15.9771 |
| 34 | 1 | 3 | 2871.1170942 | 0.14728261 | 15.16233 |
| 35 | 1 | 3 | 2871.0975481 | 0.01954603 | 13.85224 |
| 36 | 1 | 3 | 2871.0962749 | 0.00127323 | 13.76206 |
| 37 | 1 | 3 | 2871.0962339 | 0.00004100 | 13.88421 |
| 38 | 1 | 3 | 2871.0962329 | 0.00000101 | 13.88789 |
| 39 | 1 | 4 | 2871.0962321 | 0.00000083 | 13.88983 |
| 40 | 1 | 4 | 2871.096229 | 0.00000301 | 13.88234 |
| 41 | 1 | 6 | 2871.0960383 | 0.00019073 | 13.9745 |
| 42 | 1 | 2 | 2871.0958219 | 0.00021644 | 13.87216 |
| 43 | 1 | 2 | 2871.0957717 | 0.00005018 | 13.90266 |
| 44 | 1 | 4 | 2871.0954025 | 0.00036926 | 13.85584 |
| 45 | 1 | 8 | 2870.4699851 | 0.62541733 | 8.126829 |
| 46 | 1 | 3 | 2870.2810078 | 0.18897729 | 10.60846 |
| 47 | 1 | 3 | 2870.2729554 | 0.00805244 | 10.48051 |
| 48 | 1 | 6 | 2869.2271257 | 1.04582971 | 5.688627 |
| 49 | 1 | 3 | 2869.0240612 | 0.20306452 | 3.295322 |
| 50 | 1 | 3 | 2868.9990763 | 0.02498482 | 2.217486 |
| 51 | 1 | 4 | 2868.8763929 | 0.12268348 | 0.763875 |
| 52 | 1 | 3 | 2868.8705403 | 0.00585261 | 0.096985 |
| 53 | 1 | 3 | 2868.8704971 | 0.00004311 | 0.004328 |
| 54 | 1 | 3 | 2868.8704971 | 0.00000007 | 0.000227 |
| 55 | 1 | 3 | 2868.8704971 | 0.00000000 | 5.573E-6 |
| Convergence criterion (GCONV=1E-12) satisfied. |
| Fit Statistics | |
|---|---|
| -2 Log Likelihood | 2868.87 |
| AIC (smaller is better) | 2888.87 |
| AICC (smaller is better) | 2889.06 |
| BIC (smaller is better) | 2926.01 |
| CAIC (smaller is better) | 2936.01 |
| HQIC (smaller is better) | 2903.73 |
| Fit Statistics for Conditional Distribution | |
|---|---|
| -2 log L(y | r. effects) | 1961.62 |
| Estimated G Matrix | |||
|---|---|---|---|
| Effect | Row | Col1 | Col2 |
| Intercept | 1 | 4.1424 | -0.05161 |
| sqrtmonth | 2 | -0.05161 | 0.3243 |
| Covariance Parameter Estimates | |||
|---|---|---|---|
| Cov Parm | Subject | Estimate | Standard Error |
| UN(1,1) | id | 4.1424 | 0.8549 |
| UN(2,1) | id | -0.05161 | 0.2626 |
| UN(2,2) | id | 0.3243 | 0.1617 |
| Solutions for Fixed Effects | ||||||
|---|---|---|---|---|---|---|
| Effect | y | Estimate | Standard Error | DF | t Value | Pr > |t| |
| Intercept | 1 | -5.2945 | 0.3289 | 301 | -16.10 | <.0001 |
| Intercept | 2 | -2.0085 | 0.2483 | 301 | -8.09 | <.0001 |
| Intercept | 3 | 1.0753 | 0.2382 | 301 | 4.51 | <.0001 |
| Intercept | 4 | 3.8683 | 0.3006 | 301 | 12.87 | <.0001 |
| trt | 0.1140 | 0.3184 | 586 | 0.36 | 0.7205 | |
| sqrtmonth | 0.4000 | 0.1018 | 300 | 3.93 | 0.0001 | |
| trt*sqrtmonth | 0.4005 | 0.1432 | 586 | 2.80 | 0.0053 | |
| Type III Tests of Fixed Effects | ||||
|---|---|---|---|---|
| Effect | Num DF | Den DF | F Value | Pr > F |
| trt | 1 | 586 | 0.13 | 0.7205 |
| sqrtmonth | 1 | 300 | 15.44 | 0.0001 |
| trt*sqrtmonth | 1 | 586 | 7.82 | 0.0053 |