The SAS System 1 10:22 Wednesday, January 16, 2002 ------------------------------------------------------------------------------- | y1 | |-----------------------------------------------------------------------------| | 1 | 2 | 3 | |-------------------------+-------------------------+-------------------------| | rotate | rotate | rotate | |-------------------------+-------------------------+-------------------------| | 0 | 1 | 0 | 1 | 0 | 1 | |------------+------------+------------+------------+------------+------------| | N | N | N | N | N | N | |------------+------------+------------+------------+------------+------------| | 18.00| 2.00| 14.00| 6.00| 7.00| 5.00| ------------------------------------------------------------------------------- (Continued) The SAS System 2 10:22 Wednesday, January 16, 2002 --------------------------- | y1 | |-------------------------| | 4 | |-------------------------| | rotate | |-------------------------| | 0 | 1 | |------------+------------| | N | N | |------------+------------| | 7.00| 30.00| --------------------------- The SAS System 3 10:22 Wednesday, January 16, 2002 ------------------------------------------------------------------------------- | y8 | |-----------------------------------------------------------------------------| | 1 | 2 | 3 | |-------------------------+-------------------------+-------------------------| | rotate | rotate | rotate | |-------------------------+-------------------------+-------------------------| | 0 | 1 | 0 | 1 | 0 | 1 | |------------+------------+------------+------------+------------+------------| | N | N | N | N | N | N | |------------+------------+------------+------------+------------+------------| | 28.00| 17.00| 10.00| 10.00| 4.00| 5.00| ------------------------------------------------------------------------------- (Continued) The SAS System 4 10:22 Wednesday, January 16, 2002 --------------------------- | y8 | |-------------------------| | 4 | |-------------------------| | rotate | |-------------------------| | 0 | 1 | |------------+------------| | N | N | |------------+------------| | 4.00| 11.00| --------------------------- The SAS System 5 10:22 Wednesday, January 16, 2002 ------------------------------------------------------------------------------- | y8 | |-----------------------------------------------------------------------------| | 1 | 2 | |---------------------------------------------------+-------------------------| | y1 | y1 | |---------------------------------------------------+-------------------------| | 1 | 2 | 3 | 4 | 1 | 2 | |------------+------------+------------+------------+------------+------------| | N | N | N | N | N | N | |------------+------------+------------+------------+------------+------------| | 14.00| 11.00| 5.00| 15.00| 2.00| 3.00| ------------------------------------------------------------------------------- (Continued) The SAS System 6 10:22 Wednesday, January 16, 2002 ------------------------------------------------------------------------------- | y8 | |-----------------------------------------------------------------------------| | 2 | 3 | |-------------------------+---------------------------------------------------| | y1 | y1 | |-------------------------+---------------------------------------------------| | 3 | 4 | 1 | 2 | 3 | 4 | |------------+------------+------------+------------+------------+------------| | N | N | N | N | N | N | |------------+------------+------------+------------+------------+------------| | 4.00| 11.00| 1.00| 4.00| 1.00| 3.00| ------------------------------------------------------------------------------- (Continued) The SAS System 7 10:22 Wednesday, January 16, 2002 ----------------------------------------------------- | y8 | |---------------------------------------------------| | 4 | |---------------------------------------------------| | y1 | |---------------------------------------------------| | 1 | 2 | 3 | 4 | |------------+------------+------------+------------| | N | N | N | N | |------------+------------+------------+------------| | 3.00| 2.00| 2.00| 8.00| ----------------------------------------------------- The SAS System 8 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Model Information Data Set WORK.TENHAVE Response Variable y1 Number of Response Levels 4 Number of Observations 89 Model cumulative logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value y1 Frequency 1 1 20 2 2 20 3 3 12 4 4 37 Probabilities modeled are cumulated over the lower Ordered Values. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Score Test for the Proportional Odds Assumption Chi-Square DF Pr > ChiSq 0.4883 2 0.7834 Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 238.473 207.318 SC 245.939 217.273 -2 Log L 232.473 199.318 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 33.1550 1 <.0001 Score 30.1039 1 <.0001 Wald 28.2031 1 <.0001 The SAS System 9 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 1 -0.4541 0.2954 2.3640 0.1242 Intercept 2 1 0.8790 0.3116 7.9576 0.0048 Intercept 3 1 1.6438 0.3537 21.5945 <.0001 rotate 1 -2.4620 0.4636 28.2031 <.0001 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits rotate 0.085 0.034 0.212 Association of Predicted Probabilities and Observed Responses Percent Concordant 51.3 Somers' D 0.450 Percent Discordant 6.2 Gamma 0.783 Percent Tied 42.5 Tau-a 0.323 Pairs 2804 c 0.725 The SAS System 10 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Model Information Data Set WORK.TENHAVE Response Variable y8 Number of Response Levels 4 Number of Observations 89 Model cumulative logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value y8 Frequency 1 1 45 2 2 20 3 3 9 4 4 15 Probabilities modeled are cumulated over the lower Ordered Values. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Score Test for the Proportional Odds Assumption Chi-Square DF Pr > ChiSq 0.5000 2 0.7788 Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 221.757 218.156 SC 229.223 228.111 -2 Log L 215.757 210.156 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 5.6004 1 0.0180 Score 5.5238 1 0.0188 Wald 5.4659 1 0.0194 The SAS System 11 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 1 0.4740 0.2979 2.5324 0.1115 Intercept 2 1 1.4951 0.3356 19.8480 <.0001 Intercept 3 1 2.1210 0.3759 31.8434 <.0001 rotate 1 -0.9543 0.4082 5.4659 0.0194 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits rotate 0.385 0.173 0.857 Association of Predicted Probabilities and Observed Responses Percent Concordant 35.9 Somers' D 0.203 Percent Discordant 15.6 Gamma 0.393 Percent Tied 48.4 Tau-a 0.134 Pairs 2595 c 0.601 The SAS System 12 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Model Information Data Set WORK.TENHAVE Response Variable y8 Number of Response Levels 4 Number of Observations 89 Model cumulative logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value y8 Frequency 1 1 45 2 2 20 3 3 9 4 4 15 Probabilities modeled are cumulated over the lower Ordered Values. Class Level Information Design Variables Class Value 1 2 3 y1 1 1 0 0 2 0 1 0 3 0 0 1 4 -1 -1 -1 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Score Test for the Proportional Odds Assumption Chi-Square DF Pr > ChiSq 12.2243 8 0.1415 The SAS System 13 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 221.757 223.163 SC 229.223 240.584 -2 Log L 215.757 209.163 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 6.5934 4 0.1590 Score 6.1677 4 0.1870 Wald 6.5937 4 0.1590 Type III Analysis of Effects Wald Effect DF Chi-Square Pr > ChiSq rotate 1 3.1185 0.0774 y1 3 1.0095 0.7989 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 1 0.4198 0.3125 1.8042 0.1792 Intercept 2 1 1.4501 0.3473 17.4356 <.0001 Intercept 3 1 2.0750 0.3857 28.9428 <.0001 rotate 1 -0.8797 0.4982 3.1185 0.0774 y1 1 1 0.3787 0.4259 0.7904 0.3740 y1 2 1 -0.0345 0.3777 0.0083 0.9272 y1 3 1 -0.3405 0.4377 0.6050 0.4367 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits rotate 0.415 0.156 1.101 y1 1 vs 4 1.466 0.403 5.325 y1 2 vs 4 0.970 0.311 3.021 y1 3 vs 4 0.714 0.202 2.526 The SAS System 14 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Association of Predicted Probabilities and Observed Responses Percent Concordant 52.9 Somers' D 0.245 Percent Discordant 28.3 Gamma 0.302 Percent Tied 18.8 Tau-a 0.163 Pairs 2595 c 0.623 The SAS System 15 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Model Information Data Set WORK.TENHAVE Response Variable y8 Number of Response Levels 4 Number of Observations 89 Model cumulative logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value y8 Frequency 1 1 45 2 2 20 3 3 9 4 4 15 Probabilities modeled are cumulated over the lower Ordered Values. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Score Test for the Proportional Odds Assumption Chi-Square DF Pr > ChiSq 12.2243 8 0.1415 Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 221.757 223.163 SC 229.223 240.584 -2 Log L 215.757 209.163 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 6.5934 4 0.1590 Score 6.1677 4 0.1870 Wald 6.5937 4 0.1590 The SAS System 16 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 1 0.4161 0.5148 0.6533 0.4189 Intercept 2 1 1.4464 0.5371 7.2527 0.0071 Intercept 3 1 2.0714 0.5634 13.5191 0.0002 rotate 1 -0.8797 0.4982 3.1185 0.0774 y11 1 0.3823 0.6582 0.3374 0.5613 y12 1 -0.0308 0.5797 0.0028 0.9576 y13 1 -0.3368 0.6446 0.2730 0.6013 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits rotate 0.415 0.156 1.101 y11 1.466 0.403 5.325 y12 0.970 0.311 3.021 y13 0.714 0.202 2.526 Association of Predicted Probabilities and Observed Responses Percent Concordant 52.9 Somers' D 0.245 Percent Discordant 28.3 Gamma 0.302 Percent Tied 18.8 Tau-a 0.163 Pairs 2595 c 0.623 The SAS System 17 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Model Information Data Set WORK.TENHAVE Response Variable y8 Number of Response Levels 4 Number of Observations 89 Model cumulative logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value y8 Frequency 1 1 45 2 2 20 3 3 9 4 4 15 Probabilities modeled are cumulated over the lower Ordered Values. Class Level Information Design Variables Class Value 1 2 3 y1 1 1 0 0 2 0 1 0 3 0 0 1 4 -1 -1 -1 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Score Test for the Proportional Odds Assumption Chi-Square DF Pr > ChiSq 53.9235 14 <.0001 The SAS System 18 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 221.757 221.940 SC 229.223 246.826 -2 Log L 215.757 201.940 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 13.8167 7 0.0545 Score 12.9866 7 0.0724 Wald 13.1192 7 0.0693 Type III Analysis of Effects Wald Effect DF Chi-Square Pr > ChiSq rotate 1 1.8672 0.1718 y1 3 4.1111 0.2497 rotate*y1 3 6.6890 0.0825 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 1 0.4014 0.3302 1.4779 0.2241 Intercept 2 1 1.5155 0.3665 17.0966 <.0001 Intercept 3 1 2.1623 0.4047 28.5534 <.0001 rotate 1 -0.7705 0.5638 1.8672 0.1718 y1 1 1 0.4666 0.4849 0.9259 0.3359 y1 2 1 0.2520 0.5070 0.2471 0.6192 y1 3 1 -1.1589 0.5854 3.9191 0.0477 rotate*y1 1 1 -0.9772 1.1207 0.7603 0.3832 rotate*y1 2 1 -1.0642 0.8624 1.5228 0.2172 rotate*y1 3 1 2.6953 1.0576 6.4945 0.0108 The SAS System 19 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Association of Predicted Probabilities and Observed Responses Percent Concordant 57.5 Somers' D 0.339 Percent Discordant 23.7 Gamma 0.417 Percent Tied 18.8 Tau-a 0.224 Pairs 2595 c 0.669 The SAS System 20 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Model Information Data Set WORK.TENHAVE Response Variable y8 Number of Response Levels 4 Number of Observations 89 Model cumulative logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value y8 Frequency 1 1 45 2 2 20 3 3 9 4 4 15 Probabilities modeled are cumulated over the lower Ordered Values. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Score Test for the Proportional Odds Assumption Chi-Square DF Pr > ChiSq 53.9235 14 <.0001 Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 221.757 221.940 SC 229.223 246.826 -2 Log L 215.757 201.940 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 13.8167 7 0.0545 Score 12.9866 7 0.0724 Wald 13.1192 7 0.0693 The SAS System 21 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 1 0.8417 0.8111 1.0768 0.2994 Intercept 2 1 1.9557 0.8336 5.5043 0.0190 Intercept 3 1 2.6025 0.8535 9.2980 0.0023 rotate 1 -1.4243 0.8797 2.6218 0.1054 y11 1 0.0264 0.9566 0.0008 0.9780 y12 1 -0.1882 0.9797 0.0369 0.8476 y13 1 -1.5991 1.0635 2.2611 0.1327 rotate*y11 1 -0.3233 1.6253 0.0396 0.8423 rotate*y12 1 -0.4104 1.2702 0.1044 0.7467 rotate*y13 1 3.3492 1.5350 4.7606 0.0291 Association of Predicted Probabilities and Observed Responses Percent Concordant 57.5 Somers' D 0.339 Percent Discordant 23.7 Gamma 0.417 Percent Tied 18.8 Tau-a 0.224 Pairs 2595 c 0.669 The SAS System 22 10:22 Wednesday, January 16, 2002 ----------------------------------------------------- | fast1 | |---------------------------------------------------| | 0 | 1 | |-------------------------+-------------------------| | rotate | rotate | |-------------------------+-------------------------| | 0 | 1 | 0 | 1 | |------------+------------+------------+------------| | N | N | N | N | |------------+------------+------------+------------| | 14.00| 35.00| 32.00| 8.00| ----------------------------------------------------- The SAS System 23 10:22 Wednesday, January 16, 2002 ----------------------------------------------------- | fast8 | |---------------------------------------------------| | 0 | 1 | |-------------------------+-------------------------| | rotate | rotate | |-------------------------+-------------------------| | 0 | 1 | 0 | 1 | |------------+------------+------------+------------| | N | N | N | N | |------------+------------+------------+------------| | 8.00| 16.00| 38.00| 27.00| ----------------------------------------------------- The SAS System 24 10:22 Wednesday, January 16, 2002 ------------------------------------------------------------------------------- | rotate | |-----------------------------------------------------------------------------| | 0 | 1 | |---------------------------------------------------+-------------------------| | fast8 | fast8 | |---------------------------------------------------+-------------------------| | 0 | 1 | 0 | |-------------------------+-------------------------+-------------------------| | fast1 | fast1 | fast1 | |-------------------------+-------------------------+-------------------------| | 0 | 1 | 0 | 1 | 0 | 1 | |------------+------------+------------+------------+------------+------------| | N | N | N | N | N | N | |------------+------------+------------+------------+------------+------------| | 3.00| 5.00| 11.00| 27.00| 11.00| 5.00| ------------------------------------------------------------------------------- (Continued) The SAS System 25 10:22 Wednesday, January 16, 2002 --------------------------- | rotate | |-------------------------| | 1 | |-------------------------| | fast8 | |-------------------------| | 1 | |-------------------------| | fast1 | |-------------------------| | 0 | 1 | |------------+------------| | N | N | |------------+------------| | 24.00| 3.00| --------------------------- The SAS System 26 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Model Information Data Set WORK.TENHAVE Response Variable fast8 Number of Response Levels 2 Number of Observations 89 Model binary logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value fast8 Frequency 1 0 24 2 1 65 Probability modeled is fast8=0. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 105.760 104.536 SC 108.249 112.002 -2 Log L 103.760 98.536 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 5.2241 2 0.0734 Score 5.0963 2 0.0782 Wald 4.8421 2 0.0888 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -1.9300 0.6020 10.2776 0.0013 rotate 1 1.3079 0.6060 4.6585 0.0309 fast1 1 0.5093 0.6000 0.7204 0.3960 The SAS System 27 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits rotate 3.698 1.128 12.128 fast1 1.664 0.513 5.394 Association of Predicted Probabilities and Observed Responses Percent Concordant 50.2 Somers' D 0.290 Percent Discordant 21.2 Gamma 0.407 Percent Tied 28.7 Tau-a 0.116 Pairs 1560 c 0.645 The SAS System 28 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Model Information Data Set WORK.TENHAVE Response Variable fast8 Number of Response Levels 2 Number of Observations 89 Model binary logit Optimization Technique Fisher's scoring Response Profile Ordered Total Value fast8 Frequency 1 0 24 2 1 65 Probability modeled is fast8=0. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 105.760 104.445 SC 108.249 114.399 -2 Log L 103.760 96.445 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 7.3155 3 0.0625 Score 7.7907 3 0.0505 Wald 6.7935 3 0.0788 The SAS System 29 10:22 Wednesday, January 16, 2002 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -1.2993 0.6513 3.9792 0.0461 rotate 1 0.5191 0.7462 0.4840 0.4866 fast1 1 -0.3871 0.8132 0.2266 0.6340 rotate*fast1 1 1.6781 1.1520 2.1217 0.1452 Association of Predicted Probabilities and Observed Responses Percent Concordant 51.9 Somers' D 0.324 Percent Discordant 19.5 Gamma 0.454 Percent Tied 28.7 Tau-a 0.129 Pairs 1560 c 0.662