The SAS System 1 The FREQ Procedure Table 1 of X by Y Controlling for Z=z1 X Y Frequency| Row Pct |y1 |y2 | Total ---------+--------+--------+ x1 | 0 | 5 | 5 | 0.00 | 100.00 | ---------+--------+--------+ x2 | 16 | 7 | 23 | 69.57 | 30.43 | ---------+--------+--------+ Total 16 12 28 Statistics for Table 1 of X by Y Controlling for Z=z1 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 8.1159 0.0044 Likelihood Ratio Chi-Square 1 9.9757 0.0016 Continuity Adj. Chi-Square 1 5.5239 0.0188 Mantel-Haenszel Chi-Square 1 7.8261 0.0051 Phi Coefficient -0.5384 Contingency Coefficient 0.4740 Cramer's V -0.5384 WARNING: 50% of the cells have expected counts less than 5. Chi-Square may not be a valid test. Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 0 Left-sided Pr <= F 0.0081 Right-sided Pr >= F 1.0000 Table Probability (P) 0.0081 Two-sided Pr <= P 0.0081 Sample Size = 28 The SAS System 2 The FREQ Procedure Table 2 of X by Y Controlling for Z=z2 X Y Frequency| Row Pct |y1 |y2 | Total ---------+--------+--------+ x1 | 6 | 9 | 15 | 40.00 | 60.00 | ---------+--------+--------+ x2 | 5 | 0 | 5 | 100.00 | 0.00 | ---------+--------+--------+ Total 11 9 20 Statistics for Table 2 of X by Y Controlling for Z=z2 Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 5.4545 0.0195 Likelihood Ratio Chi-Square 1 7.3352 0.0068 Continuity Adj. Chi-Square 1 3.2997 0.0693 Mantel-Haenszel Chi-Square 1 5.1818 0.0228 Phi Coefficient -0.5222 Contingency Coefficient 0.4629 Cramer's V -0.5222 WARNING: 50% of the cells have expected counts less than 5. Chi-Square may not be a valid test. Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 6 Left-sided Pr <= F 0.0298 Right-sided Pr >= F 1.0000 Table Probability (P) 0.0298 Two-sided Pr <= P 0.0379 Sample Size = 20 Yaturated model: (XYZ) 3 The GENMOD Procedure Model Information Data Set WORK.ZEROS Distribution Poisson Link Function Log Dependent Variable count Observations Used 8 Class Level Information Class Levels Values X 2 x1 x2 Y 2 y1 y2 Z 2 z1 z2 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 0 0.0000 . Scaled Deviance 0 0.0000 . Pearson Chi-Square 0 0.0000 . Scaled Pearson X2 0 0.0000 . Log Likelihood 56.6027 WARNING: Negative of Hessian not positive definite. Analysis Of Parameter Estimates Standard Wald 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept 1 -24.2173 0.6367 -25.4652 -22.9695 1446.82 <.0001 X x1 1 26.4146 0.7187 25.0060 27.8231 1350.96 <.0001 X x2 0 0.0000 0.0000 0.0000 0.0000 . . Y y1 1 25.8268 0.4532 24.9386 26.7150 3248.11 <.0001 Y y2 0 0.0000 0.0000 0.0000 0.0000 . . Z z1 1 26.1632 0.5123 25.1591 27.1674 2607.68 <.0001 Z z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x1 y1 1 -26.2322 0.6951 -27.5946 -24.8699 1424.30 <.0001 X*Y x1 y2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x2 y1 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x2 y2 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x1 z1 1 -26.7510 0.7574 -28.2355 -25.2666 1247.57 <.0001 X*Z x1 z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x2 z1 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x2 z2 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y1 z1 0 -25.0001 0.0000 -25.0001 -25.0001 . . Y*Z y1 z2 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y2 z1 0 0.0000 0.0000 0.0000 0.0000 . . Yaturated model: (XYZ) 4 The GENMOD Procedure Analysis Of Parameter Estimates Standard Wald 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Y*Z y2 z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y*Z x1 y1 z1 1 0.0001 146974.4 -288065 288064.5 0.00 1.0000 X*Y*Z x1 y1 z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y*Z x1 y2 z1 0 0.0000 0.0000 0.0000 0.0000 . . X*Y*Z x1 y2 z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y*Z x2 y1 z1 0 0.0000 0.0000 0.0000 0.0000 . . X*Y*Z x2 y1 z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y*Z x2 y2 z1 0 0.0000 0.0000 0.0000 0.0000 . . X*Y*Z x2 y2 z2 0 0.0000 0.0000 0.0000 0.0000 . . Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. Observation Statistics Observation count X Y Z Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 0 x1 y1 z1 4.629E-11 -23.79603 146974.38 4.629E-11 0 . -4.63E-11 -6.804E-6 -9.622E-6 -910.3203 -643.6936 -643.6936 2 6 x1 y1 z2 6 1.7917595 0.4082483 6 2.6955642 13.355275 2.665E-15 1.088E-15 0 . . . 3 5 x1 y2 z1 5 1.6094379 0.4472136 5 2.0811391 12.012652 3.553E-15 1.589E-15 6.585E-10 . . . 4 9 x1 y2 z2 9 2.1972246 0.3333333 9 4.6828329 17.297222 1.066E-14 3.553E-15 0 . . . 5 16 x2 y1 z1 16 2.7725887 0.25 16 9.8021106 26.116824 -7.11E-15 -1.78E-15 0 0 -1.289E-9 -1.289E-9 6 5 x2 y1 z2 5 1.6094379 0.4472136 5 2.0811391 12.012652 3.553E-15 1.589E-15 6.585E-10 0.0002672 6.446E-10 9.215E-10 7 7 x2 y2 z1 7 1.9459101 0.3779645 7 3.3371375 14.683243 1.155E-14 4.364E-15 6.585E-10 0.0003161 2.0951E-9 2.1961E-9 8 0 x2 y2 z2 3.038E-11 -24.21734 0.6366766 3.038E-11 8.722E-12 1.058E-10 -3.04E-11 -5.512E-6 -7.794E-6 -7.794E-6 -5.512E-6 -7.794E-6 Complete independence model: (X,Y,Z) 5 The GENMOD Procedure Model Information Data Set WORK.ZEROS Distribution Poisson Link Function Log Dependent Variable count Observations Used 8 Class Level Information Class Levels Values X 2 x1 x2 Y 2 y1 y2 Z 2 z1 z2 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 4 33.7655 8.4414 Scaled Deviance 4 33.7655 8.4414 Pearson Chi-Square 4 25.3257 6.3314 Scaled Pearson X2 4 25.3257 6.3314 Log Likelihood 39.7200 Algorithm converged. Analysis Of Parameter Estimates Standard Wald 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept 1 1.6301 0.3028 1.0366 2.2235 28.99 <.0001 X x1 1 -0.3365 0.2928 -0.9103 0.2373 1.32 0.2504 X x2 0 0.0000 0.0000 0.0000 0.0000 . . Y y1 1 0.2513 0.2910 -0.3190 0.8216 0.75 0.3877 Y y2 0 0.0000 0.0000 0.0000 0.0000 . . Z z1 1 0.3365 0.2928 -0.2373 0.9103 1.32 0.2504 Z z2 0 0.0000 0.0000 0.0000 0.0000 . . Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. Complete independence model: (X,Y,Z) 6 The GENMOD Procedure Observation Statistics Observation count X Y Z Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 0 x1 y1 z1 6.5625 1.8813716 0.2847537 6.5625 3.7556624 11.46706 -6.5625 -2.561738 -3.622844 -5.296409 -3.745127 -4.537452 2 6 x1 y1 z2 4.6875 1.5448994 0.3088209 4.6875 2.5590126 8.5863807 1.3125 0.6062178 0.5807934 0.7810488 0.8152395 0.7965151 3 5 x1 y2 z1 5.1041667 1.6300572 0.302765 5.1041667 2.8197511 9.2392967 -0.104167 -0.046107 -0.046265 -0.063423 -0.063207 -0.063322 4 9 x1 y2 z2 3.6458333 1.293585 0.3255033 3.6458333 1.9263177 6.9002639 5.3541667 2.8040999 2.3573671 3.0091494 3.5793982 3.2413415 5 16 x2 y1 z1 9.1875 2.2178439 0.2584549 9.1875 5.5360516 15.247357 6.8125 2.2475421 2.0314614 3.2685476 3.6162136 3.4860279 6 5 x2 y1 z2 6.5625 1.8813716 0.2847537 6.5625 3.7556624 11.46706 -1.5625 -0.609938 -0.636917 -0.931139 -0.891697 -0.910364 7 7 x2 y2 z1 7.1458333 1.9665294 0.2781743 7.1458333 4.1425759 12.326373 -0.145833 -0.054554 -0.054742 -0.081873 -0.081593 -0.081718 8 0 x2 y2 z2 5.1041667 1.6300572 0.302765 5.1041667 2.8197511 9.2392967 -5.104167 -2.25924 -3.195048 -4.379993 -3.097123 -3.83358 Joint Independence: (XY,Z) 7 The GENMOD Procedure Model Information Data Set WORK.ZEROS Distribution Poisson Link Function Log Dependent Variable count Observations Used 8 Class Level Information Class Levels Values X 2 x1 x2 Y 2 y1 y2 Z 2 z1 z2 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 3 23.9006 7.9669 Scaled Deviance 3 23.9006 7.9669 Pearson Chi-Square 3 19.1020 6.3673 Scaled Pearson X2 3 19.1020 6.3673 Log Likelihood 44.6524 Algorithm converged. Analysis Of Parameter Estimates Standard Wald 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept 1 1.0704 0.4148 0.2575 1.8834 6.66 0.0099 X x1 1 0.6931 0.4629 -0.2141 1.6004 2.24 0.1343 X x2 0 0.0000 0.0000 0.0000 0.0000 . . Y y1 1 1.0986 0.4364 0.2432 1.9540 6.34 0.0118 Y y2 0 0.0000 0.0000 0.0000 0.0000 . . Z z1 1 0.3365 0.2928 -0.2373 0.9103 1.32 0.2504 Z z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x1 y1 1 -1.9459 0.6547 -3.2290 -0.6628 8.84 0.0030 X*Y x1 y2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x2 y1 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x2 y2 0 0.0000 0.0000 0.0000 0.0000 . . Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. Joint Independence: (XY,Z) 8 The GENMOD Procedure Observation Statistics Observation count X Y Z Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 0 x1 y1 z1 3.5000012 1.2527633 0.426084 3.5000012 1.5183953 8.0677334 -3.500001 -1.870829 -2.645752 -4.381781 -3.098387 -3.619393 2 6 x1 y1 z2 2.5000009 0.9162911 0.4425305 2.5000009 1.0501649 5.9514506 3.4999991 2.2135934 1.8723307 2.6207172 3.0983854 2.8645451 3 5 x1 y2 z1 8.1666667 2.1000608 0.2937848 8.1666667 4.591713 14.524959 -3.166667 -1.108103 -1.194615 -2.198946 -2.039702 -2.087965 4 9 x1 y2 z2 5.8333333 1.7635886 0.3171675 5.8333333 3.1328768 10.861512 3.1666667 1.3111246 1.2133072 1.8875286 2.039702 1.9782444 5 16 x2 y1 z1 12.25 2.5055259 0.25 12.25 7.5047409 19.995694 3.75 1.0714286 1.0227459 2.1125748 2.2131333 2.1899792 6 5 x2 y1 z2 8.75 2.1690537 0.2771024 8.75 5.0832106 15.061839 -3.75 -1.267731 -1.379798 -2.408773 -2.213133 -2.279179 7 7 x2 y2 z1 4.0833333 1.4069136 0.3971626 4.0833333 1.8747763 8.8936537 2.9166667 1.4433757 1.3086702 2.1936358 2.4194335 2.3415685 8 0 x2 y2 z2 2.9166667 1.0704414 0.4147575 2.9166667 1.2937327 6.575504 -2.916667 -1.707825 -2.415229 -3.421596 -2.419434 -2.961473 Joint Independence: (XZ,Y) 9 The GENMOD Procedure Model Information Data Set WORK.ZEROS Distribution Poisson Link Function Log Dependent Variable count Observations Used 8 Class Level Information Class Levels Values X 2 x1 x2 Y 2 y1 y2 Z 2 z1 z2 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 3 17.3327 5.7776 Scaled Deviance 3 17.3327 5.7776 Pearson Chi-Square 3 13.5840 4.5280 Scaled Pearson X2 3 13.5840 4.5280 Log Likelihood 47.9364 Algorithm converged. Analysis Of Parameter Estimates Standard Wald 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept 1 0.7828 0.4762 -0.1506 1.7161 2.70 0.1002 X x1 1 1.0986 0.5164 0.0865 2.1107 4.53 0.0334 X x2 0 0.0000 0.0000 0.0000 0.0000 . . Y y1 1 0.2513 0.2910 -0.3190 0.8216 0.75 0.3877 Y y2 0 0.0000 0.0000 0.0000 0.0000 . . Z z1 1 1.5261 0.4934 0.5589 2.4932 9.56 0.0020 Z z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x1 z1 1 -2.6247 0.7142 -4.0246 -1.2248 13.50 0.0002 X*Z x1 z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x2 z1 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x2 z2 0 0.0000 0.0000 0.0000 0.0000 . . Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. Joint Independence: (XZ,Y) 10 The GENMOD Procedure Observation Statistics Observation count X Y Z Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 0 x1 y1 z1 2.8125006 1.034074 0.4649771 2.8125006 1.1305856 6.9965156 -2.812501 -1.677051 -2.371708 -3.788425 -2.678821 -3.160472 2 6 x1 y1 z2 8.4375 2.1326861 0.2878721 8.4375 4.7992854 14.833751 -2.4375 -0.839146 -0.885371 -1.614357 -1.530074 -1.555905 3 5 x1 y2 z1 2.1875005 0.7827595 0.4762202 2.1875005 0.8601789 5.5629802 2.8124995 1.9015966 1.6253568 2.2896749 2.6788199 2.4903396 4 9 x1 y2 z2 6.5625 1.8813716 0.3056998 6.5625 3.6046007 11.947622 2.4375 0.9515026 0.9001961 1.4475699 1.5300737 1.4987066 5 16 x2 y1 z1 12.9375 2.5601301 0.2442989 12.9375 8.0149855 20.883245 3.0625 0.8514339 0.8207782 1.7194414 1.7836617 1.7692333 6 5 x2 y1 z2 2.8125 1.0340738 0.4649771 2.8125 1.1305852 6.9965148 2.1875 1.304373 1.1741556 1.8755257 2.0835271 2.0045792 7 7 x2 y2 z1 10.0625 2.3088156 0.2650735 10.0625 5.9851481 16.917527 -3.0625 -0.965435 -1.021921 -1.888021 -1.783662 -1.814857 8 0 x2 y2 z2 2.1875 0.7827593 0.4762202 2.1875 0.8601787 5.5629795 -2.1875 -1.47902 -2.09165 -2.946552 -2.083527 -2.55511 Joint Independence: (YZ,X) 11 The GENMOD Procedure Model Information Data Set WORK.ZEROS Distribution Poisson Link Function Log Dependent Variable count Observations Used 8 Class Level Information Class Levels Values X 2 x1 x2 Y 2 y1 y2 Z 2 z1 z2 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 3 33.7437 11.2479 Scaled Deviance 3 33.7437 11.2479 Pearson Chi-Square 3 24.7792 8.2597 Scaled Pearson X2 3 24.7792 8.2597 Log Likelihood 39.7309 Algorithm converged. Analysis Of Parameter Estimates Standard Wald 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept 1 1.6582 0.3550 0.9625 2.3539 21.82 <.0001 X x1 1 -0.3365 0.2928 -0.9103 0.2373 1.32 0.2504 X x2 0 0.0000 0.0000 0.0000 0.0000 . . Y y1 1 0.2007 0.4495 -0.6803 1.0816 0.20 0.6553 Y y2 0 0.0000 0.0000 0.0000 0.0000 . . Z z1 1 0.2877 0.4410 -0.5766 1.1519 0.43 0.5141 Z z2 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y1 z1 1 0.0870 0.5898 -1.0690 1.2430 0.02 0.8827 Y*Z y1 z2 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y2 z1 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y2 z2 0 0.0000 0.0000 0.0000 0.0000 . . Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. Joint Independence: (YZ,X) 12 The GENMOD Procedure Observation Statistics Observation count X Y Z Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 0 x1 y1 z1 6.6666668 1.89712 0.302765 6.6666668 3.6829403 12.067653 -6.666667 -2.581989 -3.651484 -5.8554 -4.140393 -4.8795 2 6 x1 y1 z2 4.5833334 1.5224265 0.3465195 4.5833334 2.3239326 9.0393951 1.4166666 0.6617241 0.6313967 0.941594 0.9868208 0.9667463 3 5 x1 y2 z1 5 1.6094379 0.3354102 5 2.5910055 9.648764 -3.607E-8 -1.613E-8 -1.614E-8 -2.441E-8 -2.439E-8 -2.44E-8 4 9 x1 y2 z2 3.7500002 1.3217559 0.3745367 3.7500002 1.7998033 7.8133547 5.2499998 2.7110882 2.2931282 3.3308743 3.9379805 3.6628034 5 16 x2 y1 z1 9.3333334 2.2335922 0.2781743 9.3333334 5.4107114 16.099752 6.6666666 2.1821789 1.9785233 3.7539841 4.1403933 4.0367693 6 5 x2 y1 z2 6.4166666 1.8588988 0.3252538 6.4166666 3.3919772 12.138528 -1.416667 -0.559259 -0.582001 -1.026949 -0.986821 -0.999885 7 7 x2 y2 z1 7 1.9459101 0.3133916 7 3.7873779 12.937711 2.1774E-8 8.2298E-9 8.212E-9 1.469E-8 1.4722E-8 1.4712E-8 8 0 x2 y2 z2 5.2500002 1.6582281 0.3549536 5.2500002 2.6183172 10.5268 -5.25 -2.291288 -3.24037 -5.569146 -3.937981 -4.556061 Conditional Independence: (XY,XZ) 13 The GENMOD Procedure Model Information Data Set WORK.ZEROS Distribution Poisson Link Function Log Dependent Variable count Observations Used 8 Class Level Information Class Levels Values X 2 x1 x2 Y 2 y1 y2 Z 2 z1 z2 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 2 7.4678 3.7339 Scaled Deviance 2 7.4678 3.7339 Pearson Chi-Square 2 4.8861 2.4431 Scaled Pearson X2 2 4.8861 2.4431 Log Likelihood 52.8688 Algorithm converged. Analysis Of Parameter Estimates Standard Wald 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept 1 0.2231 0.5542 -0.8631 1.3094 0.16 0.6872 X x1 1 2.1282 0.6287 0.8960 3.3604 11.46 0.0007 X x2 0 0.0000 0.0000 0.0000 0.0000 . . Y y1 1 1.0986 0.4364 0.2432 1.9540 6.34 0.0118 Y y2 0 0.0000 0.0000 0.0000 0.0000 . . Z z1 1 1.5261 0.4934 0.5589 2.4932 9.56 0.0020 Z z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x1 y1 1 -1.9459 0.6547 -3.2290 -0.6628 8.84 0.0030 X*Y x1 y2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x2 y1 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x2 y2 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x1 z1 1 -2.6247 0.7142 -4.0246 -1.2248 13.50 0.0002 X*Z x1 z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x2 z1 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x2 z2 0 0.0000 0.0000 0.0000 0.0000 . . Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. Conditional Independence: (XY,XZ) 14 The GENMOD Procedure Observation Statistics Observation count X Y Z Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 0 x1 y1 z1 1.5 0.4054651 0.5627314 1.5 0.4978441 4.5194868 -1.5 -1.224745 -1.732051 -2.390457 -1.690309 -2.087377 2 6 x1 y1 z2 4.5 1.5040774 0.4281744 4.5 1.9442396 10.415383 1.5 0.7071068 0.6724469 1.6074556 1.6903085 1.6761049 3 5 x1 y2 z1 3.5 1.252763 0.470562 3.5 1.3916338 8.8026032 1.5 0.8017837 0.7528276 1.5871 1.6903085 1.6676436 4 9 x1 y2 z2 10.5 2.3513753 0.2968084 10.5 5.8687487 18.785947 -1.5 -0.46291 -0.474645 -1.733158 -1.690309 -1.69356 5 16 x2 y1 z1 17.25 2.8478121 0.235336 17.25 10.876039 27.359455 -1.25 -0.300965 -0.304714 -1.442169 -1.424425 -1.425221 6 5 x2 y1 z2 3.75 1.3217558 0.4603311 3.75 1.5212363 9.2441258 1.25 0.6454972 0.6138573 1.3546044 1.4244246 1.4103686 7 7 x2 y2 z1 5.75 1.7491999 0.3880994 5.75 2.6873057 12.303215 1.25 0.521286 0.5039287 1.3769953 1.4244246 1.4181645 8 0 x2 y2 z2 1.25 0.2231436 0.5542047 1.25 0.4218617 3.7038204 -1.25 -1.118034 -1.581139 -2.014441 -1.424425 -1.810797 Conditional Independence: (XY,YZ) 15 The GENMOD Procedure Model Information Data Set WORK.ZEROS Distribution Poisson Link Function Log Dependent Variable count Observations Used 8 Class Level Information Class Levels Values X 2 x1 x2 Y 2 y1 y2 Z 2 z1 z2 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 2 23.8789 11.9394 Scaled Deviance 2 23.8789 11.9394 Pearson Chi-Square 2 19.0958 9.5479 Scaled Pearson X2 2 19.0958 9.5479 Log Likelihood 44.6633 Algorithm converged. Analysis Of Parameter Estimates Standard Wald 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept 1 1.0986 0.4543 0.2083 1.9889 5.85 0.0156 X x1 1 0.6931 0.4629 -0.2141 1.6004 2.24 0.1343 X x2 0 0.0000 0.0000 0.0000 0.0000 . . Y y1 1 1.0480 0.5548 -0.0395 2.1354 3.57 0.0589 Y y2 0 0.0000 0.0000 0.0000 0.0000 . . Z z1 1 0.2877 0.4410 -0.5766 1.1519 0.43 0.5141 Z z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x1 y1 1 -1.9459 0.6547 -3.2290 -0.6628 8.84 0.0030 X*Y x1 y2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x2 y1 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x2 y2 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y1 z1 1 0.0870 0.5898 -1.0690 1.2430 0.02 0.8827 Y*Z y1 z2 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y2 z1 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y2 z2 0 0.0000 0.0000 0.0000 0.0000 . . Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. Conditional Independence: (XY,YZ) 16 The GENMOD Procedure Observation Statistics Observation count X Y Z Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 0 x1 y1 z1 3.5555556 1.2685113 0.4383259 3.5555556 1.5059265 8.3948162 -3.555556 -1.885618 -2.666667 -4.737252 -3.349743 -3.844 2 6 x1 y1 z2 2.4444445 0.8938179 0.4696155 2.4444445 0.9737394 6.1364559 3.5555555 2.2741409 1.9142069 2.8195707 3.3497431 3.1166087 3 5 x1 y2 z1 8 2.0794415 0.3273268 8 4.211811 15.195364 -3 -1.06066 -1.14016 -3.016579 -2.806243 -2.837246 4 9 x1 y2 z2 6 1.7917595 0.3673154 6 2.9207325 12.325675 3 1.2247449 1.1394613 2.6108337 2.806243 2.7700852 5 16 x2 y1 z1 12.444444 2.5212743 0.2703368 12.444444 7.3259571 21.139108 3.5555556 1.0079053 0.9648578 3.2066762 3.3497431 3.3370431 6 5 x2 y1 z2 8.5555556 2.1465808 0.3185767 8.5555556 4.5822128 15.974276 -3.555556 -1.215579 -1.31897 -3.634654 -3.349743 -3.388632 7 7 x2 y2 z1 4 1.3862944 0.4225771 4 1.7472767 9.1571071 3 1.5 1.3544818 2.5340035 2.806243 2.7312307 8 0 x2 y2 z2 3 1.0986123 0.4542568 3 1.2315646 7.3077774 -3 -1.732051 -2.44949 -3.968627 -2.806243 -3.297726 Conditional Independence: (XZ, YZ) 17 The GENMOD Procedure Model Information Data Set WORK.ZEROS Distribution Poisson Link Function Log Dependent Variable count Observations Used 8 Class Level Information Class Levels Values X 2 x1 x2 Y 2 y1 y2 Z 2 z1 z2 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 2 17.3109 8.6555 Scaled Deviance 2 17.3109 8.6555 Pearson Chi-Square 2 13.5705 6.7852 Scaled Pearson X2 2 13.5705 6.7852 Log Likelihood 47.9473 Algorithm converged. Analysis Of Parameter Estimates Standard Wald 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept 1 0.8109 0.5110 -0.1906 1.8125 2.52 0.1125 X x1 1 1.0986 0.5164 0.0865 2.1107 4.53 0.0334 X x2 0 0.0000 0.0000 0.0000 0.0000 . . Y y1 1 0.2007 0.4495 -0.6803 1.0816 0.20 0.6553 Y y2 0 0.0000 0.0000 0.0000 0.0000 . . Z z1 1 1.4773 0.5935 0.3141 2.6404 6.20 0.0128 Z z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x1 z1 1 -2.6247 0.7142 -4.0246 -1.2248 13.50 0.0002 X*Z x1 z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x2 z1 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x2 z2 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y1 z1 1 0.0870 0.5898 -1.0690 1.2430 0.02 0.8827 Y*Z y1 z2 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y2 z1 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y2 z2 0 0.0000 0.0000 0.0000 0.0000 . . Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. Conditional Independence: (XZ, YZ) 18 The GENMOD Procedure Observation Statistics Observation count X Y Z Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 0 x1 y1 z1 2.8571429 1.0498221 0.4762202 2.8571429 1.1234987 7.2659325 -2.857143 -1.690309 -2.390457 -4.028881 -2.848849 -3.312565 2 6 x1 y1 z2 8.25 2.1102132 0.3279874 8.25 4.3378101 15.690521 -2.25 -0.783349 -0.823745 -2.455932 -2.335497 -2.349354 3 5 x1 y2 z1 2.1428571 0.7621401 0.4976134 2.1428571 0.8080235 5.6828013 2.8571429 1.9518001 1.6609313 2.4242969 2.8488492 2.6580277 4 9 x1 y2 z2 6.75 1.9095425 0.3574602 6.75 3.3499098 13.601112 2.25 0.8660254 0.8235759 2.2210191 2.3354968 2.3200911 5 16 x2 y1 z1 13.142857 2.5758784 0.2650735 13.142857 7.8173362 22.096362 2.8571429 0.7881104 0.7618686 2.7539906 2.8488492 2.8417016 6 5 x2 y1 z2 2.75 1.0116009 0.4908249 2.75 1.0508525 7.1965378 2.25 1.3568011 1.2158824 2.0929299 2.3354968 2.2565474 7 7 x2 y2 z1 9.8571429 2.2881964 0.3018233 9.8571429 5.4555506 17.809983 -2.857143 -0.910032 -0.960353 -3.006382 -2.848849 -2.865321 8 0 x2 y2 z2 2.25 0.8109302 0.5109903 2.25 0.8264694 6.1254538 -2.25 -1.5 -2.12132 -3.302891 -2.335497 -2.775706 Homogeneous Association: (XY,XZ,YZ) 19 The GENMOD Procedure Model Information Data Set WORK.ZEROS Distribution Poisson Link Function Log Dependent Variable count Observations Used 8 Class Level Information Class Levels Values X 2 x1 x2 Y 2 y1 y2 Z 2 z1 z2 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 1 0.0000 0.0000 Scaled Deviance 1 0.0000 0.0000 Pearson Chi-Square 1 0.0000 0.0000 Scaled Pearson X2 1 0.0000 0.0000 Log Likelihood 56.6027 Algorithm converged. Analysis Of Parameter Estimates Standard Wald 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept 1 -24.2173 0.6367 -25.4652 -22.9694 1446.82 <.0001 X x1 1 26.4145 0.7187 25.0060 27.8231 1350.96 <.0001 X x2 0 0.0000 0.0000 0.0000 0.0000 . . Y y1 1 25.8267 0.4532 24.9386 26.7149 3248.10 <.0001 Y y2 0 0.0000 0.0000 0.0000 0.0000 . . Z z1 1 26.1632 0.5123 25.1590 27.1674 2607.67 <.0001 Z z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x1 y1 1 -26.2322 0.6951 -27.5945 -24.8699 1424.30 <.0001 X*Y x1 y2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x2 y1 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x2 y2 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x1 z1 1 -26.7510 0.7574 -28.2354 -25.2666 1247.56 <.0001 X*Z x1 z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x2 z1 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x2 z2 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y1 z1 0 -25.0001 0.0000 -25.0001 -25.0001 . . Y*Z y1 z2 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y2 z1 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y2 z2 0 0.0000 0.0000 0.0000 0.0000 . . Homogeneous Association: (XY,XZ,YZ) 20 The GENMOD Procedure Analysis Of Parameter Estimates Standard Wald 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. Observation Statistics Observation count X Y Z Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 0 x1 y1 z1 4.629E-11 -23.79609 0.6912147 4.629E-11 1.194E-11 1.794E-10 -4.63E-11 -6.804E-6 -9.622E-6 -9.622E-6 -6.804E-6 -9.622E-6 2 6 x1 y1 z2 6 1.7917595 0.4082483 6 2.6955642 13.355275 -1.87E-14 -7.61E-15 0 0 -2.741E-9 -2.741E-9 3 5 x1 y2 z1 5 1.6094379 0.4472136 5 2.0811391 12.012652 3.553E-15 1.589E-15 6.585E-10 0.0002164 5.222E-10 8.405E-10 4 9 x1 y2 z2 9 2.1972246 0.3333333 9 4.6828329 17.297222 1.066E-14 3.553E-15 0 0 1.5665E-9 1.5665E-9 5 16 x2 y1 z1 16 2.7725887 0.25 16 9.8021106 26.116824 -7.11E-15 -1.78E-15 0 0 -1.29E-9 -1.29E-9 6 5 x2 y1 z2 5 1.6094379 0.4472136 5 2.0811391 12.012652 3.553E-15 1.589E-15 6.585E-10 0.0002672 6.447E-10 9.216E-10 7 7 x2 y2 z1 7 1.9459101 0.3779645 7 3.3371375 14.683243 1.155E-14 4.364E-15 6.585E-10 0.0003162 2.0952E-9 2.1962E-9 8 0 x2 y2 z2 3.038E-11 -24.21731 0.6366766 3.038E-11 8.722E-12 1.058E-10 -3.04E-11 -5.512E-6 -7.795E-6 -7.795E-6 -5.512E-6 -7.795E-6 Homogeneous Association with zero margin: (XY,XZ,YZ) 21 The GENMOD Procedure Model Information Data Set WORK.ZEROS Distribution Poisson Link Function Log Dependent Variable count Observations Used 8 Class Level Information Class Levels Values X 2 x1 x2 Y 2 y1 y2 Z 2 z1 z2 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 1 0.0000 0.0000 Scaled Deviance 1 0.0000 0.0000 Pearson Chi-Square 1 0.0000 0.0000 Scaled Pearson X2 1 0.0000 0.0000 Log Likelihood 56.6027 Algorithm converged. Analysis Of Parameter Estimates Standard Wald 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept 1 1.9459 0.3780 1.2051 2.6867 26.51 <.0001 X x1 1 0.2513 0.5040 -0.7364 1.2390 0.25 0.6180 X x2 0 0.0000 0.0000 0.0000 0.0000 . . Y y1 1 -0.3365 0.5855 -1.4841 0.8112 0.33 0.5655 Y y2 0 0.0000 0.0000 0.0000 0.0000 . . Z z1 1 0.8267 0.4532 -0.0615 1.7149 3.33 0.0681 Z z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x1 y1 1 -0.0690 0.7878 -1.6131 1.4751 0.01 0.9302 X*Y x1 y2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x2 y1 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x2 y2 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x1 z1 1 -1.4145 0.7187 -2.8230 -0.0059 3.87 0.0490 X*Z x1 z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x2 z1 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x2 z2 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y1 z1 1 -26.0000 115148.2 -225712 225660.3 0.00 0.9998 Y*Z y1 z2 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y2 z1 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y2 z2 0 0.0000 0.0000 0.0000 0.0000 . . Homogeneous Association with zero margin: (XY,XZ,YZ) 22 The GENMOD Procedure Analysis Of Parameter Estimates Standard Wald 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. Observation Statistics Observation count X Y Z Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 0 x1 y1 z1 1.703E-11 -24.79603 115148.18 1.703E-11 0 . -1.7E-11 -4.127E-6 -5.836E-6 -6.633E-6 -4.69E-6 -6.247E-6 2 6 x1 y1 z2 6 1.7917595 0.4082483 6 2.6955642 13.355275 0 0 0 0 0 0 3 5 x1 y2 z1 5 1.6094379 0.4472136 5 2.0811391 12.012652 1.776E-15 7.944E-16 4.657E-10 0.0002868 4.892E-10 6.754E-10 4 9 x1 y2 z2 9 2.1972246 0.3333333 9 4.6828329 17.297222 1.776E-15 5.921E-16 0 0 4.891E-10 4.891E-10 5 0 x2 y1 z1 5.839E-11 -23.56388 115148.18 5.839E-11 0 . -5.84E-11 -7.641E-6 -0.000011 -0.000023 -0.000016 -0.000018 6 5 x2 y1 z2 5 1.6094379 0.4472136 5 2.0811391 12.012652 8.882E-16 3.972E-16 0 0 2.446E-10 2.446E-10 7 16 x2 y2 z1 16 2.7725887 0.25 16 9.8021106 26.116824 8.882E-15 2.22E-15 0 0 2.4456E-9 2.4456E-9 8 7 x2 y2 z2 7 1.9459101 0.3779645 7 3.3371375 14.683243 8.882E-16 3.357E-16 1.0413E-9 0.0007588 2.446E-10 1.0696E-9 Homogeneous Association with zero margin: (XY,XZ,YZ) 23 The GENMOD Procedure Model Information Data Set WORK.ZEROS1 Distribution Poisson Link Function Log Dependent Variable count Observations Used 6 Class Level Information Class Levels Values X 2 x1 x2 Y 2 y1 y2 Z 2 z2 z1 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 0 0.0000 . Scaled Deviance 0 0.0000 . Pearson Chi-Square 0 0.0000 . Scaled Pearson X2 0 0.0000 . Log Likelihood 56.6027 Algorithm converged. Analysis Of Parameter Estimates Standard Wald 95% Chi- Parameter DF Estimate Error Confidence Limits Square Pr > ChiSq Intercept 1 2.7726 0.2500 2.2826 3.2626 123.00 <.0001 X x1 1 -1.1632 0.5123 -2.1673 -0.1590 5.15 0.0232 X x2 0 0.0000 0.0000 0.0000 0.0000 . . Y y1 1 -0.3365 0.5855 -1.4841 0.8112 0.33 0.5655 Y y2 0 0.0000 0.0000 0.0000 0.0000 . . Z z2 1 -0.8267 0.4532 -1.7149 0.0615 3.33 0.0681 Z z1 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x1 y1 1 -0.0690 0.7878 -1.6131 1.4751 0.01 0.9302 X*Y x1 y2 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x2 y1 0 0.0000 0.0000 0.0000 0.0000 . . X*Y x2 y2 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x1 z2 1 1.4145 0.7187 0.0059 2.8230 3.87 0.0490 X*Z x1 z1 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x2 z2 0 0.0000 0.0000 0.0000 0.0000 . . X*Z x2 z1 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y1 z2 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y2 z2 0 0.0000 0.0000 0.0000 0.0000 . . Y*Z y2 z1 0 0.0000 0.0000 0.0000 0.0000 . . Scale 0 1.0000 0.0000 1.0000 1.0000 Homogeneous Association with zero margin: (XY,XZ,YZ) 24 The GENMOD Procedure NOTE: The scale parameter was held fixed. Observation Statistics Observation count X Y Z Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 6 x1 y1 z2 6 1.7917595 0.4082483 6 2.6955642 13.355275 2.665E-15 1.088E-15 0 . . . 2 5 x1 y2 z1 5 1.6094379 0.4472136 5 2.0811391 12.012652 6.217E-15 2.78E-15 4.657E-10 . . . 3 9 x1 y2 z2 9 2.1972246 0.3333333 9 4.6828329 17.297222 1.776E-15 5.921E-16 0 . . . 4 5 x2 y1 z2 5 1.6094379 0.4472136 5 2.0811391 12.012652 1.776E-15 7.944E-16 4.657E-10 . . . 5 16 x2 y2 z1 16 2.7725887 0.25 16 9.8021106 26.116824 8.882E-15 2.22E-15 0 0 1.2167E-7 1.2167E-7 6 7 x2 y2 z2 7 1.9459101 0.3779645 7 3.3371375 14.683243 5.329E-15 2.014E-15 6.585E-10 . . .