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Observation Y X1 X2 … X20 1 Y1 X11 X12 … X1,20 2 Y2 X21 X22 … X2,20 3 Y3 X31 X32 … X3,20 … … … … … … 200 Y200 X200,1 X200,2 … X200,20 Table 1.
The complete data matrix.
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V Complete data SAS macro SAS forward MI Mean N MSE Mean N MSE Mean N MSE Mean N MSE x1 1.161 100 0.250 1.162 100 0.345 1.152 99 0.322 1.092 100 0.244 x2 −0.880 100 0.252 −0.938 99 0.334 −0.947 89 0.287 −0.837 100 0.266 x3 −0.679 96 0.186 −0.712 87 0.239 −0.750 61 0.233 −0.626 98 0.208 x4 −0.130 8 0.474 0.049 8 0.621 −0.013 15 0.452 −0.009 62 0.267 x5 −0.083 5 0.393 0.060 7 0.563 −0.015 15 0.445 0.007 58 0.240 x6 0.118 22 0.428 0.168 10 0.472 0.107 13 0.525 0.021 65 0.286 x7 0.229 10 0.337 −0.066 10 0.608 0.254 15 0.314 0.016 65 0.255 x8 0.446 9 0.057 0.012 15 0.543 −0.014 15 0.336 0.027 60 0.262 x9 0.187 8 0.406 0.110 16 0.478 −0.037 17 0.360 0.065 57 0.251 x10 0.095 14 0.403 −0.060 17 0.554 0.045 12 0.362 0.040 61 0.269 x11 −0.041 7 0.407 −0.059 9 0.567 0.079 7 0.348 0.007 57 0.232 x12 0.018 9 0.474 0.000 13 0.596 −0.091 8 0.376 0.009 58 0.243 x13 −0.085 13 0.443 0.101 20 0.482 −0.161 14 0.417 0.036 59 0.265 x14 0.071 6 0.578 0.212 11 0.544 0.010 17 0.334 −0.022 51 0.268 x15 −0.135 8 0.426 −0.022 12 0.553 −0.086 13 0.352 −0.017 63 0.253 x16 0.040 6 0.480 −0.090 11 0.455 −0.122 18 0.415 −0.078 59 0.240 x17 0.034 11 0.417 0.042 12 0.547 0.017 13 0.351 −0.034 57 0.248 x18 0.038 8 0.435 0.016 12 0.511 0.174 15 0.401 0.041 59 0.236 x19 −0.431 4 0.085 0.002 15 0.510 −0.228 10 0.311 0.005 55 0.239 x20 −0.029 7 0.482 −0.246 6 0.524 0.092 15 0.298 0.001 59 0.253 Table 2.
Model selection at 5% missing for 200 sample size, MCAR.
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V Complete data SAS macro SAS forward MI Mean N MSE Mean N MSE Mean N MSE Mean N MSE x1 1.161 100 0.250 1.197 100 0.576 1.045 54 0.312 0.985 100 0.221 x2 −0.880 100 0.252 −1.012 97 0.418 −0.867 35 0.346 −0.748 100 0.224 x3 −0.679 96 0.186 −0.867 79 0.365 −0.677 25 0.266 −0.571 98 0.193 x4 −0.130 8 0.474 0.132 16 0.884 0.020 13 0.343 −0.019 54 0.265 x5 −0.083 5 0.393 −0.233 13 0.746 0.011 14 0.246 −0.001 60 0.223 x6 0.118 22 0.428 −0.018 19 0.710 0.029 9 0.229 0.018 63 0.276 x7 0.229 10 0.337 −0.028 14 1.206 0.012 9 0.221 0.009 59 0.224 x8 0.446 9 0.057 0.335 9 0.746 0.077 14 0.210 0.049 66 0.228 x9 0.187 8 0.406 0.374 9 0.707 0.121 15 0.281 0.055 64 0.240 x10 0.095 14 0.403 0.14 17 0.725 0.091 15 0.224 0.025 62 0.256 x11 −0.041 7 0.407 −0.397 17 0.586 −0.083 9 0.281 −0.026 51 0.229 x12 0.018 9 0.474 −0.207 16 0.739 0.037 12 0.328 −0.010 52 0.238 x13 −0.085 13 0.443 0.018 17 0.727 0.028 15 0.297 0.015 55 0.261 x14 0.071 6 0.578 0.014 12 0.828 −0.012 15 0.241 0.004 60 0.238 x15 −0.135 8 0.426 −0.133 13 0.750 −0.060 14 0.308 0.007 60 0.240 x16 0.040 6 0.480 0.051 10 0.748 −0.079 14 0.224 −0.076 46 0.246 x17 0.034 11 0.417 −0.93 10 0.898 0.027 21 0.322 −0.028 64 0.229 x18 0.038 8 0.435 −0.102 10 1.034 0.124 16 0.298 0.018 58 0.254 x19 −0.431 4 0.085 −0.026 8 0.866 −0.024 15 0.258 −0.038 56 0.216 x20 −0.029 7 0.482 0.071 10 0.860 −0.021 14 0.184 0.009 59 0.234 Table 3.
Model selection at 10% missing for 200 sample size, MCAR.
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V Complete data SAS macro SAS forward MI Mean N MSE Mean N MSE Mean N MSE Mean N MSE x1 1.161 100 0.250 1.635 99 1.790 0.959 14 0.212 0.879 100 0.203 x2 −0.880 100 0.252 −1.608 97 3.742 −0.721 12 0.292 −0.685 100 0.201 x3 −0.679 96 0.186 −1.364 75 2.802 −0.656 4 0.223 −0.525 97 0.156 x4 −0.130 8 0.474 0.731 13 2.760 0.087 5 0.250 −0.015 59 0.235 x5 −0.083 5 0.393 0.847 9 1.421 0.023 4 0.129 0.002 52 0.239 x6 0.118 22 0.428 −0.065 15 1.023 −0.015 9 0.145 0.026 60 0.262 x7 0.229 10 0.337 1.715 17 6.451 −0.076 6 0.323 0.010 55 0.218 x8 0.446 9 0.057 −1.392 16 5.247 0.092 2 0.024 0.059 53 0.242 x9 0.187 8 0.406 0.252 12 1.769 −0.030 3 0.093 0.070 59 0.234 x10 0.095 14 0.403 −0.736 11 2.755 0.060 9 0.087 0.040 58 0.236 x11 −0.041 7 0.407 0.146 15 1.496 0.048 6 0.204 0.011 56 0.221 x12 0.018 9 0.474 0.127 10 0.969 0.094 4 0.214 0.027 59 0.218 x13 −0.085 13 0.443 0.493 15 1.020 0.009 7 0.144 0.033 56 0.259 x14 0.071 6 0.578 0.089 16 1.213 0.177 6 0.190 −0.021 58 0.223 x15 −0.135 8 0.426 −0.107 12 0.810 0.026 3 0.187 −0.017 60 0.228 x16 0.040 6 0.480 −0.318 18 0.769 −0.087 5 0.268 −0.064 54 0.203 x17 0.034 11 0.417 −0.126 15 1.107 −0.002 10 0.122 −0.047 65 0.219 x18 0.038 8 0.435 −0.342 13 1.420 0.021 5 0.285 0.000 58 0.231 x19 −0.431 4 0.085 1.089 14 4.293 −0.035 5 0.159 −0.032 56 0.223 x20 −0.029 7 0.482 2.323 19 9.146 −0.056 6 0.068 0.051 61 0.230 Table 4.
Model selection at 15% missing for 200 sample size, MCAR.
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V Complete data SAS macro SAS forward MI Mean N MSE Mean N MSE Mean N MSE Mean N MSE x1 1.161 100 0.250 3.586 99 8.270 0.916 10 0.147 0.795 100 0.191 x2 −0.880 100 0.252 −3.931 95 12.843 −0.882 6 0.204 −0.599 100 0.205 x3 −0.679 96 0.186 −3.412 65 9.724 . . . −0.446 98 0.149 x4 −0.130 8 0.474 −3.784 8 12.557 0.084 3 0.101 0.040 53 0.207 x5 −0.083 5 0.393 4.551 14 12.84 0.013 6 0.145 0.041 58 0.226 x6 0.118 22 0.428 6.864 9 13.589 −0.065 6 0.115 0.025 56 0.236 x7 0.229 10 0.337 −1.193 12 5.979 −0.067 4 0.092 −0.020 57 0.229 x8 0.446 9 0.057 0.864 15 6.120 −0.075 2 0.370 0.053 59 0.224 x9 0.187 8 0.406 −0.884 13 20.753 . . . 0.063 54 0.225 x10 0.095 14 0.403 0.387 10 2.697 0.025 21 0.196 0.047 57 0.217 x11 −0.041 7 0.407 1.571 20 8.790 −0.014 1 . −0.002 60 0.215 x12 0.018 9 0.474 −0.349 10 1.559 −0.069 8 0.111 0.000 60 0.188 x13 −0.085 13 0.443 0.512 16 2.378 0.013 6 0.240 0.054 61 0.221 x14 0.071 6 0.578 0.622 16 2.122 . . . −0.011 55 0.236 x15 −0.135 8 0.426 2.194 18 15.942 0.040 4 0.234 −0.033 58 0.236 x16 0.040 6 0.480 −2.824 18 11.498 . . . −0.028 60 0.195 x17 0.034 11 0.417 −2.208 13 7.217 −0.010 8 0.175 −0.031 53 0.205 x18 0.038 8 0.435 −0.337 9 1.457 0.115 3 0.113 −0.007 51 0.196 x19 −0.431 4 0.085 −1.937 11 11.302 . . . −0.040 56 0.199 x20 −0.029 7 0.482 −1.990 13 5.940 −0.014 22 0.160 −0.026 55 0.212 Table 5.
Model selection at 20% missing for 200 sample size, MCAR.
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V Complete data SAS macro SAS forward MI Mean N MSE Mean N MSE Mean N MSE Mean N MSE x1 1.122 100 0.226 1.090 100 0.307 1.171 92 0.349 1.051 100 0.234 x2 −0.884 98 0.223 −0.892 100 0.248 −0.967 82 0.322 −0.822 100 0.244 x3 −0.644 95 0.193 −0.733 91 0.226 −0.726 67 0.265 −0.583 100 0.210 x4 −0.029 13 0.448 0.147 7 0.482 0.186 11 0.468 0.024 65 0.271 x5 0.007 15 0.460 −0.057 13 0.468 −0.079 22 0.480 −0.001 60 0.297 x6 −0.132 12 0.386 0.156 11 0.487 −0.262 12 0.418 −0.028 60 0.268 x7 −0.209 11 0.383 0.110 12 0.551 0.015 13 0.481 −0.024 62 0.264 x8 0.114 15 0.415 0.034 14 0.561 0.095 17 0.488 0.026 59 0.295 x9 −0.001 12 0.415 0.072 8 0.495 −0.123 16 0.418 0.025 63 0.256 x10 −0.068 7 0.468 −0.091 11 0.475 −0.207 15 0.277 −0.049 54 0.259 x11 −0.186 6 0.403 −0.147 10 0.504 −0.054 8 0.422 −0.034 61 0.233 x12 −0.099 13 0.420 −0.056 16 0.555 −0.057 17 0.531 −0.035 64 0.254 x13 0.143 16 0.360 −0.198 7 0.464 0.002 16 0.369 0.012 65 0.249 x14 0.147 14 0.400 0.157 7 0.582 −0.081 15 0.534 0.048 70 0.259 x15 −0.080 12 0.465 0.187 14 0.483 −0.071 12 0.529 −0.006 58 0.274 x16 −0.177 11 0.435 −0.363 4 0.554 0.129 10 0.349 −0.050 51 0.254 x17 0.268 10 0.358 −0.211 17 0.466 0.014 15 0.416 0.053 51 0.256 x18 0.033 10 0.428 0.172 12 0.456 0.231 8 0.240 0.063 66 0.246 x19 0.242 9 0.386 0.160 10 0.514 0.049 11 0.472 0.018 62 0.265 x20 0.039 8 0.472 0.084 10 0.470 −0.132 10 0.333 0.031 56 0.246 Table 6.
Model selection at 5% missing for 200 sample size, MAR.
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V Complete data SAS macro Mean N MSE Mean N MSE x1 1.097 100 0.258 1.145 100 0.316 x2 −0.859 100 0.206 −0.949 100 0.271 x3 −0.656 95 0.205 −0.718 87 0.268 x4 0.009 9 0.486 0.098 19 0.535 x5 0.027 10 0.451 0.003 13 0.656 x6 0.106 9 0.463 0.185 12 0.432 x7 0.134 16 0.442 0.004 10 0.559 x8 0.001 16 0.409 0.012 5 0.481 x9 −0.171 8 0.463 −0.013 14 0.521 x10 0.057 11 0.419 0.200 15 0.410 x11 −0.147 11 0.448 0.000 15 0.562 x12 −0.154 10 0.419 0.049 10 0.583 x13 0.248 10 0.342 −0.042 18 0.558 x14 −0.032 12 0.409 0.197 16 0.559 x15 0.053 9 0.409 0.009 13 0.607 x16 −0.091 12 0.378 0.048 12 0.641 x17 0.193 12 0.402 0.140 13 0.552 x18 0.197 8 0.410 0.043 10 0.561 x19 0.416 7 0.371 −0.125 14 0.660 x20 −0.001 11 0.486 0.085 10 0.668 Table 7.
Model selection at 5% missing for 200 sample size, NMAR.
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Parameter Estimate Standard error Pr > ChiSq Intercept 9.130 0.476 < 0.0001 Male −0.561 0.107 < 0.0001 Age −0.066 0.006 < 0.0001 cigsPerDay −0.019 0.004 < 0.0001 totChol −0.002 0.001 0.043 sysBP −0.018 0.002 < 0.0001 Glucose −0.007 0.002 < 0.0001 Male: gender, male or female (Nominal); Age: Age of the patient (Continuous); cigsPerDay: the number of cigarettes that the person smoked on average in one day (continuous); totChol: total cholesterol level (Continuous); sysBP: systolic blood pressure (Continuous); Glucose: glucose level (Continuous). Table 8.
SAS forward selection results.
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Parameter Estimate Standard error Pr > ChiSq Intercept 9.125 0.463 < 0.0001 Age −0.066 0.006 < 0.0001 sysBP −0.017 0.002 < 0.0001 cigsPerDay −0.020 0.004 < 0.0001 Male −0.549 0.104 < 0.0001 Glucose −0.008 0.002 < 0.0001 PrevalentStroke −1.064 0.442 0.016 totChol −0.003 0.001 0.018 Age: Age of the patient (Continuous); sysBP: systolic blood pressure (Continuous); cigsPerDay: the number of cigarettes that the person smoked on average in one day (continuous); Male: gender, male or female (Nominal); Glucose: glucose level (Continuous); PrevalentStroke: whether or not the patient had previously had a stroke (Nominal); totChol: total cholesterol level (Continuous). Table 9.
SAS macro-based selection results.
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Tables
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