Beetle mortality and pesticide dose 13:52 Monday, February 19, 2007 1 Obs y n dose 1 15 50 1.08 2 24 49 1.16 3 26 50 1.21 4 24 50 1.26 5 29 50 1.31 6 29 49 1.35 Beetle mortality and pesticide dose 13:52 Monday, February 19, 2007 2 Fit a linear dose effect to the binomial data The GENMOD Procedure Model Information Data Set WORK.BEETLE Distribution Binomial Link Function Identity Response Variable (Events) y number killed in group Response Variable (Trials) n number in dose group Observations Used 6 Number Of Events 147 Number Of Trials 298 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 4 2.2044 0.5511 Scaled Deviance 4 2.2044 0.5511 Pearson Chi-Square 4 2.2004 0.5501 Scaled Pearson X2 4 2.2004 0.5501 Log Likelihood -201.9817 Algorithm converged. Analysis Of Parameter Estimates Standard Wald 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept 1 -0.6923 0.3854 -1.4476 0.0630 3.23 0.0724 dose 1 0.9648 0.3128 0.3516 1.5779 9.51 0.0020 Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. Observation Statistics number number killed in in dose insecticide Observation group group dose Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 15 50 1.08 0.349634 0.349634 0.0544829 205.45251 0.2428495 0.4564185 -2.481699 -0.736001 -0.744997 -1.22811 -1.21328 -1.218758 2 24 49 1.16 0.4268144 0.4268144 0.0356483 207.83851 0.3569451 0.4966838 3.0860922 0.8913406 0.8869944 1.0229737 1.0279862 1.02422 3 26 50 1.21 0.4750522 0.4750522 0.0290856 202.30228 0.4180455 0.532059 2.2473885 0.6364502 0.6359267 0.6972853 0.6978593 0.6973819 4 24 50 1.26 0.52329 0.52329 0.0301745 202.05507 0.464149 0.582431 -2.164501 -0.612879 -0.612437 -0.677952 -0.678441 -0.678042 Beetle mortality and pesticide dose 13:52 Monday, February 19, 2007 3 Fit a linear dose effect to the binomial data The GENMOD Procedure Observation Statistics number number killed in in dose insecticide Observation group group dose Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 5 29 50 1.31 0.5715278 0.5715278 0.0382673 203.16796 0.4965252 0.6465304 0.4236099 0.1210601 0.1211632 0.1449313 0.1448081 0.1448942 6 29 49 1.35 0.610118 0.610118 0.0475377 209.47795 0.5169458 0.7032902 -0.895784 -0.26238 -0.261676 -0.358267 -0.359232 -0.358717 Beetle mortality and pesticide dose 13:52 Monday, February 19, 2007 4 Logistic regression in GENMOD The GENMOD Procedure Model Information Data Set WORK.BEETLE Distribution Binomial Link Function Logit Response Variable (Events) y number killed in group Response Variable (Trials) n number in dose group Observations Used 6 Number Of Events 147 Number Of Trials 298 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 4 2.2786 0.5696 Scaled Deviance 4 2.2786 0.5696 Pearson Chi-Square 4 2.2718 0.5680 Scaled Pearson X2 4 2.2718 0.5680 Log Likelihood -202.0188 Algorithm converged. Analysis Of Parameter Estimates Standard Wald 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept 1 -4.8098 1.6210 -7.9870 -1.6327 8.80 0.0030 dose 1 3.8930 1.3151 1.3153 6.4706 8.76 0.0031 Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. Observation Statistics number number killed in in dose insecticide Observation group group dose Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 15 50 1.08 0.3531051 -0.605418 0.2289221 11.421094 0.2584391 0.4608953 -2.655255 -0.785692 -0.795774 -1.255918 -1.240006 -1.246418 2 24 49 1.16 0.4270296 -0.293981 0.148835 11.989091 0.3576239 0.4994326 3.0755493 0.8882384 0.8839345 1.0314497 1.0364718 1.0327858 3 26 50 1.21 0.4751873 -0.099332 0.1203575 12.469217 0.416969 0.534088 2.2406339 0.6345288 0.6340123 0.7004178 0.7009883 0.7005209 4 24 50 1.26 0.523811 0.0953161 0.1243706 12.471652 0.4629565 0.5839666 -2.19055 -0.620285 -0.619819 -0.689929 -0.690448 -0.690029 Beetle mortality and pesticide dose 13:52 Monday, February 19, 2007 5 Logistic regression in GENMOD The GENMOD Procedure Observation Statistics number number killed in in dose insecticide Observation group group dose Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 5 29 50 1.31 0.5719874 0.2899645 0.1584243 12.24089 0.4948648 0.6457639 0.4006282 0.1145078 0.1146004 0.1376861 0.1375748 0.1376519 6 29 49 1.35 0.6096124 0.4456832 0.1975576 11.661271 0.5146152 0.6969654 -0.871007 -0.255064 -0.2544 -0.344643 -0.345542 -0.345053 Beetle mortality and pesticide dose 13:52 Monday, February 19, 2007 6 Probit regression in GENMOD The GENMOD Procedure Model Information Data Set WORK.BEETLE Distribution Binomial Link Function Probit Response Variable (Events) y number killed in group Response Variable (Trials) n number in dose group Observations Used 6 Number Of Events 147 Number Of Trials 298 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 4 2.2631 0.5658 Scaled Deviance 4 2.2631 0.5658 Pearson Chi-Square 4 2.2569 0.5642 Scaled Pearson X2 4 2.2569 0.5642 Log Likelihood -202.0110 Algorithm converged. Analysis Of Parameter Estimates Standard Wald 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept 1 -3.0088 1.0054 -4.9793 -1.0383 8.96 0.0028 dose 1 2.4351 0.8158 0.8362 4.0340 8.91 0.0028 Scale 0 1.0000 0.0000 1.0000 1.0000 NOTE: The scale parameter was held fixed. Observation Statistics number number killed in in dose insecticide Observation group group dose Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 1 15 50 1.08 0.35239 -0.378876 0.1420256 29.774819 0.255513 0.4599695 -2.619502 -0.77547 -0.785326 -1.250155 -1.234466 -1.240681 2 24 49 1.16 0.4269801 -0.184068 0.0924577 31.059333 0.3574506 0.4988614 3.0779742 0.8889519 0.8846383 1.0298106 1.0348321 1.0311289 3 26 50 1.21 0.4751568 -0.062313 0.0748978 31.847022 0.4171813 0.5336642 2.2421576 0.6349622 0.6344442 0.6997861 0.7003575 0.6998879 4 24 50 1.26 0.5237 0.0594421 0.0774485 31.846772 0.4632083 0.5836494 -2.185001 -0.618707 -0.618246 -0.687367 -0.68788 -0.687465 Beetle mortality and pesticide dose 13:52 Monday, February 19, 2007 7 Probit regression in GENMOD The GENMOD Procedure Observation Statistics number number killed in in dose insecticide Observation group group dose Pred Xbeta Std HessWgt Lower Upper Resraw Reschi Resdev StResdev StReschi Reslik 5 29 50 1.31 0.5718936 0.1811971 0.0985606 31.421138 0.4952215 0.6459364 0.4053211 0.1158459 0.1159406 0.1391702 0.1390565 0.1391354 6 29 49 1.35 0.6097245 0.2786011 0.1228113 30.431521 0.5151144 0.6982266 -0.876502 -0.256686 -0.256013 -0.3476 -0.348513 -0.348018