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Predictions in Binary Choice Predict y = 1 if P P* Success depends on the assumed P* 精品文档 ROC Curve Plot %Y=1 correctly predicted vs. %y=1 incorrectly predicted 450 is no fit. Curvature implies fit. Area under the curve compares models 精品文档 精品文档 Aggregate Predictions Frequencies of actual predicted outcomes Predicted outcome has maximum probability. Threshold value for predicting Y=1 = .5000 Predicted ------ ---------- + ----- Actual 0 1 | Total ------ ---------- + ----- 0 151 1 | 152 1 20 38 | 58 ------ ---------- + ----- Total 171 39 | 210 精品文档 Analyzing Predictions Frequencies of actual predicted outcomes Predicted outcome has maximum probability. Threshold value for predicting Y=1 is P* .5000. (This table can be computed with any P*.) Predicted ------ -------------------- + ----- Actual 0 1 | Total ------ ----------------------+------- 0 N(a0,p0) N(a0,p1) | N(a0) 1 N(a1,p0) N(a1,p1) | N(a1) ------ ----------------------+ ----- Total N(p0) N(p1) | N 精品文档 Analyzing Predictions - Success Sensitivity = % actual 1s correctly predicted = 100N(a1,p1)/N(a1) % [100(38/58)=65.5%] Specificity = % actual 0s correctly predicted = 100N(a0,p0)/N(a0) % [100(151/152)=99.3%] Positive predictive value = % predicted 1s that were actual 1s = 100N(a1,p1)/N(p1) % [100(38/39)=97.4%] Negative predictive value = % predicted 0s that were actual 0s = 100N(a0,p0)/N(p0) % [100(151/171)=88.3%] Correct prediction = %actual 1s and 0s correctly predicted = 100[N(a1,p1)+N(a0,p0)]/N [100(151+38)/210=90.0%] 精品文档 Analyzing Predictions - Failures False positive for true negative = %actual 0s predicted as 1s = 100N(a0,p1)/N(a0) % [100(1/152)=0.668%] False negative for true positive = %actual 1s predicted as 0s = 100N(a1,p0)/N(a1) % [100(20/258)=34.5%] False positive for predicted positive = % predicted 1s
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