pacman::p_load(caTools, ggplot2, dplyr)
D = read.csv("data/quality.csv")  # Read in dataset
set.seed(88)
split = sample.split(D$PoorCare, SplitRatio = 0.75)  # split vector
TR = subset(D, split == TRUE)
TS = subset(D, split == FALSE)
glm1 = glm(PoorCare ~ OfficeVisits + Narcotics, TR, family=binomial)
summary(glm1)

【A】傳統準確性指標

Fig 13.1 - 混淆矩陣與模型準確性指標

Fig 13.1 - 混淆矩陣與模型準確性指標


Training Data

預測機率 Predicted Probability (Training)

par(cex=0.8)
pred = predict(glm1, type="response")
hist(pred)
abline(v=0.5, col='red')

混淆矩陣 Confusion Matrix (Training)

cmx = table(Acture=TR$PoorCare, Predict=pred > 0.5)
cmx
      Predict
Acture FALSE TRUE
     0    70    4
     1    15   10

模型準確性指標 Accuracy Matrices (Training)

A2x2 = function(x, k=3) c(
  accuracy = sum(diag(x))/sum(x),
  sensitivity = as.numeric(x[2,2]/rowSums(x)[2]),
  specificity = as.numeric(x[1,1]/rowSums(x)[1])
  ) %>% round(k)
A2x2(cmx)
   accuracy sensitivity specificity 
      0.808       0.400       0.946


Testing Data

預測機率 Predicted Probability (Testing)

par(cex=0.8)
pred2 = predict(glm1, newdata=TS, type="response")
hist(pred2, 10)
abline(v=0.5, col='red')

混淆矩陣 Confusion Matrix (Testing)

cmx2 = table(Acture=TS$PoorCare, Predict=pred2 > 0.5)
cmx2
      Predict
Acture FALSE TRUE
     0    23    1
     1     5    3

模型準確性指標 Accuracy Matrices (Testing)

sapply(list(Train=cmx, Test=cmx2), A2x2)
            Train  Test
accuracy    0.808 0.812
sensitivity 0.400 0.375
specificity 0.946 0.958


【B】預測機率分佈、臨界機率、混淆矩陣

Fig 13.2 - 預測機率分佈、臨界機率、混淆矩陣

Fig 13.2 - 預測機率分佈、臨界機率、混淆矩陣


預測機率分佈 (DPP) - Distribution of Predicted Probability (Training)

data.frame(y=factor(TR$PoorCare), pred=pred) %>% 
  ggplot(aes(x=pred, fill=y)) + 
  geom_histogram(bins=20, col='white', position="stack", alpha=0.5) +
  ggtitle("Distribution of Predicted Probability (DPP)") +
  xlab("predicted probability")



【C】作業曲線(ROC)與辨識率(AUC)

ROC - Receiver Operation Curve

par(mfrow=c(1,2), cex=0.8)
trAUC = colAUC(pred, y=TR$PoorCare, plotROC=T)
tsAUC = colAUC(pred2, y=TS$PoorCare, plotROC=T)

AUC - Area Under Curve

c(trAUC, tsAUC)
[1] 0.77459 0.79948

🗿 練習：
使用TR$MemberID以外的所有欄位，建立一個邏輯式回歸模型來預測PoorCare，並：
  【A】 分別畫出Training和Testing的DPP
  【B】 分別畫出Training和Testing的ROC
  【C】 分別算出Training和Testing的ACC、SENS和SPEC
  【D】 分別算出Training和Testing的AUC
  【E】 跟用兩個預測變數的模型相比，這一個模型有比較準嗎？
  【F】 為什麼它比較準(或比較不準)呢？