Regression Analysis
Module 4: Logistic and Poisson Regression
Outline of Lessons
1. Logistic Regression
2. Poisson Regression
3. Classification Methods and Measurements
4. Case Study1: Logistic Regression
5. Case Study 2
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Logistic and Poisson Regression: A Case Study Using the Framingham Heart Study, Cheat Sheet of Statistics
Churn Rate Regression Analysis
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2022/2023
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Regression Analysis
Module 4: Logistic and Poisson Regression
Outline of Lessons
1. Logistic Regression
2. Poisson Regression
3. Classification Methods and Measurements
4. Case Study1: Logistic Regression
5. Case Study 2
Nicoleta Serban
Gamze Tokol-Goldsman
Dave Goldsman
Regression Analysis
Module 4: Logistic and Poisson Regression
H. Milton Stewart School of Industrial and Systems Engineering
4.5 Case Study 2
Variables deep-dive
Variable Description Sex Male or female(Nominal) Age Age of the patient Current Smoker Whether or not the patient is a current smoker (Nominal) Cigs per day the number of cigarettes that the person smoked on average in one day BP Meds whether or not the patient was on blood pressure medication (Nominal) Prevalent Stroke whether or not the patient had previously had a stroke (Nominal) Diabetes whether or not the patient had diabetes (Nominal) Variable Description Tot Chol Total cholesterol level Sys BP Systolic blood pressure BMI Body Mass Index Heart Rate heart rate Glucose glucose level Prevalent Hyp whether or not the patient was hypertensive (Nominal) 10 - year CHD risk( Y Var ) 10 - year risk of coronary heart disease(CHD) (“1”, means “Yes”, “0” means “No”)
CHD vs Age
barplot(prop.table(age), axes=T, space=0.3, horiz=T, xlab="Proportion of No Heart Disease (blue) vs Heart Disease (Brown)", col=c("blue","brown"), main="Heart Disease by Age Group")
Younger adults are less likely to have
heart disease
Education Level vs CHD
barplot(prop.table(edu), axes=T, space=0.3, horiz=T, xlab="Proportion of No Heart Disease (blue) vs Heart Disease (Brown)", col=c("blue","brown"), main="Heart Disease by Education Level")
Those with 0-11 years of education (1) have the
highest rates of heart disease as compared to High
school diploma/GED (2), Some College, Vocational
School (3) and College degree or more (4)
Current Smoking vs CHD
barplot(prop.table(smoker), axes=T, space=0.3, horiz=T, xlab="Proportion of No Heart Disease (blue) vs Heart Disease (Brown)", col=c("blue","brown"), main="Heart Disease by Smoker")
Smokers have only slightly higher rates of
heart disease than non-smokers
- #GOF test using deviance residuals
- deviance_test <- c(deviance(lr),
- 1 - pchisq(deviance(lr),df.residual(lr)))
- # GOF test using Pearson residuals
- pearres <- residuals(lr, type = "pearson")
- pearson_tvalue <- sum(pearres^2)
- pearson_test <- c(pearson_tvalue,
- 1 - pchisq(pearson_tvalue, df.residual(lr)))
Logistic Regression: GOF
Deviance Test for GOF: Chi-squared statistic: 2549. P-value: 1 Pearson Test for GOF: Chi-squared statistic: 3357.441 P-value: 0.
As the p-value is large, we
accept the null hypothesis,
hence the logistic model is a
good fit the data.
Cross-Validation Set-up
R function for computing classification accuracy measures R function for outputting accuracy measures given a training model R function for computing classification accuracy measures
Naïve Bayes: Classification Accuracy
Cross Validation: K=5 folds model <- caret::train(TenYearCHD ~ ., data = data2, method = "naive_bayes", trControl = myControl, metric = "Accuracy") average_metrics <- colMeans(model$resample[, c("Accuracy.Accuracy", "Precision.Pos Pred Value", "Recall.Sensitivity", "F1.Pos Pred Value", "AUC")], na.rm = TRUE) print(average_metrics) Results Measure Accuracy 0. Sensitivity 0. Precision 0. F- Measure
AUC ROC 0.
Other ML Methods
Cross Validation: K=5 folds model <- caret::train(TenYearCHD ~ ., data = data2, method = “ ", trControl = myControl, metric = "Accuracy") average_metrics <- colMeans(model$resample[, c("Accuracy.Accuracy", "Precision.Pos Pred Value", "Recall.Sensitivity", "F1.Pos Pred Value", "AUC")], na.rm = TRUE) print(average_metrics) Classification Method:
- Random Forest Method=“rf”
- Gradient Bosting Method= “xgbTree”
- Support Vector Machine Method = “svmRadial”
- Decision Tree Method=“rpart”