Predicting Probability of Default (PD) using Logistic Regression/Trees Logistic Regression: Logistic regression is a statistical technique used to predic...
Logistic Regression:
Logistic regression is a statistical technique used to predict the probability of an event occurring. It creates a mathematical model that captures the relationship between independent and dependent variables.
Assumptions:
There are two types of features:
Independent features: These influence the probability of default.
Dependent feature: This is the outcome we're trying to predict, which is the probability of default.
The model learns the relationship between these features from data.
How it works:
We divide the data into training and testing sets.
We use the training data to build a logistic regression model.
The model predicts the probability of default for each observation in the test set.
We use the model to evaluate its performance on the test set.
Trees:
Tree-based models, such as Random Forests and Gradient Boosting Machines, are another widely used approach for predicting PD. These models recursively split the data based on various features, creating a tree-like structure.
Key Differences:
Logistic regression focuses on linear relationships, while trees can handle non-linear relationships.
Logistic regression relies on assumptions about feature distribution, while trees are less sensitive to these assumptions.
Trees can be more complex than logistic regression, but they can sometimes produce more accurate predictions.
Examples:
Imagine a model predicting the probability of a loan defaulting.
Independent features could be loan amount, credit score, and borrower's demographics.
The dependent feature would be the loan default status.
The model would learn the relationship between these variables and use them to predict the probability of default.
Conclusion:
Predicting PD is a complex financial task, but by utilizing appropriate statistical techniques, we can gain valuable insights into loan risk and make informed decisions