Which modeling approach uses the logistic distribution to relate input factors to default probability?

• A. Linear Probability Model
• B. Logit Model
• C. Probit Model
• D. Neural Network

Answer: (B)

The main idea is to map a linear combination of input factors into a probability using the logistic link. In the logit model, you form z as a linear predictor from the inputs (z = β0 + β1x1 + ...), then convert z into a probability with the logistic function p = 1 / (1 + exp(-z)). This means the log-odds, log(p/(1-p)), change linearly with the inputs, which makes it easy to interpret how each factor affects the odds of default.

This approach is ideal for default probability because it keeps predicted probabilities between 0 and 1, and it ties the relationship to a well-understood distribution—the logistic distribution—through the logistic CDF. Compared to the linear probability model, it avoids predictions outside the [0,1] range. Compared to the probit model, it uses a logistic rather than a normal distribution for the link, and compared to a neural network, it provides a simple, interpretable parametric form tied to odds ratios.