How to estimate a probit model?

The model's estimation process involves fitting the Probit model to the observed data, where the linear predictor is a function of explanatory variables. These variables, which could include factors like credit score, income, and debt-to-income ratio, are used to predict the likelihood of a mortgage denial.

One of the key advantages of Probit models is their ability to handle binary dependent variables in a probabilistic manner. Unlike simple linear regression, which may produce predictions outside the [0,1] interval, Probit models ensure that the predicted probabilities always lie within this range, making them more suitable for modeling binary outcomes.

Probit models, a popular tool in statistical analysis, can be efficiently estimated in the R programming language through the versatile glm() function within the stats package. This function provides a robust framework for fitting generalized linear models, enabling users to explore various relationships in data.

Additionally, Probit models offer interpretability advantages. The coefficients estimated by the model can be interpreted as the change in the standard normal deviate (z-score) associated with a unit change in the respective explanatory variable, holding all other variables constant. This interpretation allows researchers and practitioners to assess the impact of different factors on the probability of a mortgage denial.

When specifying a Probit model with glm(), the key lies in the family argument. This argument instructs glm() to employ a Probit link function, which is particularly suited for modeling binary outcomes such as the probability of a mortgage denial. By selecting the appropriate family, glm() transforms the linear predictor into a probability estimate, fitting seamlessly with the Probit model's requirements.