Probit and Logit Models

Logit Models	Probit Models
-         Based on Logistic Distribution. ·   In equation 5.2 if x (  tends to infinity  tends to 0, limiting the power bound to 1. ·     if x tends to negative infinity  tends to infinity limiting power bound of 0.	-         Based on Cumulative Standard Normal Distribution.

The difficulty with a Probability Model is that we do not know the “TRUE” probability values. We can only observe of the event happened (Y=1) or it did not happen (Y=0).

-      Logistic Distribution:   

-Odds Ratio-  expressing the effect of X on the likelihood of a categorical Y having a specific value through probability, the effect is not constant. Odds ratio represents the constant effect of a predictor X, on the likelihood that one outcome will occur.

 

-          Ln (odds ratio)-  limits the lower bound to 0 and upper bound to 1.

 

 

a-  Solving a Probability Model with Multiple Variables:

Suppose that  is the parameter of the logistic distribution where,

 

Transform the Probability Model into a linear model via log transformation using the Wins-Ratio-

Above equation can be solved by-

 1) “Grouped data,”

2) “Point estimation,”

3) “Maximum Likelihood Estimates”

Validation Logistic Regression Model-

-         Using Classification Matrix to look at the true negatives and false positives.

-         Concordance that helps identify the ability of the logistic model to differentiate between the event happening and not happening.

-         Lift helps assess the logistic model by comparing it with random selection