BINARY LOGISTIC REGRESSION MODELS IN MARKETING

Binary Logit Model or Logistic Regression model is used when the dependent variable is not continuous but instead has only two possible outcomes, 1 or 0. This model is typically used when predicting an event which has two possible outcomes, for e.g. ‘Pass vs. Fail’, ‘Alive vs. Dead’, ‘Buy vs. Rent’ etc.

Regular regression models cannot be used for such variables because the predicted value needs to be constrained between 0 and 1, which is not possible in regular regression. It also violates the assumption that the variable is normally (single peak) distributed, since a 1/0 variable by definition has a binomial distribution (double peak).

Logistic regression model solves this problem by determining the ‘odds’ of 1 or 0. For e.g. if the odds of 1 are higher than the odds of 0, then we would expect a 1 and not a 0. This is accomplished by estimating something called the Log Odds Ratio, which is just the log of the odds of 1 divided by the odds of 0. Since odds are a probability; you have a ratio of 2 positive numbers, which has a maximum value of +infinity. The log of a positive number can have a value between –infinity and + infinity, which removes the upper and lower bound on the dependent variable, which can now be estimated by a regular regression model.

Binary logit models in business are most popularly used in direct marketing, to identify who is most likely to respond to an offer (dependent variable is ‘Will Respond=1’ and ‘Will Not Respond=0’).

Binary Logistic Regression models for direct marketing can be evaluated using 'Lift Charts' (shown above) that compare the models ability to rank into deciles a target mail population by descending order of likelihood of responding positively to an offer. The model is compared to a base model that is expected to capture 10% of responders in each decile.