Logit Models

A Logit model is a technical term for a model that predicts the probability of a specific event. A purchase or a customer defection are two such events that can be modeled with a Logit model. In the context of retention or add-on selling we will think of the event as a purchase.

A Logit model allows a firm to pinpoint variables that affect the probability of purchase. It is very similar to a regression model, except that the dependent variable is:

	logit(p) =
	where: p = the probability of the event

Mathematically, the Logit equation looks like this:

	logit(p) = a + bx1 + bx2+ ....+ bxn
	where: the x's are distinct independent variable and the b's are coefficients or weights. The intercept coefficient, a, captures the probability of purchase in the absences of other variables.

A Logit model cannot use a regression program to estimate its parameters. More sophisticated estimation programs are required. These can be found in software packages such as SPSS and SAS.

Logit Model Examples
A large financial institution developed a model to determine which of its checking account customers would be good targets for its financial planning service.  The factors it thought would be good predictors were checking account balance, savings account balance, the ownership of the bank credit card (1= own a card, 0 otherwise), and home ownership (1=own a home, 0 otherwise).  Using these factors as independent variables it developed a Logit model:

	Logit (pi) = a + b1 (checking balancei) + b2 (savings balancei,) + b3 (credit card customeri,) + b4 (home ownershipi)
	where: the subscript i refers to an individual.

To estimate this model, the firm sampled its current customers some of whom use financial planning and others who do not.  They gathered the relevant data on this sample and estimated the model in a statistical software package.  As with the regression scoring model, the output from the estimation was a set of coefficients that were used to predict the likelihood that other customers who were not in the sample and who did not did use the service would respond favorably to an offer for the service.  The firm then used these predictions to identify customers who would be targeted for a financial planning service promotion.

Advantages and Disadvantages of a Logit Model
This example describes a basic application of a Logit model.  However Logit models can become significantly more complex.  One area that analysis tend to expand upon is allowing for a differential response from different consumers.  In the model this equates to having a different coefficient for each individual or group of individuals.  This can allow firms to begin to tailor their marketing mix elements at the individual or small group level. 

Individually tailored marketing mix models have two primary disadvantages. First of all, they are very difficult to develop and to estimate. Complex computer programs are required to optimize their mathematical functions. This adds significant complexity to the process.  Also, because of the complexity and the sample sizes required per customer, model estimates may not be very accurate. This leads to the problem of product offerings, market communications, pricing and promotions that do not reflect customers’ underlying preferences. Unless the methods provide accurate estimates, using them can be more detrimental than simply offering every customer the same marketing mix. The same methods applied at the segment level can address this problem and provide significantly better estimates, as long as one can accurately segment the customer base.