Statistical Methods in Customer Relationship Management

3.2 Response Probability

The first issue in customer acquisition is to model the probability of prospects being acquired. Hansotia and Wang [5] argued that prospects' response likelihood varies based on their profiles and the promotional materials they received. The authors adopted a logistic regression to model prospects' probability of response and used prospect profile variables as predictors. In logistic regression, because we can only observe whether the prospects respond or not, a latent response variable indicating unobserved utility is assumed. Thus, is usually defined such that

(3.1)

where the acquisition of customer i (1 = acquired, 0 = not acquired) and = a vector of covariates affecting the acquisition of customer i. The probability that the prospect responds is given by

(3.2)

For a logistic regression, has a logistic distribution, with mean 0 and variance equal to /. The ...