3.2 Response Probability
The first issue in customer acquisition is to model the probability of prospects being acquired. Hansotia and Wang  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
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
For a logistic regression, has a logistic distribution, with mean 0 and variance equal to /. The ...