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 img indicating unobserved utility is assumed. Thus, img is usually defined such that

(3.1) equation

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

(3.2) equation

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

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