Advanced Business Analytics by Saumitra N. Bhaduri & David Fogarty

Author:Saumitra N. Bhaduri & David Fogarty
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

Applying this to the marketing campaign example, we get

Here, the dependent variable S is the observed selection for direct mailing, which can take the values of 0 or 1. The second dependent variable R is the observed response for selected customer with possible values of 0 or 1. μ and ν are the error terms which follow a standard bivariate normal distribution with correlation ρ. Here, we need to note that the dependent variable R is observed only when the other dependent variable S has a value of 1, suggesting a partial observability with the selection bias. A statistically significant estimated value of ρ will indicate the presence of selection bias.

The parameters β 1, β 2, and ρ are estimated using the maximum likelihood method. Based on the MLE estimates, the probabilities P 11, P 10, P 01, and P 00 are calculated, where P 11 is the probability of response and selection, P 10 is the probability of response and non-selection, P 01 is the probability of selection and non-response, and P 00 is the probability of non-selection and non-response. The probabilities P 11, P 10, P 01, and P 00 are calculated as follows:

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