Statistical Methods in Customer Relationship Management

Appendix E

Type-1 Tobit Model

(Source: Franses and Paap [1])

For a type-1 Tobit model, the censored variable is 0 if the unobserved latent variable is less than or equal to 0 and if is positive,

(E.1)

(E.2)

with . For observations that are 0, we know only that

(E.3)

Maximum likelihood estimation is used to estimate the Tobit model. The likelihood function consists of two parts: the probability that an observation is censored is given by Equation E.3; and the density of the non-censored observations is a standard normal density. The likelihood function is

(E.4)

where . It is more convenient ...