Modeling the Switching Matrix
Thus, the modeling of CLV requires modeling of the switch- ing matrix for each individual customer. Using individual- level data from a cross-sectional sample of customers, com- bined with purchase (or purchase intention) data, we model each customer’s switching matrix and estimate model para- meters that enable the modeling of CLV at the individual customer level.
The utility model. In addition to the individual-specific customer-equity driver ratings, we also include the effect of brand inertia, which has been shown to be a useful predic- tive factor in multinomial logit choice models (Guadagni and Little 1983). The utility formulation can be conceptual- ized as
(1) Utility = inertia + impact of drivers.
To make this more explicit, Uijk is the utility of brand k to individual i, who most recently purchased brand j. The dummy variable LASTijk is equal to one if j = k and is equal to zero otherwise; X is a row vector of drivers. We then model