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Hazard Model June 10, 2007

Posted by jyu in Qualifying.
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PHM =Proportional Hazard Model (Cox 1972)

Empirical studies in recent years have largely used the PHM to characterize purchase-timing behavior of households (Jain and vilcassim 1991, 1994; Helsen and Schmittlein 1993; Gonal and Srinivasan 1993 etc.)

The construct of interest is a household’s instaneous probability of making a purchase in a product category, conditional on the elasped time since the household’s previous purchase in the product category.

This conditional probability, also called the hazard function, is multiplicatively decomposed into two components: (1) baseline function: captures the household’s intrinsic temporal purchase pattern (2) Covariate function: captures the influence of marketing variables.

Two types: continuous time PHM vs. discrete time PHM.  Discrete time is preferrable than the continuous time PHM because it explicitly accounts for nonpurchases.  Also, a household undertakes shopping trips at discrete points of time, often weekly, which makes the household’s purchase timing in a particular product category conditional on the household’s discrete time interval of shopping.

Cause-specific competing risk harzard models distinguish between two types of purchase events based on whether or not hte shopping trip immediately preceding the purchase also involved a purchase.  One hazard for the case when the household made a purchase during its previous shopping trip and another for the case when the household did not.  In application, involving more than two possible competing states (e.g. switching between brands), such as the investigation of households’ brand switching over time, this framework can easily be extended to estimate more than two cause-specific hazards.

One way to flexibly accommodate the effects of unobserved heterogeneity in PHM is to allow the parameters of the model to follow a multivariate discrete distribution across households, whose locations and masses are estimated using the available data.

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