| Dunn, Reader and Wrigley (1983) first observed in their UK diary data that, when the frequencies of inter-purchase times are plotted, the histograms are dominated by intervals of seven days and multiples of a week. This phenomenon has been corroborated by many authors. For example, Kahn and Schmittlein (1989) found this phenomenon in cracker data. They indicated that this peculiar seven-day spike regularity may be a simple byproduct of consumers' regular shopping trip schedules. Specifically, inferring from a histogram of household inter-shopping times, they found that a substantial portion of households evidently make major grocery shopping trips weekly. Similar evidence has been found in many surveys. For example, when respondents were asked in one study to give the reason for entering grocery stores, 83% answered "weekly grocery shopping" (Chain Drug Review, 1993). Hence, if most purchases are made at seven-day interval or multiples thereof; we would expect that when the frequencies of inter-purchase times are plotted for all consumers, the weekly spike phenomenon would be the dominating feature of the histogram.; But this weekly shopping inter-purchase time leads to an interesting question: Are promotions effective in changing consumers' purchase timing? In other words, can a typical consumer be persuaded to make unplanned trips just for promoted products? Or can a consumer be persuaded to shift to a shorter purchase interval and "buy early"?; In this thesis, we utilize different method to answer this question. Attention will be focused on the relative risk or the Cox regression model approach and Markov approach.; It may be true that, in the marketing research, each customer has specific effect which is not yet described by covariates included in the model. This is the so-called heterogeneity phenomena and usually modeled by using random effects (Stiratelli et al, 1984). In such context, it is of primary interest to test whether heterogeneity exists across the population. In this thesis, we also propose a score-test type statistics for homogeneity testing problem in market data. We will illustrate the methods in both parametric and semiparametirc models. |
