以多變量伽瑪分配模式探討多品項購買期間行為

Abstract

購買間隔時間 (Inter-Purchase time)在行銷領域中是非常重要的議題，公司經理人可以藉由購買間隔時間衡量消費者的流失率和活躍度。但是在現行的研究中，較少學者探討不同產品之間的購買間隔時間，也就是說，如果兩種產品的購買間隔時間有相關性，或許可以幫助我們做出更好的預測以及更瞭解使用者的行為。我們的研究中引入了關聯結構 (Copula)， 建構跨產品類別購買間隔時間的多變量模型，並提出了三種預測的架構以及四種模型。當預測一個感興趣的類別的下次購買時間的時候，我們可以隨著觀察到其他類別的購買紀錄，而去更新預測的結果；當沒有觀察到其他類別的購買行為或是剛買完該類別時，預測結果也回歸到單變量的預測結果。最後得出當顧客購買次數較少時、相關性越明顯時、購買間隔時間較長以及給定觀察到的類別的時間較短時，以關聯結構的條件機率的預測架構的結果會比傳統單類別的好，也會比加權的預測架構還要好。同時，模型中的相關係數矩陣也對消費者的購買行為有了更好的解釋。

Managers can measure customers' churn rate and activation by Inter-Purchase time for CRM. Current studies mostly focus on single category behavior. In our study, we introduce copula and construct a multivariate model of the Multi-Category Inter-Purchase Time, which may help us make better predictions or better understand customer behavior, providing three prediction architectures and four models. We can update the predictive value as we observe a purchasing record of other category. When not happening purchasing records of other categories or the customers just buy the category, the predictive result will return to single category model. Finally, our model performs better than single and weighted category architecture when number of purchase times is less, correlation coefficient is different from 0, purchase interval is longer, and interval of the given category is shorter. Moreover, our model provides better explanation of the customer purchasing behavior with correlation matrix.