以層級貝氏統計方法建構一般化迦瑪分配購買期間預測模型

Abstract

如何瞭解顧客的偏好結構，並準確預測顧客未來消費行為，一直是行銷人員孜孜不倦的方向。由於電腦設備的發展，龐大的資訊與強大的計算能力擴大了行銷人員瞭解消費者的能力。然而在消費者行為存在異質性的前提下，若繼續沿用傳統統計方法來描述消費者的行為，將往往面臨以下抉擇：以全體顧客資料推估總體平均行為，但忽略個別顧客之間的異質性；若僅依個別顧客資料推估個別顧客行為，則往往因資料量不足導致估計不具效率性的問題。 本研究在建立顧客購買期間的預測模型上，以一般化迦瑪分配為模型建立的基礎，搭配顧客行為異質性服從反一般化迦瑪分配的設定。如此，不但能夠增加模型的適用彈性，提高模型描述顧客行為的準確度，更能夠反映消費者行為的異質性與不穩定性。並且，搭配顧客人口統計變數，建立一個能夠預測新進顧客消費行為的層級貝氏模型。最後，本研究以貝氏統計方法推估模型中的個人化參數，由於貝氏統計方法結合了先驗訊息與樣本訊息，因此所得的後驗估計具有自動調節的機制，可以處理資料量不足顧客之參數不具效率性的問題，避免上述異質性與估計效率性之間的抉擇窘境。 本研究為了驗證此層級貝氏模型的預測能力，將以國內某油品領導廠商的實際資料帶入模型，用以比較不同參數估計方法間的優劣。並且在最後，將列出本研究的發現、研究進行時所遭遇的限制，以及未來的研究方向。

Marketing researchers are always striving for how to identify the customers’ preference structure, and how to predict the customers’ purchase behavior precisely. Due to technology development, the enormous amount of information storage and the ability of data computation enable the researchers to further comprehend the purchases and preferences of consumers more directly. However, on the premise that heterogeneity is existed, if we still continuously use the traditional statistics methods to characterize the consumers’ behavior, then we always face a trade-off: while estimating the behavior of consumers, if based on the information of whole customers, then we may ignore the heterogeneity between them; or if solely based on identical customer, then the estimation may lack efficiency because of insufficient data amount. We construct a prediction model of customer inter-purchase times based on the generalized gamma distribution, which can make the model fit the data more flexible than the other distributions. We also assume the heterogeneity of customer behavior follow the inverse generalized gamma distribution, so that the difference and the instability of consumer behavior between each customer can be reflected clearly. Additionally, our model is formulated with a hierarchical Bayesian framework with demographic variables, which can predict the behavior of new customers without gathering any purchasing information. At last, we estimate the parameters of the model by Bayesian statistics. Because of the integration of prior and sample information, Bayesian statistics can provide individualized estimation of parameters for each customer and also ensure both the heterogeneity of customers and efficiency of parameter estimating at the same time. In order to verify the prediction capability of this hierarchical Bayesian model, the purchase records of a domestic leading petroleum company will be employed in the model and also list the pros and cons with different parameters estimated. Finally, we draw a conclusion, indicate the limitation of this investigation, and suggest the direction to be studied on possible future work.