購買量與購買時程雙變量之預測－層級貝氏潛藏行為模型之建構

The Prediction of Purchase Quantity and Timing: A Latent HB Model

陳靜怡(Ching-I Chen)

指導教授 ： 任立中

國立臺灣大學/管理學院/國際企業學研究所/博士(2005年)

https://doi.org/10.6342/NTU.2005.00073

摘要

購買時程與購買量的預測具有非常重要的策略涵意。購買時程的預測有助於廠商決定行銷策略的執行時點，購買量的預測是零售商決定舖貨量以及製造商決定產能規劃的依據，二者亦是行銷人員評估行銷策略績效的重要指標。過去的相關研究多半是根據購買數量及購買時程本身的變化，分別建構兩個獨立的行為預測模型。本研究認為購買數量與購買時程之間具有環環相扣的相依關係，乃提出以存貨消耗模型為基礎之整合預測模型。
存貨消耗行為係一無法觀察的潛藏變量，故在文獻上經常以操作型定義的型式做為購買量或購買時程模型的外生解釋變數。然而，此一行為實則是消費者的內生行為，理應會受到存貨消耗當時情境之影響，故本研究認為存貨消耗量不宜被設定為外生變數。因此，本研究另以資料擴充(data augmentation)的觀念將可觀察的購買行為擴充至不可觀察的存貨消耗行為，並以存貨消耗率為參數建立存貨消耗模型，試圖透過層級貝氏模型的理論架構建立購買量和購買時程雙變量之整合預測模型。
為驗證層級貝氏模型的優越性，本研究以平均購買次數、平均存貨消耗率、存貨消耗量變異做為資料模擬的三個因子，交叉構成八個資料模擬情境，並藉此比較層級貝氏估計法與傳統最小平方估計法的參數回復程度與行為預測效度。結果顯示在參數回復程度與購買期間的樣本內預測效度上，層級貝氏估計法皆優於傳統最小平方估計法，這說明了本模型的健全性。本研究再以國內某油品領導品牌各地加油站之購買紀錄為分析對象驗證層級貝氏模型的效度；實證分析顯示購買時點層次的層級貝氏估計元之參數估計能力與行為預測能力最佳。最後，結論與建議彚整各章之研究發現，並說明研究限制與未來研究方向。

關鍵字

存貨消耗模型 ； 層級貝氏模型 ； 資料擴充

並列摘要

The prediction of purchase quantity and timing has very important strategic implications. Purchase quantity prediction can provide a criterion for retailers’ assortment strategy and manufacturers’ production planning; purchase timing prediction can help firms to decide the timing to put strategies in practice. The relationship between marketing strategies and purchase quantity and timing are also important indices to measure marketing performance. The two purchase behaviors were often viewed as independent but not interdependent response variables in previous related literature. This paper attempts to construct a prediction model of the two purchase behaviors based on the concept of the inventory consumption model. However, the inventory consumption behavior of customers is unobservable in nature, so this employed the concept of data augmentation to model this unobservable response variable. Besides, this paper adopted hierarchical Bayesian (HB) approach to combine three analysis levels of models to incorporate each kind of information from data, including the inventory consumption model of unit timing level, the purchase quantity and consumption rate model of purchase timing level, and the marketing effects model of individual customer level.
To examine the relative advantage of hierarchical Bayesian models, this paper formed an eight-scenario simulation analysis to compare the ability of parameter estimation recovery and behavior prediction validity of hierarchical Bayesian (HB) approach to traditional ordinary least square (OLS) approach. The comparison results showed that in each scenario the HB approach had dominant advantage over the traditional OLS approach and this result demonstrated the validity of HB approach. Moreover, we employed the purchase records of every gas station of a domestic leading petroleum brand to investigate the validity of HB approach, and the empirical result also showed that the HB estimators of purchase timing level had the best predictive ability.

並列關鍵字

Hierarchical Bayesian Model ； Data Augmentation ； Inventory Consumption Model

參考文獻

Ailawadi, Kusum L. and Scott A. Neslin (1998), “The Effect of Promotion on Consumption: Buying More and Consuming It Faster,” Journal of Marketing Research, Vol. 35, Augsut, 390-398.

Allenby, Greg M., Robert P. Leone, and Lichung Jen (1999), “A Dynamic Model of Purchase Timing With Application to Direct Marketing,” Journal of American Statistical Association, Vol. 94, No. 446, 365-374.

Banerjee, A. K. and G. K. Bhattacharyya (1976), “A Purchase Incidence Model with Inverse Gaussian Interpurchase Times,” Journal of the American Statistical Association, Vol. 71, No. 356, 823-829.

Bass, Frank M. (1969), “A New Product Growth For Model Consumer Durables,” Management Science, Vol. 15, No. 5, 215-227.

Bucklin, Randolph E. and James M. Lattin (1991), “A Two-State Model of Purchase Incidence and Brand Choice,” Marketing Science, Vol. 10, No. 1, 24-39.