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A Factorial Hidden Markov Model for the Analysis of Temporal Change in Choice Models

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Abstract

Consumers’ preferences for various product attributes change over time. Modeling such temporal changes through a single process assumes that all the attributes’ preferences change together with the same dynamics; however, this assumption is not appropriate when there are several processes with distinct characteristics. We propose a new non-homogeneous factorial hidden Markov model (FHMM) for choice models to dynamically segment consumers into distinct states while each preference parameter may follow a distinct Markov process. The transition probabilities are modeled as time-varying at the individual level, affected by covariates of a feedback term of the consumer’s previous purchase decision, specific to each Markov process. We motivate the proposed approach by an application to a scanner panel choice dataset and find two processes with entirely different characteristics governing the shifts in two preference attributes. Model fit and prediction power based on Brier scores show the superiority of the proposed non-homogeneous FHMM in capturing temporal changes in preferences compared to a traditional hidden Markov model as well as a benchmark comparison model.

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Notes

  1. In-store display indicates whether or not a particular brand was advertised in the store on the purchase date, while feature advertising indicates whether or not the brand was advertised in the local media (e.g., newspapers) on the date of purchase.

  2. In the empirical application discussed in Section 5, we used 20 random starting values and examined the numerically differentiated Hessian matrix to confirm picking the solution.

References

  1. Allaway AW, D’Souza G, Berkowitz D, Kim K(K) (2014) Dynamic segmentation of loyalty program behavior. J Mark Anal 2(1):18–32. https://doi.org/10.1057/jma.2014.2

    Article  Google Scholar 

  2. Bartolucci F, Solis-Trapala IL (2010) Multidimensional latent Markov models in a developmental study of inhibitory control and attentional flexibility in early childhood. Psychometrika 75(4):725–743. https://doi.org/10.1007/s11336-010-9177-1

    Article  Google Scholar 

  3. Bartolucci F, Farcomeni A, Pennoni F (2012) Latent Markov models for longitudinal data. CRC Press, Boca Raton

    Book  Google Scholar 

  4. Bartolucci F, Farcomeni A, Pennoni F (2014) Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates. TEST 23(3):433–465. https://doi.org/10.1007/s11749-014-0381-7

    Article  Google Scholar 

  5. Bridges E, Briesch RA, Yim CKB (2006) Effects of prior brand usage and promotion on consumer promotional response. J Retail 82(4):295–307. https://doi.org/10.1016/j.jretai.2006.08.003

    Article  Google Scholar 

  6. DeSarbo WS, Wang Q, Blanchard SJ (2010) Exploring intra-industry competitive heterogeneity. J Model Manag 5(2):94–123. https://doi.org/10.1108/17465661011060970

    Article  Google Scholar 

  7. Du RY, Kamakura WA (2006) Household life cycles and lifestyles in the United States. J Mark Res 43(1):121–132. https://doi.org/10.1509/jmkr.43.1.121

    Article  Google Scholar 

  8. Ebbes P, Grewal R, DeSarbo WS (2010) Modeling strategic group dynamics: a hidden Markov approach. Quant Mark Econ 8(2):241–274. https://doi.org/10.1007/s11129-010-9081-0

    Article  Google Scholar 

  9. Ebbes P, Liechty JC, Grewal R (2015) Attribute-level heterogeneity. Manag Sci 61(4):885–897. https://doi.org/10.1287/mnsc.2014.1898

    Article  Google Scholar 

  10. Fiebig DG, Keane MP, Louviere J, Wasi N (2010) The generalized multinomial logit model: accounting for scale and coefficient heterogeneity. Mark Sci 29(3):393–421. https://doi.org/10.1287/mksc.1090.0508

    Article  Google Scholar 

  11. Fong DK, Kim S, Chen Z, DeSarbo WS (2016) A Bayesian multinomial probit model for the analysis of panel choice data. Psychometrika 81(1):161–183. https://doi.org/10.1007/s11336-014-9437-6

    Article  Google Scholar 

  12. Gedenk K, Neslin SA (1999) The role of retail promotion in determining future brand loyalty: its effect on purchase event feedback. J Retail 75(4):433–459. https://doi.org/10.1016/S0022-4359(99)00018-4

    Article  Google Scholar 

  13. Ghahramani Z (2001) An introduction to hidden Markov models and Bayesian networks. Int J Pattern Recognit Artif Intell 15(01):9–42. https://doi.org/10.1142/S0218001401000836

    Article  Google Scholar 

  14. Ghahramani Z, Jordan MI (1997) Factorial hidden Markov models. Mach Learn 29(2–3):245–273. https://doi.org/10.1023/A:1007425814087

    Article  Google Scholar 

  15. Greene WH (2003) Econometric analysis (5th ed.). Prentice Hall, Upper Saddle River

  16. Guadagni PM, Little JD (1983) A logit model of brand choice calibrated on scanner data. Mark Sci 2(3):203–238. https://doi.org/10.1287/mksc.2.3.203

    Article  Google Scholar 

  17. Humphreys K, Titterington DM (2003) Variational approximations for categorical causal modeling with latent variables. Psychometrika 68(3):391–412. https://doi.org/10.1007/BF02294734

    Article  Google Scholar 

  18. Kulic D, Takano W, Nakamura Y (2007) Representability of human motions by factorial hidden Markov models. IEEE/RSJ International Conference on Intelligent Robots and Systems, San Diego, CA, 2007, pp. 2388-2393. https://doi.org/10.1109/IROS.2007.4399325

  19. Kurve A, Kotobi K, Kesidis G (2013) An agent-based framework for performance modeling of an optimistic parallel discrete event simulator. Complex Adapt Syst Model 1(1):12. https://doi.org/10.1186/2194-3206-1-12

    Article  Google Scholar 

  20. Lee YH, von Davier AA (2013) Monitoring scale scores over time via quality control charts, model-based approaches, and time series techniques. Psychometrika 78(3):557–575. https://doi.org/10.1007/s11336-013-9317-5

    Article  Google Scholar 

  21. Lehrach WP, Husmeier D (2009) Segmenting bacterial and viral DNA sequence alignments with a trans-dimensional phylogenetic factorial hidden Markov model. J R Stat Soc: Ser C: Appl Stat 58(3):307–327. https://doi.org/10.1111/j.1467-9876.2008.00648.x

    Article  Google Scholar 

  22. Lemmens A, Croux C, Stremersch S (2012) Dynamics in the international market segmentation of new product growth. Int J Res Mark 29(1):81–92. https://doi.org/10.1016/j.ijresmar.2011.06.003

    Article  Google Scholar 

  23. Liechty J, Pieters R, Wedel M (2003) Global and local covert visual attention: evidence from a Bayesian hidden Markov model. Psychometrika 68(4):519–541. https://doi.org/10.1007/BF02295608

    Article  Google Scholar 

  24. Mark T, Lemon KN, Vandenbosch M (2014) Customer migration patterns: evidence from a North American retailer. J Mark Theory Pract 22(3):251–270. https://doi.org/10.2753/MTP1069-6679220302

    Article  Google Scholar 

  25. Maruotti A, Rocci R (2012) A mixed non-homogeneous hidden Markov model for categorical data, with application to alcohol consumption. Stat Med 31(9):871–886. https://doi.org/10.1002/sim.4478

    Article  Google Scholar 

  26. Meligkotsidou L, Dellaportas P (2011) Forecasting with non-homogeneous hidden Markov models. Stat Comput 21(3):439–449. https://doi.org/10.1007/s11222-010-9180-5

    Article  Google Scholar 

  27. Montgomery AL, Li S, Srinivasan K, Liechty JC (2004) Modeling online browsing and path analysis using clickstream data. Mark Sci 23(4):579–595. https://doi.org/10.1287/mksc.1040.0073

    Article  Google Scholar 

  28. Montoya R, Netzer O, Jedidi K (2010) Dynamic allocation of pharmaceutical detailing and sampling for long-term profitability. Mark Sci 29(5):909–924. https://doi.org/10.1287/mksc.1100.0570

    Article  Google Scholar 

  29. Moon S, Kamakura WA, Ledolter J (2007) Estimating promotion response when competitive promotions are unobservable. J Mark Res 44(3):503–515. https://doi.org/10.1509/jmkr.44.3.503

    Article  Google Scholar 

  30. Netzer O, Lattin JM, Srinivasan V (2008) A hidden Markov model of customer relationship dynamics. Mark Sci 27(2):185–204. https://doi.org/10.1287/mksc.1070.0294

    Article  Google Scholar 

  31. Ozerov A, Févotte C, Charbit M (2009) Factorial scaled hidden Markov model for polyphonic audio representation and source separation. IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA’09), Oct 2009, Mohonk, NY, United States. https://doi.org/10.1109/ASPAA.2009.5346527

  32. Park S, Gupta S (2011) A regime-switching model of cyclical category buying. Mark Sci 30(3):469–480. https://doi.org/10.1287/mksc.1110.0643

    Article  Google Scholar 

  33. R Core Team (2017) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/

  34. Ross SM (2014) Introduction to probability models (11th ed). Academic Press, New York

    Google Scholar 

  35. Rossi P, McCulloch R, Allenby G (1996) The value of purchase history data in target marketing. Mark Sci 4(15):321–340. https://doi.org/10.1287/mksc.15.4.321

    Article  Google Scholar 

  36. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464. https://doi.org/10.1214/aos/1176344136

    Article  Google Scholar 

  37. Shi SW, Zhang J (2014) Usage experience with decision aids and evolution of online purchase behavior. Mark Sci 33(6):871–882. https://doi.org/10.1287/mksc.2014.0872

    Article  Google Scholar 

  38. Van Heerde HJ, Neslin SA (2008) Sales promotion models. In: Wierenga B (ed) Handbook of marketing decision models. Springer, Boston, pp. 107–162. https://doi.org/10.1007/978-0-387-78213-3_5

    Google Scholar 

  39. Vogler C, Metaxas D (2001) A framework for recognizing the simultaneous aspects of American sign language. Comput Vis Image Underst 81(3):358–384. https://doi.org/10.1006/cviu.2000.0895

    Article  Google Scholar 

  40. Wedel M, Kamakura WA (1999) Market segmentation: conceptual and methodological foundations. Kluwer Academic Press, New York

    Google Scholar 

  41. Welch LR (2003) Hidden Markov models and the Baum-Welch algorithm. IEEE Inf Theory Soc Newsl 53(4):10–13

    Google Scholar 

  42. Wohlmayr M, Stark M, Pernkopf F (2011) A probabilistic interaction model for multipitch tracking with factorial hidden Markov models. IEEE Trans Audio Speech Lang Process 19(4):799–810. https://doi.org/10.1109/TASL.2010.2064309

    Article  Google Scholar 

  43. Zhang J, Wedel M (2009) The effectiveness of customized promotions in online and offline stores. J Mark Res 46(2):190–206. https://doi.org/10.1509/jmkr.46.2.190

    Article  Google Scholar 

  44. Zhang JZ, Netzer O, Ansari A (2014) Dynamic targeted pricing in B2B relationships. Mark Sci 33(3):317–337. https://doi.org/10.1287/mksc.2013.0842

    Article  Google Scholar 

  45. Zhang JZ, Watson GF IV, Palmatier RW, Dant RP (2016) Dynamic relationship marketing. J Mark 80(5):53–75. https://doi.org/10.1509/jm.15.0066

    Article  Google Scholar 

  46. Zucchini W, MacDonald IL, Langrock R (2017) Hidden Markov models for time series: an introduction using R. CRC Press, Boca Raton

    Google Scholar 

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Authors and Affiliations

  1. Marketing Department, Smeal College of Business, Pennsylvania State University, University Park, PA, 16802, USA

    Amirali Kani, Wayne S. DeSarbo & Duncan K. H. Fong

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  1. Amirali Kani
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  2. Wayne S. DeSarbo
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  3. Duncan K. H. Fong
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Correspondence to Amirali Kani.

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Kani, A., DeSarbo, W.S. & Fong, D.K.H. A Factorial Hidden Markov Model for the Analysis of Temporal Change in Choice Models. Cust. Need. and Solut. 5, 162–177 (2018). https://doi.org/10.1007/s40547-018-0088-0

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