Abstract
In this chapter, we present the attribute-level best-worst modeling. Structural properties are reviewed and extensions to the functional form under linear and nonlinear process are described. The time dependence is introduced via Markov decision process (MDP) along with transition probabilities of choice evolutions, under maximum utility function. Simulated and aggregated data are used to validate the functional form and the MDP scopes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arcidiacono, P., Ellickson, P.B.: Practical methods for estimation of dynamic discrete choice models. Annu. Rev. Econ. 3(1), 363–394 (2011)
Bellman, R.: The theory of dynamic programming. Bull. Am. Math. Soc. 60(6), 503–515 (1954)
Chadès, I., Chapron, G., Cros, M.-J., Garcia, F., Sabbadin, R.: Mdptoolbox: a multi-platform toolbox to solve stochastic dynamic programming problems. Ecography 37(9), 916–920 (2014)
Coast, J., Salisbury, C., De Berker, D., Noble, A., Horrocks, S., Peters, T., Flynn, T.: Preferences for aspects of a dermatology consultation. Br. J. Dermatol. 155(2), 387–392 (2006)
Finn, A., Louviere, J.J.: Determining the appropriate response to evidence of public concern: the case of food safety. J. Public Policy Mark. 11(2), 12–25 (1992)
Flynn, T.N., Louviere, J.J., Peters, T.J., Coast, J.: Best–worst scaling: what it can do for health care research and how to do it. J. Health Econ. 26(1), 171–189 (2007)
Flynn, T.N., Louviere, J.J., Marley, A.A., Coast, J., Peters, T.J.: Rescaling quality of life values from discrete choice experiments for use as QALYs: a cautionary tale. Popul. Health Metr. 6(1), 6 (2008)
Grasshoff, U., Grossmann, H., Holling, H., Schwabe, R.: Optimal paired comparison designs for first-order interactions. Statistics 37(5), 373–386 (2003)
Grasshoff, U., Grossmann, H., Holling, H., Schwabe, R.: Optimal designs for main effects in linear paired comparison models. J. Stat. Plan. Inference 126(1), 361–376 (2004)
Grasshoff, U., Grossmann, H., Holling, H., Schwabe, R.: Optimal design for discrete choice experiments. J. Stat. Plan. Inference 143(1), 167–175 (2013)
Grossmann, H., Grasshoff, U., Schwabe, R.: Approximate and exact optimal designs for paired comparisons of partial profiles when there are two groups of factors. J. Stat. Plan. Inference 139(3), 1171–1179 (2009)
Hole, A.R.: A discrete choice model with endogenous attribute attendance. Econ. Lett. 110(3), 203–205 (2011)
Knox, S.A., Viney, R.C., Street, D.J., Haas, M.R., Fiebig, D.G., Weisberg, E., Bateson, D.: What’s good and bad about contraceptive products? Pharmacoeconomics 30(12), 1187–1202 (2012)
Knox, S.A., Viney, R.C., Gu, Y., Hole, A.R., Fiebig, D.G., Street, D.J., Haas, M.R., Weisberg, E., Bateson, D.: The effect of adverse information and positive promotion on women’s preferences for prescribed contraceptive products. Soc. Sci. Med. 83, 70–80 (2013)
Lancsar, E., Louviere, J., Donaldson, C., Currie, G., Burgess, L.: Best worst discrete choice experiments in health: methods and an application. Soc. Sci. Med. 76, 74–82 (2013)
Lee, T.C., Judge, G., Zellner, A.: Maximum likelihood and Bayesian estimation of transition probabilities. J. Am. Stat. Assoc. 63(324), 1162–1179 (1968)
Louviere, J., Timmermans, H.: Stated preference and choice models applied to recreation research: a review. Leis. Sci. 12(1), 9–32 (1990)
Louviere, J.J., Woodworth, G.: Design and analysis of simulated consumer choice or allocation experiments: an approach based on aggregate data. J. Mark. Res. 20(4), 350–367 (1983)
Louviere, J.J., Woodworth, G.G.: Best-worst scaling: a model for the largest difference judgments. Working Paper. University of Alberta (1991)
Louviere, J.J., Hensher, D.A., Swait, J.D.: Stated Choice Methods: Analysis and Applications. Cambridge University Press, Cambridge (2000)
Louviere, J., Lings, I., Islam, T., Gudergan, S., Flynn, T.: An introduction to the application of (case 1) best–worst scaling in marketing research. Int. J. Res. Mark. 30(3), 292–303 (2013)
Louviere, J.J., Flynn, T.N., Marley, A.A.J.: Best-Worst Scaling: Theory, Methods and Applications. Cambridge University Press, Cambridge (2015)
Luce, R.D.: On the possible psychophysical laws. Psychol. Rev. 66(2), 81 (1959)
Marley, A.A., Louviere, J.J.: Some probabilistic models of best, worst, and best–worst choices. J. Math. Psychol. 49(6), 464–480 (2005)
Marley, A., Pihlens, D.: Models of best–worst choice and ranking among multiattribute options (profiles). J. Math. Psychol. 56(1), 24–34 (2012)
Marley, A., Flynn, T.N., Louviere, J.: Probabilistic models of set-dependent and attribute-level best–worst choice. J. Math. Psychol. 52(5), 281–296 (2008)
Marschak, J.: Binary choice constraints on random utility indicators. Technical Report 74 (1960)
McFadden, D.: Conditional logit analysis of qualitative choice behavior. In: Zarembka, P. (ed.) Frontiers in Econometrics, pp. 105–142. Academic Press, New York (1974)
McFadden, D.: Modeling the choice of residential location. Transp. Res. Rec. 673, 72–77 (1978)
Parvin, S., Wang, P., Uddin, J.: Using best-worst scaling method to examine consumers’ value preferences: a multidimensional perspective. Cogent Bus. Manag. 3(1), 1199110 (2016)
Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, New York (2014)
Rust, J.: Structural estimation of Markov decision processes. Handb. Econ. 4, 3081–3143 (1994)
Rust, J.: Dynamic programming. In: Durlauf, S.N., Blume, L.E. (eds.) The New Palgrave Dictionary of Economics. Palgrave Macmillan, Ltd, London (2008)
Stenberg, F., Manca, R., Silvestrov, D.: An algorithmic approach to discrete time non-homogeneous backward semi-Markov reward processes with an application to disability insurance. Methodol. Comput. Appl. Probab. 9(4), 497–519 (2007)
Street, D.J., Burgess, L.: The Construction of Optimal Stated Choice Experiments: Theory and Methods, vol. 647. Wiley, New York (2007)
Street, D.J., Knox, S.A.: Designing for attribute-level best–worst choice experiments. J. Stat. Theory Pract. 6(2):363–375 (2012)
Thurstone, L.L.: A law of comparative judgment. Psychol. Rev. 34(4), 273 (1927)
Van Der Pol, M., Currie, G., Kromm, S., Ryan, M.: Specification of the utility function in discrete choice experiments. Value Health 17(2), 297–301 (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Working, A., Alqawba, M., Diawara, N. (2019). Functional Form of Markovian Attribute-Level Best-Worst Discrete Choice Modeling. In: Diawara, N. (eds) Modern Statistical Methods for Spatial and Multivariate Data. STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health. Springer, Cham. https://doi.org/10.1007/978-3-030-11431-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-11431-2_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11430-5
Online ISBN: 978-3-030-11431-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)