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Research Papers: Design Automation

A Simulation Method to Estimate Nonparametric Distribution of Heterogeneous Consumer Preference From Market-Level Choice Data

[+] Author and Article Information
Changmuk Kang

Assistant Professor
Department of Industrial and Information Systems Engineering,
Soongsil University,
Seoul 06978, South Korea
e-mail: changmuk.kang@ssu.ac.kr

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 9, 2016; final manuscript received August 4, 2016; published online September 13, 2016. Assoc. Editor: Gul E. Okudan Kremer.

J. Mech. Des 138(12), 121402 (Sep 13, 2016) (9 pages) Paper No: MD-16-1113; doi: 10.1115/1.4034470 History: Received February 09, 2016; Revised August 04, 2016

In recent decision-based design trends, product design is optimized for maximizing utility to consumers. A discrete-choice analysis (DCA) model is a widely utilized tool for quantitatively assessing how consumers evaluate utility of a product. Ordinary DCA models specify utility as linear combination of attribute values of a product and coefficients that represent preference of consumers. Assuming that the coefficient value is heterogenous between individual consumers, this study proposes a method to estimate its nonparametric distribution using market-level data, which is the market share of existing products. Where consumers consider k attributes of a product, his/her preference is represented by a k-dimensional vector of coefficient values. This method simulates an empirical distribution of the vectors in k-dimensional space. The whole space is first fragmented by disjoint regions, vectors in which prefer a specific product than others, and then, random points are sampled in each region as much as market share of the corresponding product. In a sense that more points are sampled for a more popular product, the empirical distribution is population of preference vectors. This method is practically useful since it utilizes only market-level data, which are relatively easy to gather than individual-level choice instances. In addition, the simulation procedure is intuitive and easy to implement.

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Figures

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Fig. 1

A flowchart of the proposed sampling procedure

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Fig. 2

An example of redundant inequalities (l4 and l5)

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Fig. 3

A graphical representation of the rejection sampling. Dots are sampled points.

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Fig. 4

A graphical representation of the importance sampling. Vector ei’s are extreme rays, b¯ is a random convex combination of ei’s, and b is a resulting sample scaled to the sphere surface.

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Fig. 5

Histograms of sampled βn values by the proposed method. The solid lines are drawn from the true distribution g(b).

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Fig. 6

Contour graphs representing joint distributions between row and column attributes. Each contour line represents increase of relative frequency by 0.2%. Graph (a) is the true distributions and (b) is the sampled ones by the proposed method.

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Fig. 7

Histograms of relative frequency of sampled βn values weighted by their estimated shares. The solid lines are drawn from the true distribution g(b).

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