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.

References

References
1.
Wassenaar
,
H. J.
, and
Chen
,
W.
,
2003
, “
An Approach to Decision-Based Design With Discrete Choice Analysis for Demand Modeling
,”
ASME J. Mech. Des.
,
125
(
3
), pp.
490
497
.
2.
McFadden
,
D.
,
2009
, “
Conditional Logit Analysis of Qualitative Choice Behavior
,”
Frontiers in Econometrics
,
P.
Zarembka
, ed.,
Academic Press
,
New York
, pp.
105
142
.
3.
Hausman
,
J. A.
, and
Wise
,
D. A.
,
1978
, “
A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences
,”
Econometrica
,
46
(
2
), pp.
403
426
.
4.
Boyd
,
J. H.
, and
Mellman
,
R. E.
,
1980
, “
The Effect of Fuel Economy Standards on the US Automotive Market: An Hedonic Demand Analysis
,”
Transp. Res. Part A
,
14
(
5
), pp.
367
378
.
5.
Cardell
,
N. S.
, and
Dunbar
,
F. C.
,
1980
, “
Measuring the Societal Impacts of Automobile Downsizing
,”
Transp. Res. Part A
,
14
(
5
), pp.
423
434
.
6.
Anderson
,
S. P.
,
De Palma
,
A.
, and
Thisse
,
J. F.
,
1992
,
Discrete Choice Theory of Product Differentiation
,
MIT Press
,
Cambridge, MA
.
7.
Train
,
K. E.
,
2009
,
Discrete Choice Methods With Simulation
,
Cambridge University Press
,
Cambridge, UK
.
8.
Michalek
,
J. J.
,
Feinberg
,
F. M.
, and
Papalambros
,
P. Y.
,
2005
, “
Linking Marketing and Engineering Product Design Decisions Via Analytical Target Cascading
,”
J. Prod. Innovation Manage.
,
22
(
1
), pp.
42
62
.
9.
Michalek
,
J. J.
,
Ceryan
,
O.
,
Papalambros
,
P. Y.
, and
Koren
,
Y.
,
2006
, “
Balancing Marketing and Manufacturing Objectives in Product Line Design
,”
ASME J. Mech. Des.
,
128
(
6
), pp.
1196
1204
.
10.
Haaf
,
C. G.
,
Michalek
,
J. J.
,
Morrow
,
W. R.
, and
Liu
,
Y.
,
2014
, “
Sensitivity of Vehicle Market Share Predictions to Discrete Choice Model Specification
,”
ASME J. Mech. Des.
,
136
(
12
), p.
121402
.
11.
Kang
,
K.
,
Kang
,
C.
, and
Hong
,
Y. S.
,
2014
, “
Data-Driven Optimized Vehicle-Level Engineering Specifications
,”
Ind. Manage. Data Syst.
,
114
(
3
), pp.
338
364
.
12.
Frischknecht
,
B. D.
,
Whitefoot
,
K.
, and
Papalambros
,
P. Y.
,
2010
, “
On the Suitability of Econometric Demand Models in Design for Market Systems
,”
ASME J. Mech. Des.
,
132
(
12
), p.
121007
.
13.
Sullivan
,
E.
,
Ferguson
,
S.
, and
Donndelinger
,
J.
,
2011
, “
Exploring Differences in Preference Heterogeneity Representation and Their Influence in Product Family Design
,”
ASME
Paper No. DETC2011-48596.
14.
Michalek
,
J. J.
,
Ebbes
,
P.
,
Adigüzel
,
F.
,
Feinberg
,
F. M.
, and
Papalambros
,
P. Y.
,
2011
, “
Enhancing Marketing With Engineering: Optimal Product Line Design for Heterogeneous Markets
,”
Int. J. Res. Mark.
,
28
(
1
), pp.
1
12
.
15.
Rossi
,
P. E.
,
Allenby
,
G. M.
, and
McCulloch
,
R.
,
2005
,
Bayesian Statistics and Marketing
,
Wiley
,
Chichester, UK
.
16.
Gautier
,
E.
, and
Kitamura
,
Y.
,
2013
, “
Nonparametric Estimation in Random Coefficients Binary Choice Models
,”
Econometrica
,
81
(
2
), pp.
581
607
.
17.
Ichimura
,
H.
, and
Thompson
,
T. S.
,
1998
, “
Maximum Likelihood Estimation of a Binary Choice Model With Random Coefficients of Unknown Distribution
,”
J. Econometrics
,
86
(
2
), pp.
269
295
.
18.
Briesch
,
R. A.
,
Chintagunta
,
P. K.
, and
Matzkin
,
R. L.
,
2010
, “
Nonparametric Discrete Choice Models With Unobserved Heterogeneity
,”
J. Bus. Econ. Stat.
,
28
(
2
), pp.
291
307
.
19.
Bajari
,
P.
,
Fox
,
J. T.
, and
Ryan
,
S. P.
,
2007
, “
Linear Regression Estimation of Discrete Choice Models With Nonparametric Distributions of Random Coefficients
,”
Am. Econ. Rev.
,
97
(
2
), pp.
459
463
.
20.
Fox
,
J. T.
,
Kim
,
K.
,
Ryan
,
S. P.
, and
Bajari
,
P.
,
2012
, “
The Random Coefficients Logit Model Is Identified
,”
J. Econometrics
,
166
(
2
), pp.
204
212
.
21.
Fox
,
J. T.
, and
Gandhi
,
A.
,
2016
, “
Nonparametric Identification and Estimation of Random Coefficients in Multinomial Choice Models
,”
RAND J. Econ.
,
47
(
1
), pp.
118
139
.
22.
Fosgerau
,
M.
, and
Hess
,
S.
,
2009
, “
A Comparison of Methods for Representing Random Taste Heterogeneity in Discrete Choice Models
,”
Eur. Transp. Trasporti Europei
,
42
, pp.
1
25
.http://www.openstarts.units.it/dspace/bitstream/10077/6127/1/42_1_FosgerauHess.pdf
23.
Train
,
K. E.
,
2008
, “
Em Algorithms for Nonparametric Estimation of Mixing Distributions
,”
J. Choice Model.
,
1
(
1
), pp.
40
69
.
24.
Berry
,
S.
,
Levinsohn
,
J.
, and
Pakes
,
A.
,
1995
, “
Automobile Prices in Market Equilibrium
,”
Econometrica
,
63
(
4
), pp.
841
890
.
25.
Berry
,
S. T.
, and
Haile
,
P. A.
,
2014
, “
Identification in Differentiated Products Markets Using Market Level Data
,”
Econometrica
,
82
(
5
), pp.
1749
1797
.
26.
Cho
,
Y.
, and
Kim
,
H.
,
1999
, “
On the Volume Formula for Hyperbolic Tetrahedra
,”
Discrete Comput. Geom.
,
22
(
3
), pp.
347
366
.
27.
Boot
,
J. C. G.
,
1962
, “
On Trivial and Binding Constraints in Programming Problems
,”
Manage. Sci.
,
8
(
4
), pp.
419
441
.
28.
Muller
,
M. E.
,
1959
, “
A Note on a Method for Generating Points Uniformly on n-Dimensional Spheres
,”
Commun. ACM
,
2
(
4
), pp.
19
20
.
29.
Ross
,
S.
, and
Peköz
,
E.
,
2007
, A Second Course in Probability, ProbabilityBookstore, Boston,
MA.
30.
Rubinstein
,
R. Y.
, and
Kroese
,
D. P.
,
2011
,
Simulation and the Monte Carlo Method
,
Wiley
,
New York
.
31.
Motzkin
,
T. S.
,
Raiffa
,
H.
,
Thompson
,
G. L.
, and
Thrall
,
R. M.
,
1953
, “
The Double Description Method
,”
Contributions to Theory of Games
, Vol. 2.,
H. W.
Kuhn
and
A. W.
Tucker
, eds.,
Princeton University Press
,
Princeton, NJ
.
You do not currently have access to this content.