Practical design for discrete choice experiments
This presentation is the property of its rightful owner.
Sponsored Links
1 / 19

Practical Design for Discrete Choice Experiments PowerPoint PPT Presentation


  • 82 Views
  • Uploaded on
  • Presentation posted in: General

Practical Design for Discrete Choice Experiments. Bradley Jones, SAS Institute August 13, 2008. Discrete Choice Experiment Setup. Respondents indicate the alternative they prefer most in each choice set A lternatives are called profiles Each profile is a combination of attribute levels

Download Presentation

Practical Design for Discrete Choice Experiments

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Practical design for discrete choice experiments

Practical Design for Discrete Choice Experiments

Bradley Jones, SAS Institute

August 13, 2008


Practical design for discrete choice experiments

Discrete Choice Experiment Setup

  • Respondents indicate the alternative they prefer most in each choice set

  • Alternatives are called profiles

  • Each profile is a combination of attribute levels

  • Choice sets typically consist of two, three or four profiles

DEMA 2008, August 2008, Cambridge

2


Example marketing a new laptop computer

Example: Marketing a new laptop computer

Attributes Levels

Hard Drive 40 GB80 GB

Speed 1.5 GHz2.0 GHz

Battery Life 4 hours6 hours

Price $1,000$1,200 $1,500

DEMA 2008, August 2008, Cambridge

3


Sample choice set

Sample Choice Set

Check the box for the laptop you prefer.

Hard DiskSpeedBatteryPrice

40Gig1.5GHz6hours$1,000

40Gig2.0GHz4hours$1,500

Profile 1

Profile 2

DEMA 2008, August 2008, Cambridge

4


Practical design for discrete choice experiments

Statistical model

  • multinomial logit model

  • based on the random utilities model

  • where xjs represents the attribute levels and βis the set of parameter values

  • probability of choosing alternative j in choice set s

DEMA 2008, August 2008, Cambridge

5


Practical design for discrete choice experiments

Design optimality criterion

  • Dcriterion-minimizethe determinant of the variance matrix of the estimators:

  • Equivalently– maximize the determinant of the information matrix, M.

DEMA 2008, August 2008, Cambridge

6


Practical design for discrete choice experiments

Dependence on the unknown parameter, β

Bayesian optimal designs:

  • construct a prior distribution for the parameters

  • find design thatperforms best on average

  • Sándor & Wedel (2001, 2002, 2005)

DEMA 2008, August 2008, Cambridge

7


Design for nonlinear models

Design for Nonlinear Models

To design an informative experiment …..

You need to know something about the response function …..

And about the parameter values.

DEMA 2008, August 2008, Cambridge

8


Bayesian d optimal design

Bayesian D-Optimal Design

Bayesian ideas are natural to cope with the fact that the information matrix, M, depends on b.

Chaloner and Larntz (1986) developed a Bayesian D-Optimality criterion:

Φ(d) = ∫ log det[M(b;d)] p(b) db

DEMA 2008, August 2008, Cambridge

9


Computing bayesian d optimal designs

Computing Bayesian D-Optimal Designs

A major impediment to Bayesian D-optimal design has been COMPUTATIONAL.

The integral over bcan be VERY SLOW.

It must be computed MANY TIMES in the course of finding an optimal design.

DEMA 2008, August 2008, Cambridge

10


Bayesian computations

Bayesian Computations

Gotwalt, Jones and Steinberg (2007) use a quadraturemethod, due to Mysovskikh.

This method is guaranteed to exactly integrate all polynomials up to 5th degree and all odd-degree monomials.

With p parameters, it requires just O(p2) function evaluations.

DEMA 2008, August 2008, Cambridge

11


Mysovskikh quadrature

Mysovskikhquadrature

Assume a normal prior with independence.

• Center the integral about the prior mean.

• Scale each variable by its standard deviation.

• Integrate over distance from the prior mean and, at each distance, over a spherical shell.

DEMA 2008, August 2008, Cambridge

12


Mysovskikh quadrature continued

Mysovskikhquadrature continued…

Radial integral: Generalized Gauss-LaGuerrequadrature, with an extra point at the origin.

Spherical integrals: The Mysovskikhquadraturescheme.

DEMA 2008, August 2008, Cambridge

13


Spherical integral

Spherical integral

A simplex, its edge midpoints on the sphere, and the inverses of all of these points.

Simplex point weights: p(7-p)/2(p+1)2(p+2).

Mid-point weights: 2(p-1)2/p(p+1)2(p+2).

DEMA 2008, August 2008, Cambridge

14


Practical design for discrete choice experiments

Quadrature points in two dimensions

Each point is both a simplex point and a mid-point.

All weights equal1/6.

Simplex point

Mid-point

DEMA 2008, August 2008, Cambridge

15


Study description

Study Description

16 Respondents – 8 developers 8 sales & marketing

9 Male 7 Female

2 Surveys with 6 choice sets in each

Respondents were assigned randomly to surveys

blocked by job function

DEMA 2008, August 2008, Cambridge

16


Practical design for discrete choice experiments

Software Demonstration

DEMA 2008, August 2008, Cambridge

17


Conclusions

Conclusions

Discrete Choice Conjoint Experiments require design methods for nonlinear models.

D-Optimal Bayesian designs reduce the dependence of the design on the unknown parameters.

New quadrature methods make computation of these designs much faster.

Commercial software makes carrying out such studies simple and efficient.

DEMA 2008, August 2008, Cambridge

18


References

References

Atkinson, A. C. and Donev, A. N. (1992). Optimum Experimental Designs, Oxford U.K.: Clarendon Press.

Cassity C.R., (1965) “Abscissas, Coefficients, and Error Term for the Generalized Gauss-LaguerreQuadrature Formula Using the Zero Ordinate,” Mathematics ofComputation, 19, 287-296.

Chaloner, K. and Verdinelli, I. (1995). Bayesian experimental design: a re-view, Statistical Science 10: 273-304.

Grossmann, H., Holling, H. and Schwabe, R. (2002). Advances in optimum experimental design for conjoint analysis and discrete choice models, in Advances in Econometrics, Econometric Models in Marketing, Vol. 16, Franses, P. H. and Montgomery, A. L., eds. Amsterdam: JAI Press, 93-117.

Gotwalt, C., Jones, B. and Steinberg, D. (2009) Fast Computation of Designs Robust to Parameter Uncertainty for Nonlinear Settings accepted at Technometrics.

Huber, J. and Zwerina, K. (1996). The importance of utility balance in efficient choice designs, Journal of Marketing Research 33: 307-317.

McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior, in Frontiers in Econometrics, Zarembka, P., ed. New York: Academic Press, 105-142.

Meyer, R. K. and Nachtsheim, C. J. (1995). The coordinate-exchange algorithm for constructing exact optimal experimental designs, Technometrics37: 60-69.

Monahan, J. and Genz, A. (1997). Spherical-radial integration rules for Bayesian computation, Journal of the American Statistical Association 92: 664-674.

Sandor, Z. and Wedel, M. (2001). Designing conjoint choice experiments using managers' prior beliefs, Journal of Marketing Research 38: 430-444.

DEMA 2008, August 2008, Cambridge

19


  • Login