Flash Player 9 (or above) is needed to view presentations.
We have detected that you do not have it on your computer. To install it, go here.

• 140 views

More in: Technology
• Comment goes here.
Are you sure you want to
Be the first to comment
Be the first to like this

Total Views
140
On Slideshare
0
From Embeds
0
Number of Embeds
0

Shares
0
0
Likes
0

No embeds

### Report content

No notes for slide

### Transcript

• 2. 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, 2 Copyright © 2008, SAS Institute Inc. All rights reserved. Cambridge
• 3. Example: Marketing a new laptop computer Attributes Levels Hard Drive 40 GB 80 GB Speed 1.5 GHz 2.0 GHz Battery Life 4 hours 6 hours Price \$1,000 \$1,200 \$1,500 DEMA 2008, August 2008, 3 Copyright © 2008, SAS Institute Inc. All rights reserved. Cambridge
• 4. Sample Choice Set Check the box for the laptop you prefer. Hard Disk Speed Battery Price 40Gig 1.5GHz 6hours \$1,000 Profile 1 40Gig 2.0GHz 4hours \$1,500 Profile 2 DEMA 2008, August 4 Copyright © 2008, SAS Institute Inc. All rights reserved. 2008, Cambridge
• 5. Statistical model multinomial logit model based on the random utilities model U js  xjsβ   js where xjs represents the attribute levels and β is the set of parameter values probability of choosing alternative j in choice set s x jsβ  option j chosen  e p js    t =1  J  in choice set s  e xtsβ DEMA 2008, August 5 Copyright © 2008, SAS Institute Inc. All rights reserved. 2008, Cambridge
• 6. Design optimality criterion D criterion - minimize the determinant of the variance matrix of the estimators: det  M 1  X,β   Equivalently – maximize the determinant of the information matrix, M. DEMA 2008, August 2008, 6 Copyright © 2008, SAS Institute Inc. All rights reserved. Cambridge
• 7. Dependence on the unknown parameter, β S M  X,β    X Ps β   ps β  p β   Xs s s s1 Bayesian optimal designs: • construct a prior distribution for the parameters • find design that performs best on average • Sándor & Wedel (2001, 2002, 2005) DEMA 2008, August 7 Copyright © 2008, SAS Institute Inc. All rights reserved. 2008, Cambridge
• 8. 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, 8 Copyright © 2008, SAS Institute Inc. All rights reserved. Cambridge
• 9. 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 9 Copyright © 2008, SAS Institute Inc. All rights reserved. 2008, Cambridge
• 10. Computing Bayesian D-Optimal Designs A major impediment to Bayesian D-optimal design has been COMPUTATIONAL. The integral over b can be VERY SLOW. It must be computed MANY TIMES in the course of finding an optimal design. DEMA 2008, August 10 Copyright © 2008, SAS Institute Inc. All rights reserved. 2008, Cambridge
• 11. Bayesian Computations Gotwalt, Jones and Steinberg (2007) use a quadrature method, 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 11 Copyright © 2008, SAS Institute Inc. All rights reserved. 2008, Cambridge
• 12. Mysovskikh quadrature 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 12 Copyright © 2008, SAS Institute Inc. All rights reserved. 2008, Cambridge