Chris SkedgelResearch Health EconomistAtlantic Clinical Cancer Research Unit, Capital Health

Discrete choice experiments (DCE)Full factorial designsFractional factorial designsBlocking the designBriefly, analysis of choice data in

SAS

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Choice-based form of stated preference elicitation

Based on idea that even if people can’t provide a direct measure of value, they can usually indicate which scenario they prefer

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DCE elicitations rely on an effective experimental design -- the combination of attributes and attribute levels presented to respondents

Degrees of freedom (d.f.)

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Each parameter to be estimated by choice model requires 1 d.f., plus 1 d.f. to estimate model

Each choice task (not each respondent) provides 1 d.f.

Number of attribute-level combinations in a simple full factorial design = LA

L: number of levels A: number of attributes

Each possible attribute-level combination appears once; no correlations

%MktEx(3**6) → 729 combinations

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Unless you have few attributes/levels, FF designs likely to be impractical

Fractional factorial (FrF) designs use a subset of the FF design Orthogonal FrF designs Optimized FrF designs

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Orthogonal FrF designs emphasize statistical independence no correlations

%MktRuns(3**6) ← main effects only

n Design Reference18 2 ** 1 3 ** 7 Orthogonal Array18 3 ** 6 6 ** 1 Orthogonal Array27 3 ** 13 Fractional-Factorial27 3 ** 9 9 ** 1 Fractional-Factorial36 2 ** 11 3 ** 12 Orthogonal Array36 2 ** 10 3 ** 8 6 ** 1 Orthogonal Array36 2 ** 4 3 ** 13 Orthogonal Array36 2 ** 3 3 ** 9 6 ** 1 Orthogonal Array36 2 ** 2 3 ** 12 6 ** 1 Orthogonal Array36 2 ** 1 3 ** 8 6 ** 2 Orthogonal Array36 3 ** 13 4 ** 1 Orthogonal Array36 3 ** 12 12 ** 1 Orthogonal Array36 3 ** 7 6 ** 3 Orthogonal Array

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Optimal FrF designs emphasize statistical efficiency at expense of independence

Maximum information from respondents for a given survey design

Usually some correlation between attributes

Requires model to be pre-specified in order to ensure sufficient d.f.’s and minimal correlation between effects

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%MktRuns(3**6, interact=@2) ←

Saturated = 73Full Factorial = 729

Some Reasonable Cannot Be Design Sizes Violations Divided By

81 0 162 0 108 15 81 135 15 81 90 35 27 81 99 35 27 81 117 35 27 81 126 35 27 81 144 35 27 81 153 35 27 81 73 S 56 3 9 27 81

S - Saturated Design - The smallest design that can be made. Note that the saturated design is not one of the recommended designs for this problem. It is shown to provide some context for the recommended sizes.

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main effects and all 2-way interactions

%ChoiceEff optimizes FF design subject to specified constraints: Candidate design (usually FF) Number of runs (# of choice tasks) Model to be estimated (main effects,

interactions) Expected β’s (huh?)

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%ChoiceEff optimizes design subject to specified constraints: Candidate design (usually FF) Number of runs (# of choice tasks) Model to be estimated (main effects,

interactions) Expected β’s (huh?)

4 principles of efficient design: Orthogonality, level balance, minimal

overlap, utility balance12

%ChoiceEff(data=FF_Logical, /* candidate design */model=class(x1-x6), /* model to be estimated */nsets=&runs, /* total choice sets */flags=f1-f2, /* alternatives per set */maxiter=100, /* optimization iterations */seed=201109,converge=1e-12, options=nodups relative,beta=0); /* expected betas, H0=0 */

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  Block Alt1_x1 Alt1_x2 Alt1_x3 Alt1_x4 Alt1_x5 Alt1_x6 Alt2_x1 Alt2_x2 Alt2_x3 Alt2_x4 Alt2_x5 Alt2_x6Block 1 0.14 0.13 0 0.14 0.15 0.12 0.14 0.12 0.14 0.13 0.25 0.17

Alt1_x1 0.14 1 0.44 0.33 0.12 0.26 0.3 0.63 0.29 0.27 0.46 0.53 0.44

Alt1_x2 0.13 0.44 1 0.32 0.39 0.41 0.35 0.25 0.76 0.14 0.35 0.29 0.34

Alt1_x3 0 0.33 0.32 1 0.43 0.33 0.41 0.23 0.32 0.57 0.3 0.27 0.14

Alt1_x4 0.14 0.12 0.39 0.43 1 0.45 0.29 0.49 0.29 0.41 0.89 0.44 0.22

Alt1_x5 0.15 0.26 0.41 0.33 0.45 1 0.38 0.43 0.27 0.36 0.42 0.67 0.37

Alt1_x6 0.12 0.3 0.35 0.41 0.29 0.38 1 0.54 0.45 0.23 0.47 0.35 0.52

Alt2_x1 0.14 0.63 0.25 0.23 0.49 0.43 0.54 1 0.3 0.28 0.24 0.39 0.28

Alt2_x2 0.12 0.29 0.76 0.32 0.29 0.27 0.45 0.3 1 0.29 0.47 0.35 0.34

Alt2_x3 0.14 0.27 0.14 0.57 0.41 0.36 0.23 0.28 0.29 1 0.35 0.39 0.43

Alt2_x4 0.13 0.46 0.35 0.3 0.89 0.42 0.47 0.24 0.47 0.35 1 0.35 0.43

Alt2_x5 0.25 0.53 0.29 0.27 0.44 0.67 0.35 0.39 0.35 0.39 0.35 1 0.21

Alt2_x6 0.17 0.44 0.34 0.14 0.22 0.37 0.52 0.28 0.34 0.43 0.43 0.21 1

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Optimized FrF design has 18 choice sets; probably still too many to present to each respondent

Solution is to block the design:

%MktBlock(data=best, /* default D-efficient design */nalts=2, /* alternatives per set */nblocks=2, /* number of blocks*/

factors=x1-x6, /* attributes in each alt */seed=201109,out=library.lineardesign2B2A18R_D);

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Block Set Age_A U0_A LE0_A U1_A LYg_A Pats_A Age_B U0_B LE0_B U1_B LYg_B Pats_B1 1 10 9 0.083 5 5 5000 70 1 5 9 10 500

1 2 40 1 10 1 5 5000 10 9 5 5 10 2500

1 3 10 5 5 9 5 2500 40 1 0.083 5 10 500

1 4 70 9 10 9 1 2500 40 5 0.083 1 5 500

1 5 70 5 5 5 10 5000 10 9 10 9 5 500

1 6 10 5 0.083 1 10 500 40 1 10 5 1 5000

1 7 40 5 0.083 9 1 2500 10 9 10 5 10 5000

1 8 40 5 10 5 1 2500 70 1 5 1 5 5000

1 9 10 1 0.083 5 1 2500 40 9 5 9 5 500

2 1 70 5 0.083 9 1 500 40 1 5 1 5 2500

2 2 40 5 10 9 10 5000 10 1 0.083 5 5 500

2 3 10 5 5 5 1 5000 70 1 0.083 9 5 2500

2 4 10 1 10 1 1 2500 70 9 0.083 5 5 5000

2 5 40 9 5 5 5 2500 10 1 10 1 10 5000

2 6 70 9 0.083 1 10 5000 10 1 5 5 1 500

2 7 70 5 10 5 5 2500 40 9 5 9 1 500

2 8 10 1 0.083 9 1 5000 40 9 10 5 10 500

2 9 40 9 0.083 1 10 2500 70 5 10 5 5 500

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Briefly, SAS doesn’t do it well

SAS can estimate McFadden’s conditional choice model (multinomial logistic) using PROC PHREG Doesn’t account for repeated choices by respondents

DCEs increasingly modelled using multinomial probit or mixed logistic models Stata, R Allow for correlated choices within respondents

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Warren Kuhfeld’s Marketing Research Methods in SAS:

http://support.sas.com/resources/papers/tnote/tnote_marketresearch.html

Bonus! Comprehensive (1165 pages) manual covering many aspects of stated preference design

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Questions?

cds.accru@gmail.com20