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Chris Skedgel Research Health Economist Atlantic Clinical Cancer Research Unit, Capital Health

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Discrete choice experiments (DCE) Full factorial designs Fractional factorial designs Blocking the design Briefly, analysis of choice data in SAS 2

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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 3

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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.) 5 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.

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Number of attribute-level combinations in a simple full factorial design = L A L: number of levels A: number of attributes Each possible attribute-level combination appears once; no correlations %MktEx(3**6) → 729 combinations 6

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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 7

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Orthogonal FrF designs emphasize statistical independence no correlations %MktRuns(3**6) ← main effects only nDesignReference 182 ** 1 3 ** 7Orthogonal Array 183 ** 6 6 ** 1Orthogonal Array 273 ** 13Fractional-Factorial 273 ** 9 9 ** 1Fractional-Factorial 362 ** 11 3 ** 12Orthogonal Array 362 ** 10 3 ** 8 6 ** 1Orthogonal Array 362 ** 4 3 ** 13Orthogonal Array 362 ** 3 3 ** 9 6 ** 1Orthogonal Array 362 ** 2 3 ** 12 6 ** 1Orthogonal Array 362 ** 1 3 ** 8 6 ** 2Orthogonal Array 363 ** 13 4 ** 1Orthogonal Array 363 ** ** 1Orthogonal Array 363 ** 7 6 ** 3Orthogonal Array 8

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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 9

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%MktRuns(3**6, ← Saturated = 73 Full Factorial = 729 Some Reasonable Cannot Be Design Sizes Violations Divided By S 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. 10 main effects and all 2-way interactions

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%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?) 11

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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 balance 12

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1. Generates a random FrF from candidate design subject to specified constraints 2. For each choice set in random FrF design, replaces one alternative with an alternative from candidate design and evaluates stat. efficiency; step 3 if eff, otherwise repeat 3. Repeats for all sets in current FrF design 4. Repeats steps 1-3 over specified iterations 5. Selects design that maximizes D-efficiency 13

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%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 */ 14

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BlockAlt1_x1Alt1_x2Alt1_x3Alt1_x4Alt1_x5Alt1_x6Alt2_x1Alt2_x2Alt2_x3Alt2_x4Alt2_x5Alt2_x6 Block Alt1_x Alt1_x Alt1_x Alt1_x Alt1_x Alt1_x Alt2_x Alt2_x Alt2_x Alt2_x Alt2_x Alt2_x

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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); 16

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BlockSetAge_AU0_ALE0_AU1_ALYg_APats_AAge_BU0_BLE0_BU1_BLYg_BPats_B

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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 18

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Warren Kuhfeld’s Marketing Research Methods in SAS: tnote/tnote_marketresearch.html Bonus! Comprehensive (1165 pages) manual covering many aspects of stated preference design 19

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Questions? 20

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