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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 ** 12 12 ** 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, interact=@2) ← Saturated = 73 Full 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. 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 Block10.140.1300.140.150.120.140.120.140.130.250.17 Alt1_x10.1410.440.330.120.260.30.630.290.270.460.530.44 Alt1_x20.130.4410.320.390.410.350.250.760.140.350.290.34 Alt1_x300.330.3210.430.330.410.230.320.570.30.270.14 Alt1_x40.140.120.390.4310.450.290.490.290.410.890.440.22 Alt1_x50.150.260.410.330.4510.380.430.270.360.420.670.37 Alt1_x60.120.30.350.410.290.3810.540.450.230.470.350.52 Alt2_x10.140.630.250.230.490.430.5410.30.280.240.390.28 Alt2_x20.120.290.760.320.290.270.450.310.290.470.350.34 Alt2_x30.140.270.140.570.410.360.230.280.2910.350.390.43 Alt2_x40.130.460.350.30.890.420.470.240.470.351 0.43 Alt2_x50.250.530.290.270.440.670.350.390.350.390.3510.21 Alt2_x60.170.440.340.140.220.370.520.280.340.43 0.211 15

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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 111090.0835550007015910500 124011015500010955 2500 1310559525004010.083510500 14709109125004050.08315500 1570555105000109 95500 161050.08311050040110515000 174050.083912500109 5 5000 18405105125007015155000 191010.083512500409595500 217050.083915004015152500 22405109 50001010.08355500 2310555150007010.083952500 24101 1125007090.083555000 254095552500101 1 5000 267090.0831105000101551500 2770510552500409591500 281010.083915000409105 500 294090.08311025007051055500 17

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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: http://support.sas.com/resources/papers/ tnote/tnote_marketresearch.html Bonus! Comprehensive (1165 pages) manual covering many aspects of stated preference design 19

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Questions? cds.accru@gmail.com 20

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