Open Access

Substitution Effects and Spatial Preference Heterogeneity in Single- and Multiple-Site Choice Experiments

Ivana Logar and Roy Brouwer

Article Figures & Data

  • Table 1

    Attributes and Attribute Levels Used in the Discrete Choice Experiment

    AttributeAttribute Levels
    Length of the river section that would be restored0 km,a 0.5 km, 1 km, 2 km
    Walking along the riverYes, Noa
    Swimming in the riverYes, Noa
    Barbecuing on the river bankYes, Noa
    BiodiversityLow (60% of potential plant and animal species present)a
    Medium (75% of potential plant and animal species present)
    High (100% of potential plant and animal species present)
    Price (increase in canton taxes per person per year)0 CHF,a 25 CHF, 50 CHF, 100 CHF, 150 CHF, 250 CHF, 500 CHF
    • a Attribute level in the status quo alternative. The status quo levels for the length and price attributes could not appear in the hypothetical choice alternatives. CHF, Swiss francs.

  • Table 2

    Explanation of the Variables Used in the Choice Models

    VariableDescriptionCoding and Units
    Length of the river section that would be restoredChoice attribute; indicates the length of the river restoration projectContinuous variable; in kilometers
    Walking along the riverChoice attribute; indicates whether river restoration would provide an option to walk along the riverDummy variable, 1 = Walking along the river is possible
    Swimming in the riverChoice attribute; indicates whether river restoration would provide an option to swim in the riverDummy variable, 1 = Swimming in the river is possible
    Barbecuing on the river bankChoice attribute; indicates whether river restoration would provide an option to barbecue on the river bankDummy variable, 1 = Barbecuing on the river bank is possible
    High biodiversityChoice attribute; indicates whether river restoration would increase biodiversity to a high levelDummy variable, 1 = High biodiversity level is achieved (100% of potential plant and animal species are present)
    Medium biodiversityChoice attribute; indicates whether river restoration would increase biodiversity to a medium levelDummy variable, 1 = Medium biodiversity level is achieved (75% of potential plant and animal species are present)
    PriceChoice attribute; indicates an increase in annual canton taxes per person for the purpose of river restorationContinuous variable; in Swiss francs
    Walking attribute × Respondents who walk when visiting the riversInteraction term between the choice attribute for walking and a dummy variable indicating whether the respondent usually walks when visiting the riversDummy variable, 1 = Walking along the river is possible and respondent usually walks when visiting the rivers
    Swimming attribute × Respondents who swim when visiting the riversInteraction term between the choice attribute for swimming and a dummy variable indicating whether the respondent usually swims when visiting the riversDummy variable, 1 = Swimming in the river is possible and respondent usually swims when visiting the rivers
    Barbecuing attribute × Respondents who barbecue when visiting the riversInteraction term between the choice attribute for barbecuing and a dummy variable indicating whether the respondent usually barbecues when visiting the riversDummy variable, 1 = Barbecuing on the river bank is possible and respondent usually barbecues when visiting the rivers
    ln(Road distance to the Thur + 1)Natural logarithm of road distance between respondent’s home and the river ThurContinuous variable; road distance in kilometers
    Road distance to the TössRoad distance between respondent’s home and the river TössContinuous variable; in kilometers
    Road distance to the valued river × Respondents living in urban areasInteraction term between the linear road distance to the valued river and a dummy variable indicating whether the respondent lives in an urban area (towns with >20,000 inhabitants)Continuous variable; in kilometers
    Longitudinal distance to the valued riverEuclidean (air) distance between respondent’s home and the valued river site in the East-West directionContinuous variable; in kilometers; positive (negative) values indicate East (West)
    Latitudinal distance to the valued riverEuclidean (air) distance between respondent’s home and the valued river site in the North-South directionContinuous variable; in kilometers; positive (negative) values indicate North (South)
    cosθCosine of the angle between respondent’s home and the valued river siteContinuous variable; range: –1 to 1; positive (negative) values indicate East (West)
    sinθSine of the angle between respondent’s home and the valued river siteContinuous variable; range: –1 to 1; positive (negative) values indicate North (South)
  • Table 3

    Estimated Mixed Logit Choice Models for the Three Samples

    SDCE (1) ThurSDCE (2) TössMDCE
    Variable(3) Thur(4) Töss
    Mean Estimates of Random Parameters
    Constant–1.690
    (6.010)
    –27.741***
    (10.103)
    –41.346**
    (16.331)
    5.140
    (12.584)
    Length of the river section that would be restored1.161**
    (0.455)
    0.617**
    (0.255)
    7.828***
    (2.142)
    6.905***
    (2.114)
    Walking along the river3.471***
    (1.110)
    2.042***
    (0.532)
    26.927***
    (6.846)
    2.411
    (1.991)
    Swimming in the river1.112*
    (0.609)
    0.923**
    (0.387)
    9.716***
    (2.605)
    4.680**
    (2.100)
    Barbecuing on the river bank1.917***
    (0.717)
    –0.048
    (0.411)
    2.520
    (1.701)
    1.280
    (1.365)
    High biodiversity1.936**
    (0.838)
    0.752
    (0.493)
    15.703***
    (4.312)
    11.947***
    (3.894)
    Medium biodiversity0.979
    (0.786)
    0.454
    (0.508)
    13.282***
    (3.554)
    12.814***
    (4.185)
    Price–0.062***
    (0.017)
    –0.024***
    (0.004)
    –0.081***
    (0.020)
    –0.081***
    (0.021)
    Nonrandom Parameters
    Walking attribute × Respondents who walk when visiting the rivers3.400***
    (1.303)
    2.005***
    (0.573)
    2.078
    (2.165)
    16.740***
    (4.576)
    Swimming attribute × Respondents who swim when visiting the rivers2.923***
    (0.880)
    1.791***
    (0.528)
    7.780***
    (2.558)
    6.396**
    (2.602)
    Barbecuing attribute × Respondents who barbecue when visiting the rivers3.985***
    (1.046)
    2.101***
    (0.617)
    18.774***
    (4.835)
    7.586**
    (3.200)
    ln(Road distance to the Thur + 1)–7.572**
    (3.766)
    10.393***
    (3.468)
    4.404
    (6.091)
    –3.248
    (4.578)
    Road distance to the Töss0.887***
    (0.276)
    –0.465***
    (0.101)
    –0.865***
    (0.289)
    –1.033***
    (0.282)
    Road distance to the valued river × Respondents living in urban areas0.871***
    (0.240)
    0.173***
    (0.058)
    5.511***
    (1.595)
    0.588***
    (0.198)
    Longitudinal distance to the valued river–0.101
    (0.070)
    –0.109
    (0.077)
    –0.805***
    (0.222)
    –1.053***
    (0.295)
    Latitudinal distance to the valued river–0.829***
    (0.270)
    0.106
    (0.116)
    0.208
    (0.251)
    –0.871***
    (0.289)
    cosθ0.571
    (0.714)
    –0.792
    (0.652)
    –7.696***
    (2.180)
    0.315
    (0.885)
    sinθ1.346
    (0.845)
    0.562
    (0.486)
    2.916***
    (1.203)
    3.077***
    (1.118)
    Standard Deviations of Random Parameters
    Constant7.090***
    (1.727)
    4.226***
    (0.736)
    6.601***
    (1.850)
    7.266***
    (1.844)
    Length of the river section that would be restored2.340***
    (0.580)
    1.389***
    (0.310)
    10.456***
    (2.663)
    10.684***
    (2.571)
    Walking along the river8.199***
    (2.039)
    4.719***
    (0.804)
    39.451***
    (9.658)
    27.737***
    (7.135)
    Swimming in the river4.049***
    (1.064)
    3.694***
    (0.713)
    31.070***
    (7.867)
    9.686***
    (2.441)
    Barbecuing on the river bank4.973***
    (1.448)
    4.863***
    (0.774)
    34.740***
    (8.600)
    28.724***
    (7.532)
    High biodiversity6.163***
    (1.617)
    2.261***
    (0.751)
    22.656***
    (5.363)
    3.357**
    (1.641)
    Medium biodiversity2.992**
    (1.456)
    0.726
    (0.676)
    18.480***
    (4.695)
    0.091
    (2.206)
    Price0.055***
    (0.016)
    0.026***
    (0.004)
    0.076***
    (0.019)
    0.102***
    (0.026)
    Log-likelihood–781.67–893.08–1,004.53
    Likelihood ratio test (χ2)1,508.37***1,311.94***1,154.94***
    Pseudo R20.4910.4230.365
    AIC/Na1.1551.3041.467
    Number of observations1,3981,4101,440
    • Note: Standard errors are reported in parentheses. MDCE, multiple-site discrete choice experiment; SDCE, single-site discrete choice experiment.

    • a Akaike information criterion with a correction for sample size.

    • * p < 0.1;

    • ** p < 0.05;

    • *** p < 0.01.

  • Table 4

    Extended Models: Marginal Willingness-to-Pay Estimates per Person per Year, in Swiss Francs

    Choice AttributeSDCE ThurSDCE TössMDCEBetween SDCE and MDCE ThurBetween SDCE and MDCE Töss
    ThurTöss
    Length of the river section that would be restored (in kilometers)18.74
    (7.37)
    26.19
    (12.42)
    96.09
    (21.03)
    85.74
    (19.21)
    p < 0.01p < 0.01
    Walking along the river56.05
    (18.52)
    86.62
    (24.89)
    330.54
    (44.44)
    29.94
    (25.54)
    p < 0.01p < 0.05
    Swimming in the river17.96
    (9.79)
    39.17
    (18.04)
    119.27
    (28.11)
    58.12
    (24.29)
    p < 0.01p = 0.26
    Barbecuing on the river bank30.96
    (11.50)
    –2.05
    (17.33)
    30.93
    (22.32)
    15.90
    (17.35)
    p = 0.48p = 0.23
    High biodiversity31.27
    (12.59)
    31.91
    (23.43)
    192.76
    (36.70)
    148.35
    (38.53)
    p < 0.01p < 0.01
    Medium biodiversity15.81
    (12.63)
    19.25
    (22.91)
    163.05
    (29.88)
    159.12
    (41.82)
    p < 0.01p < 0.01
    • Note: Standard errors are reported in parentheses. MDCE, multiple-site discrete choice experiment; SDCE, single-site discrete choice experiment.

  • Table 5

    Results of Hypothesis Testing

    HypothesisOutcome
    Embedded ImageRejected for 4 out of 5 nonmonetary choice attributes
    Embedded ImageRejected for 3 out of 5 nonmonetary choice attributes
    Thur SDCEToss SDCEThur MDCEToss MDCE
    Embedded ImageCannot be rejectedCannot be rejectedRejectedCannot be rejected
    Embedded ImageRejectedRejectedCannot be rejectedCannot be rejected
    Embedded ImageCannot be rejectedRejectedRejectedCannot be rejected
    Embedded ImageRejected in favor of Embedded Image (substitution)Rejected in favor of Embedded Image (substitution)Rejected in favor of Embedded Image (compl ementarity)Cannot be rejected
    Embedded ImageCannot be rejected for SDCEs; cannot be rejected for MDCE
    • Note: MDCE, multiple-site discrete choice experiment; SDCE, single-site discrete choice experiment.