Non-participation and Heterogeneity in Stated: A Double Hurdle Latent Class Approach for Climate Change Adaptation Plans and Ecosystem Services


We introduce a double hurdle latent class approach to model choice experiments, where serial non-participants and clustered preference patterns are present. The proposed approach is applied to a recent stated preference study in which the residents of the Eastern Shore of Virginia answer choice questions about alternative coastal climate change adaptation plans. While the double hurdle latent class model avoids self-contradictory assumptions, estimates and tests show that, compared with an unrestricted latent class model, it achieves a significantly better statistical fit and maintains the capability to link the heterogeneity of participants’ preferences to their attributes. Moreover, the double hurdle latent class model also provides important implications in how to conduct welfare analysis based on different behavioral patterns of different groups, which leads to nontrivial changes in welfare measures. The empirical results highlight that certain ecosystem services may increase the willingness to pay for coastal climate change adaptation plans.

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Fig. 1


  1. 1.

    Note that “the respondents” represent all the individuals who responded, while “the participants” refer to all the respondents who are not non-participants, that is, who are making choices in a manner that indicates that they evaluated tradeoffs and in a manner that (presumably) reflects their preferences in the choice occasions.

  2. 2.

    Burton and Rigby (2009) compared a restricted latent class model with a double hurdle random coefficient model, in which the differences are sourced from the hurdle structure as well as the differences between the latent class modeling and random coefficient modeling. We compare latent class models with double hurdle latent class models, where the double hurdle structure is the only major source of differences.

  3. 3.

    One may argue that in the restricted LC models, the “non-participation” class is not modeled to be evaluating the trade-offs among different attributes since there’s only one attribute in the choice equation. Although that seems to be true, it is still not consistent with the fundamental modeling problem. First, no matter what parameters are included or what specifications are adopted in the multinomial logit structure, that structure is generated from the random utility theory and the status quo parameter is part of the random utility model. Second, the assumed non-participation behavior reflects a decision to adopt a particular choice or response process based on a categorical variable, and generally, the non-participants’ decision is to choose the option with the status quo variable being 1. Since there’s only one status quo option in each choice occasion, no uncertainty nor random utility is involved. Thus, a multinomial logit structure conflicts with the theoretical conceptualization of the non-participant’s response process.

  4. 4.

    In the final double hurdle framework, the independence assumption here means that conditional on being a participant, the random (unobserved) part of utilities are independently distributed across different options, different choice occasions, and different individuals.

  5. 5.

    The linear terms involving income, y, are just constant across the utility for each scenario, and therefore do not affect which scenario provides the highest utility; therefore, in a linear utility model, analysts drop income (Hanemann 1984). A negative sign is not explicitly addressed by this simplification, so the estimated parameter on cost should be interpreted accordingly. That is, an estimated negative coefficient on cost suggests a positive marginal utility of income (\({\beta }_{kC}=-{\beta }_{ky}\)). Moreover, though the choice equations do not include income, income could be included as an indicator in the membership equations.

  6. 6.

    For the econometric approach for a logit model with random parameters, see Revelt and Train (1998), and Layton and Brown (2000). The random coefficient model (without hurdle structure) is presented in Online Appendix F. Also, a latent class model with random coefficients could perform better than both the standard latent class model and the plain random coefficient model, but it would not show the goodness of the double hurdle structure. Hence, we make no additional effort in random coefficient modeling for the latent class model or the double hurdle latent class model, leaving this topic outside the scope of the current paper.

  7. 7.

    Our “bathtub model” was produced by Dr. John H. Porter of the University of Virginia, Department of Environmental Sciences.

  8. 8.

    We included a preface to Section Three of the survey (see Online Appendix A for more details) in order to define certain terminology and to ensure all survey participants had a common base set of knowledge going into the choice questions.

  9. 9.

    The design was constructed by Dr. Donald A. Anderson of StatDesign, LLC (Evergreen, CO). See Yue (2017) for details.

  10. 10.

    For Northampton County, we randomly drew 759 addresses (out of 3,922) from the county’s voter registration list (the voter registration lists for both counties are generated in August 2013), 151 addresses (out of 448) from a combined membership list of Community Group #1 and Outdoors Group,and 90 addresses (out of 90) from the membership list of Community Group #2. For Accomack County, 700 addresses (out of 13,792) were randomly selected from the county’s voter registration list only, 150 addresses (out of 218) were randomly selected from the membership list of Community Group #1, and 150 addresses (out of 186) were randomly selected from the membership list of Outdoors Group. To comply with IRB guidelines to protect respondent’s confidentiality, we use generic labels to identify these groups for the purposes of this paper. Community group #2 was not present in Accomack.

  11. 11.

    Our delivery rate for Community Group #1 and Outdoors Group (combined) was 98 percent for both counties, while the delivery rate to Community Group #2 was 97 percent. For addresses only on the voter registration lists, the delivery rate was 89 percent in Northampton and 87 percent in Accomack.

  12. 12.

    Our highest useful response rate came from Community Group #1 and Outdoors Group (combined, 60 percent for Northampton, 53 percent for Accomack); this was followed by Community Group #2 (33 percent useful response rate for Northampton) and the voter registration list-only group (26 percent useful response rate for Northampton, 24 percent useful response rate for Accomack).

  13. 13.

    The distribution between bay-side and sea-side may be due to the larger portion of buildable land on the bay-side compared to the sea-side, along with the historic importance of sheltering from storms on the bay-side.

  14. 14.

    To calculate Kernel density, a smoothly curved surface is fitted over each point. Conceptually, the surface value generated by a point is highest at the location of the point and diminishes with increasing distance from the point. The density at each output cell is calculated by adding all the kernel surface values in the cell. The unit of employed Kernel density is counts per square mile.

  15. 15.

    That is, the remaining demographics after purging demographics that are insignificant across all classes.

  16. 16.

    Note that the presented process deciding the final variable set relies on the 4-segment latent class model, but the 4-segment structure is decided with the full set of variables. However, we can show statistical evidence that, with the final parsimonious set, the preferred baseline latent class model is still with four segments (these results are available upon request, and Table 2 also show that, with the final variable set, the 4-segment structure is preferred consistently in highly restricted latent class models and double hurdle models). Moreover, the variable choices only make minor changes to the statistics, comparing with the class structure. That is to say, we generally do not need to compare different specifications across different class structures.

  17. 17.

    Also, a joint likelihood ratio test of the seven interactions return a p-value of 0.0931, suggesting they are not significantly jointly different from zero at the 5-percent significance level.

  18. 18.

    We acknowledge that this assumption might be conservative, since WTP of the pro-nature group might be higher than the other participating groups. Nonetheless, we cannot infer their maximum values from this study.

  19. 19.

    Arguably, their WTP for a change that is against their will could be negative. But since we cannot infer their exact WTP from our survey study, we follow the literature to use zero to represent their WTP.

  20. 20.

    Although the underlying story here is that the serial non-participation is mostly caused by the opposition to climate science or government action instead of pure cognitive difficulties, we cannot exclude the later factor empirically.

  21. 21.

    This result is consistent with the results presented in von Haefen, et. al. (2005) (when SQ is included).

  22. 22.

    One widely perceived concern is that welfare measures from stated preference studies might be subject to hypothetical bias. Though some efforts have been made to reduce hypothetical bias in this study, we cannot claim that the hypothetical bias is totally eliminated.


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We would like to thank the Virginia Coast Reserve Long-term Ecological Research (LTER) program for financial support through the U.S. National Science Foundation grant DEB-1237733, including collaborative support from the University of Virginia VCR LTER scientists and staff. Partial support for this project was also provided through the U.S. Department of Agricultural, National Institute of Food and Agriculture (NIFA), the Storrs Agricultural Experiment Station under Hatch project CONS-00971. All activities related to this paper were conducted in compliance with Institutional Review Board (IRB) policies, under protocol #H14-304 for survey development through data collection and protocol #X17-063 for analysis supporting this paper. Thanks to Dr. John H. Porter (University of Virginia) for producing the SLR model that informed the acreage values we used for the choice questions. Thanks to Gwynn Crichton (formerly The Nature Conservancy), Dr. Karen J. McGlathery (University of Virginia), and Curtis Smith (Accomack-Northampton Planning District Commission) for their review and suggestions on survey content and wording. Also, we would like to express our sincere gratitude to Christian Vossler and three anonymous reviewers for their thoughtful and valuable comments.

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Correspondence to Zhenshan Chen.

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Chen, Z., Swallow, S.K. & Yue, I.T. Non-participation and Heterogeneity in Stated: A Double Hurdle Latent Class Approach for Climate Change Adaptation Plans and Ecosystem Services. Environ Resource Econ (2020).

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  • Built assets
  • Choice experiment
  • Double hurdle model
  • Mixture model
  • Natural assets
  • Serial non-participation
  • Valuation
  • Resilience
  • Adaptation
  • Sea-level rise