Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Change history
15 September 2020
The article was published with a typographical error in the title.
Notes
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.
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.
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.
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.
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.
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.
Our “bathtub model” was produced by Dr. John H. Porter of the University of Virginia, Department of Environmental Sciences.
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.
The design was constructed by Dr. Donald A. Anderson of StatDesign, LLC (Evergreen, CO). See Yue (2017) for details.
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.
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.
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).
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.
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.
That is, the remaining demographics after purging demographics that are insignificant across all classes.
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.
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.
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.
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.
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.
This result is consistent with the results presented in von Haefen, et. al. (2005) (when SQ is included).
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.
References
Akaike H (1998) Information theory and an extension of the maximum likelihood principle. In: Selected papers of Hirotugu Akaike. Springer, New York, pp 199–213
Basilevsky AT (2009) Statistical factor analysis and related methods: theory and applications, vol 418. Wiley, Hoboken
Bateman IJ, Day BH, Georgiou S, Lake I (2006) The aggregation of environmental benefit values: welfare measures, distance decay and total WTP. Ecol Econ 60(2):450–460
Boxall PC, Adamowicz WL (2002) Understanding heterogeneous preferences in random utility models: a latent class approach. Environ Resource Econ 23(4):421–446
Bozdogan H (1987) Model selection and Akaike's information criterion (AIC): the general theory and its analytical extensions. Psychometrika 52(3):345–370
Brouwer R, Martin-Ortega J, Berbel J (2010) Spatial preference heterogeneity: a choice experiment. Land Econ 86(3):552–568
Burton M, Rigby D (2009) Hurdle and latent class approaches to serial non-participation in choice models. Environ Resource Econ 42(2):211–226
Carson RT, Groves T (2007) Incentive and informational properties of preference questions. Environ Resource Econ 37(1):181–210
Chen HZ, Cosslett SR (1998) Environmental quality preference and benefit estimation in multinomial probit models: a simulation approach. Am J Agric Econ 80(3):512–520
Dillman DA (1978) Mail and telephone surveys: the total design method, vol 19. Wiley, New York
Dillman DA (2011) Mail and Internet surveys: the tailored design method–2007 update with new Internet, visual, and mixed-mode guide. Wiley, Hoboken
Fabrigar LR, Wegener DT, MacCallum RC, Strahan EJ (1999) Evaluating the use of exploratory factor analysis in psychological research. Psychol Methods 4(3):272
Glenk K, Martin-Ortega J, Pulido-Velazquez M, Potts J (2015) Inferring attribute non-attendance from discrete choice experiments: implications for benefit transfer. Environ Resource Econ 60(4):497–520
Greene WH, Hensher DA (2003) A latent class model for discrete choice analysis: contrasts with mixed logit. Transp Res Part B: Methodol 37(8):681–698
Hanemann WM (1982) Applied welfare analysis with qualitative response models. Department of Agricultural & Resource Economics, UCB
Hanemann WM (1984) Welfare evaluations in contingent valuation experiments with discrete responses. Am J Agric Econ 66(3):332–341
Johnston RJ, Russell M (2011) An operational structure for clarity in ecosystem service values. Ecol Econ 70(12):2243–2249
Johnston RJ, Ramachandran M (2014) Modeling spatial patchiness and hot spots in stated preference willingness to pay. Environ Resource Econ 59(3):363–387
Johnston RJ, Jarvis D, Wallmo K, Lew DK (2015) Multiscale spatial pattern in nonuse willingness to pay: applications to threatened and endangered marine species. Land Econ 91(4):739–761
Jorgensen BS, Syme GJ, Bishop BJ, Nancarrow BE (1999) Protest responses in contingent valuation. Environ Resource Econ 14(1):131–150
Kafle A, Swallow SK, Smith EC (2015) Does public funding affect preferred tradeoffs and crowd-in or crowd-out willingness to pay? A watershed management case. Environ Resource Econ 60(3):471–495
Kahneman D, Knetsch JL, Thaler RH (1991) Anomalies: the endowment effect, loss aversion, and status quo bias. J Econ Perspect 5(1):193–206
Layton DF, Brown G (2000) Heterogeneous preferences regarding global climate change. Rev Econ Stat 82(4):616–624
McCutcheon AL (1987) Latent class analysis, vol 64. Sage, New York
McFadden D (1973) Conditional logit analysis of qualitative choice models. In: Zarembka P (ed) Frontiers of econometrics. Academic Press, New York
Meyerhoff J, Liebe U (2008) Do protest responses to a contingent valuation question and a choice experiment differ? Environ Resource Econ 39(4):433–446
Meyerhoff J, Liebe U (2009) Status quo effect in choice experiments: empirical evidence on attitudes and choice task complexity. Land Econ 85(3):515–528
Meyerhoff J, Liebe U (2010) Determinants of protest responses in environmental valuation: a meta-study. Ecol Econ 70(2):366–374
Revelt D, Train K (1998) Mixed logit with repeated choices: households' choices of appliance efficiency level. Rev Econ Stat 80(4):647–657
Samuelson W, Zeckhauser R (1988) Status quo bias in decision making. J Risk Uncertain 1(1):7–59
Scarpa R, Thiene M (2005) Destination choice models for rock climbing in the Northeastern Alps: a latent-class approach based on intensity of preferences. Land Econ 81(3):426–444
Scarpa R, Zanoli R, Bruschi V, Naspetti S (2012) Inferred and stated attribute non-attendance in food choice experiments. Am J Agr Econ 95(1):165–180
Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464
Shapiro JM (2016) Special interests and the media: theory and an application to climate change. J Public Econ 144:91–108
Swait J (1994) A structural equation model of latent segmentation and product choice for cross-sectional revealed preference choice data. J Retail Consum Serv 1(2):77–89
Swallow SK, Weaver T, Opaluch JJ, Michelman TS (1994) Heterogeneous preferences and aggregation in environmental policy analysis: a landfill siting case. Am J Agric Econ 76(3):431–443
Train KE (1995) Simulation methods for probit and related models based on convenient error partitioning. Department of Economics, UCB
Train KE (1998) Recreation demand models with taste variation over people. Land Econ 74(2):230–239
U.S. Census Bureau (2011) 2010 Census redistricting data (Public Law 94–171) summary file. https://www.census.gov/data/datasets/2010/dec/redistricting-file-pl-94-171.html.
US Census Bureau (2012) American Community Survey (ACS) and Puerto Rico Community Survey (PRCS), 5-year estimates. United States Census Bureau, Suitland, Maryland
von Haefen RH, Massey DM, Adamowicz WL (2005) Serial non-participation in repeated discrete choice models. Am J Agric Econ 87(4):1061–1076
Vuong QH (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econ J Econ Soc 57(2):307–333
Yue IT (2017) Coastal protection, environmental change, and the heterogeneity of preferences: a case study of the eastern shore of Virginia. Thesis submitted in partial fulfillment of the M.S., University of Connecticut, Storrs, CT. Retrieved July 20, 2019, from https://opencommons.uconn.edu/cgi/viewcontent.cgi?article=2176&context=gs_theses
Acknowledgements
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.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
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 77, 35–67 (2020). https://doi.org/10.1007/s10640-020-00434-z
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10640-020-00434-z