# A Latent Class Nested Logit Model for Rank-Ordered Data with Application to Cork Oak Reforestation

## Abstract

We analyze stated ranking data collected from recreational visitors to the Alcornocales Natural Park (ANP) in Spain. The ANP is a large protected area which comprises mainly cork oak woodlands. The visitors ranked cork oak reforestation programs delivering different sets of environmental (reforestation technique, biodiversity, forest surface) and social (jobs and recreation sites created) outcomes. We specify a novel latent class nested logit model for rank-ordered data to estimate the distribution of willingness-to-pay for each outcome. Our modeling approach jointly exploits recent advances in discrete choice methods. The results suggest that prioritizing biodiversity would increase certainty over public support for a reforestation program. In addition, a substantial fraction of the visitor population are willing to pay more for the social outcomes than the environmental outcomes, whereas the existing reforestation subsidies are often justified by the environmental outcomes alone.

## Keywords

Discrete choice Stated preference Willingness-to-pay Forest Land use## JEL Classification

C33 C35 C51 Q23 Q51 Q57## Notes

### Acknowledgments

We thank Alejandro Caparrós and Pablo Campos for allowing us to access the data used in this study. We wish to thank Editor Christian Vossler and two anonymous referees for helpful and constructive comments. All views expressed herein are our own.

**Funding** Oviedo’s involvement in this study was funded by the Spanish Ministry of Economy and Competitiveness (VEABA ECO2013-42110-P, I + D National Plan).

### Compliance with Ethical Standards

### Conflict of interest

We declare that we have no conflict of interest.

## Supplementary material

## References

- Akaich F, Nayga RM, Gil JM (2013) Are results from non-hypothetical choice-based conjoint analyses and non-hypothetical recoded-ranking conjoint analyses similar? Am J Agric Econ 95:946–963Google Scholar
- Barberá S, Pattanaik PK (1986) Falmagne and the rationalizability of stochastic choices in terms of random orderings. Econometrica 54:707715CrossRefGoogle Scholar
- Bateman IJ, Mace GM, Fezzi C, Atkinson G, Turner K (2011) Economic analysis for ecosystem service assessments. Environ Resour Econ 48:177–218CrossRefGoogle Scholar
- Beggs S, Cardell S, Hausman J (1981) Assessing the potential demand for electric cars. J Econ 17:1–19CrossRefGoogle Scholar
- Ben-Akiva M, Morikawa T, Shiroish F (1992) Analysis of the reliability of preference ranking data. J Bus Res 24:149–164CrossRefGoogle Scholar
- Ben-Akiva M, Lerman SR (1985) Discrete choice analysis: theory and application to travel demand. MIT Press, CambridgeGoogle Scholar
- Berry S, Levinsohn J, Pakes A (2004) Differentiated products demand system from a combination of micro and macro data. J Polit Econ 112:68–105CrossRefGoogle Scholar
- Bhat C (1997) An endogenous segmentation mode choice model with an application to intercity travel. Transp Sci 31:34–48CrossRefGoogle Scholar
- Boyle KJ, Holmes TP, Teisl MF, Roe B (2001) A comparison of conjoint analysis response formats. Am J Agric Econ 83:441–454CrossRefGoogle Scholar
- Calfee J, Winston C, Stempski R (2001) Econometric issues in estimating consumer preferences from stated preference data: a case study of the value of automobile travel time. Rev Econ Stat 83:699–707CrossRefGoogle Scholar
- Cameron TA, Poe GL, Ethier RG, Schulze WD (2002) Alternative non-market value-elicitation methods: are the underlying preferences the same? J Environ Econ Manag 34:391–425CrossRefGoogle Scholar
- Caparrós A, Campos P, Montero G (2003) An operative framework for total Hicksian income measurement: application to a multiple use forest. Environ Resour Econ 26:173–198CrossRefGoogle Scholar
- Caparrós A, Oviedo JL, Campos P (2008) Would you choose your preferred option? Comparing choice and recoded ranking experiments. Am J Agric Econ 90:843–855CrossRefGoogle Scholar
- Carson RT, Groves T (2007) Incentive and information properties of preference questions. Environ Resour Econ 37:181–210CrossRefGoogle Scholar
- Chang JB, Luck JL, Norwood (2009) How closely do hypothetical surveys and laboratory experiments predict field behavior? Am J Agric Econ 91:518534CrossRefGoogle Scholar
- Chapman RG, Staelin R (1982) Exploiting rank ordered choice set data within the stochastic utility model. J Mark Res 19:288–301CrossRefGoogle Scholar
- Claassen R, Hellerstein D, Kim SG (2013) Using mixed logit in land use models: can expectation-maximization (EM) algorithms facilitate estimation? Am J Agric Econ 95:419–425CrossRefGoogle Scholar
- Clark SL, Muthén B (2009) Relating latent class analysis results to variables not included in the analysis. mimeo. https://www.statmodel.com/download/relatinglca. Cited 24 Mar 2015
- Dagsvik JK, Liu G (2009) A framework for analyzing rank-ordered data with application to automobile demand. Transp Res A 43:1–12CrossRefGoogle Scholar
- Doblas-Miranda E, Martínez-Vilalta J, Lloret F, Álvarez A, Ávila A, Bonet FJ, Brotons L, Castro J, Curiel Yuste J, Díaz M, Ferrandis P, Garca-Hurtado E, Iriondo JM, Keenan TF, Latron J, Llusiá J, Loepfe L, Mayol M, Moré G, Moya D, Peñuelas J, Pons X, Poyatos R, Sardans J, Sus O, Vallejo VR, Vayreda J, Retana J (2014) Reassessing global change research priorities in Mediterranean terrestrial ecosystems: how far have we come and where do we go from here? Glob Ecol Biogeogr 24:25–43CrossRefGoogle Scholar
- Duke JM, Ilvento TW (2004) A conjoint analysis of public preferences for agricultural land preservation. Agric Resour Econ Rev 33:209–219CrossRefGoogle Scholar
- European Commission (2014) Comission Regulation (EU) N0 702/2014 of 25 June 2014. Off J Eur Union 57:193Google Scholar
- Falmagne JC (1978) A representation theorem for finite scale systems. J Math Psychol 18:5272CrossRefGoogle Scholar
- Fok D, Paap R, Van Dijk B (2012) A rank-ordered logit model with unobserved heterogeneity in ranking capabilities. J Appl Econ 27:831–846CrossRefGoogle Scholar
- Giergiczny M, Hess S, Dekker T, Chintakayala PK (2013) Testing the consistency (or lack thereof) between choices in best-worst surveys. Paper presented at the 3rd international choice modelling conference, Sydney, 3–5 July 2013Google Scholar
- Hausman J, Ruud P (1987) Specifying and testing econometric models for rank-ordered data. J Econ 34:83–104CrossRefGoogle Scholar
- Heckman J, Singer B (1984) A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica 52:271–320CrossRefGoogle Scholar
- Herriges J, Kling C, Liu C-C, Tobias J (2010) What are the consequences of consequentiality? J Environ Econ Manag 59:6781CrossRefGoogle Scholar
- Herriges JA, Phaneuf DJ (2002) Inducing patterns of correlation and substitution in repeated logit models of recreation demand. Am J Agric Econ 84:1076–1090CrossRefGoogle Scholar
- Hess S, Ben-Akiva M, Gopinath D, Walker J (2011) Advantages of latent class over continuous mixture of logit models. mimeo. http://www.stephanehess.me.uk/papers/Hess_Ben-Akiva_Gopinath_Walker_May_2011. Cited 3 Mar 2016
- Hole AR (2015) MIXLOGITWTP: Stata module to estimate mixed logit models in WTP space. Statistical Software Components S458037, Boston College, Department of EconomicsGoogle Scholar
- Hoyos D, Mariel P, Pascual U, Etxano I (2012) Valuing a Natura 2000 Network site to inform land use options using a discrete choice experiment: an Illustration from the Basque Country. J For Econ 18:329–344Google Scholar
- Huber R, Hunziker M, Lehmann B (2011) Valuation of agricultural land-use scenarios with choice experiments: a political market share approach. J Environ Plan Manag 54:93–113CrossRefGoogle Scholar
- Johnson KA, Polasky S, Nelson E, Pennington D (2012) Uncertainty in ecosystem services valuation and implications for assessing land use tradeoffs: an agricultural case study in the Minnesota River Basin. Ecol Econ 79:71–79CrossRefGoogle Scholar
- Keane MP, Wasi N (2013) Comparing alternative models of heterogeneity in consumer choice behavior. J Appl Econ 28:1018–1045Google Scholar
- Krawczyk M (2012) Testing for hypothetical bias in willingness to support a reforestation program. J For Econ 18:282–289Google Scholar
- Layton DF (2000) Random coefficient models for stated preference surveys. J Environ Econ Manag 40:21–36CrossRefGoogle Scholar
- Layton DF, Brown G (2000) Heterogeneous preferences regarding global climate change. Rev Econ Stat 82:616–624CrossRefGoogle Scholar
- Layton DF, Lee ST (2006a) From ratings to rankings: the econometric analysis of stated preference ratings data. In: Halvorsen R, Layton DF (eds) Explorations in environmental and natural resource economics: essays in honor of Gardner M. Brown, Jr. Edward Elgar Publishing, CheltenhamGoogle Scholar
- Layton DF, Lee ST (2006b) Embracing model uncertainty: strategies for response pooling and model averaging. Environ Resour Econ 34:51–85CrossRefGoogle Scholar
- Layton DF, Levine RA (2003) How much does the far future matter? A hierarchical Bayesian analysis of the public’s willingness to mitigate ecological impacts of climate change. J Am Stat Assoc 98:533–544CrossRefGoogle Scholar
- Loomis J (2005) Economic values without prices: the importance of nonmarket values and valuation for informing public policy debates. Choices 20:179–182Google Scholar
- Louviere JJ, Flynn TN, Marley AAJ (2015) Best-worst scaling: theory, methods and applications. Cambridge University Press, CambridgeCrossRefGoogle Scholar
- McFadden D (1974) Conditional logit analysis of qualitative choice behavior. In: Zarembka P (ed) Frontiers in econometrics. Academic Press, New YorkGoogle Scholar
- McFadden D (1978) Modeling the choice of residential location. In: Karlqvist A, Lundqvist L, Snickars F, Weibull J (eds) Spatial interaction theory and planning models. North Holland, AmsterdamGoogle Scholar
- McFadden D (1986) The choice theory approach to market research. Mark Sci 5:275297CrossRefGoogle Scholar
- McFadden D, Train KE (2000) Mixed MNL models of discrete response. J Appl Econ 15:447–470CrossRefGoogle Scholar
- Mogas J, Riera P, Bennett J (2006) A comparison of contingent valuation and choice modeling with second-order interactions. J For Econ 12:5–30Google Scholar
- Nunes PALD, Schokkaert E (2003) Identifying the warm glow effect in contingent valuation. J Environ Econ Manag 45:231–245CrossRefGoogle Scholar
- Othman J, Rahajeng A (2013) Economic valuation of Jogjakarta’s tourism attributes: a contingent ranking analysis. Tour Econ 19:187–201CrossRefGoogle Scholar
- Ovando P, Campos P, Montero G (2007) Forestaciones con Encinas y Alcornoques en el Área de la Dehesa en el Marco del Reglamento (CEE) 2080/92 (1993–2000). Rev Española Estudio Agrosoc Pesq 214:173–186Google Scholar
- Pacifico D, Yoo HI (2013) lclogit: a Stata command for fitting latent-class conditional logit models via the expectation-maximization algorithm. Stata J 13:625–639Google Scholar
- Resano H, Sanjuan AI, Albisu LM (2012) Consumers response to the EU Quality policy allowing for heterogeneous preferences. Food Policy 37:355365CrossRefGoogle Scholar
- Santos T, Tellería JL, Díaz M, Carbonell R (2006) Evaluating the benefits of CAP reforms: can afforestations restore bird diversity in Mediterranean Spain? Basic Appl Ecol 7:483–495CrossRefGoogle Scholar
- Scachar R, Nalebuff B (2004) Verifying the solution from a nonlinear solver: a case study: a comment. Am Econ Rev 94:382–390CrossRefGoogle Scholar
- Scarpa R, Thiene M, Train KE (2008) Utility in willingness-to-pay space: a tool to address confounding random scale effects in destination choice to the Alps. Am J Agric Econ 90:994–1010CrossRefGoogle Scholar
- Scarpa R, Notaro S, Louviere J, Raffaelli R (2011) Exploring scale effects of best/worst rank ordered choice data to estimate benefits of tourism in Alpine Grazing Commons. Am J Agric Econ 93:813–828CrossRefGoogle Scholar
- Schulz N, Breustedt G, Latacz-Lohman U (2013) Assessing farmers’ willingness to accept “greening”: insights from a discrete choice experiment in Germany. J Agric Econ 65:26–48CrossRefGoogle Scholar
- Train KE (2008) EM algorithms for nonparametric estimation of mixing distributions. J Choice Model 1:40–69CrossRefGoogle Scholar
- Train KE (2009) Discrete choice methods with simulation, 2nd edn. Cambridge University Press, New YorkCrossRefGoogle Scholar
- Train KE, Weeks M (2005) Discrete choice models in preference space and willingness-to-pay space. In: Alberini A, Scarpa R (eds) Applications of simulation methods in environmental resource economics. Springer, DordrechtGoogle Scholar
- Train KE, Winston C (2007) Vehicle choice behavior and the declining market share of U.S. automakers. Int Econ Rev 48:1469–1496CrossRefGoogle Scholar
- Varela E, Giergiczny M, Riera P, Mahieu P-A, Soliño M (2014) Social preferences for fuel break management programs in Spain: a choice modelling application to prevention of forest fires. Int J Wildland Fire 23(2):281–289CrossRefGoogle Scholar
- Vossler CA, Doyon M, Rondeau D (2012) Truth in consequentiality: theory and field evidence on discrete choice experiments. Am Econ J Microecon 4:145–171CrossRefGoogle Scholar
- Vossler CA, Evans MF (2009) Bridging the gap between the field and the lab: environmental goods, policy maker input, and consequentiality. J Environ Econ Manag 58:338–345CrossRefGoogle Scholar
- Vossler CA, Watson SB (2013) Understanding the consequences of consequentiality: testing the validity of stated preferences in the field. J Econ Behav Organ 86:137–147CrossRefGoogle Scholar
- Wustemann H, Meyerhoff J, Ruhs M, Schafer A, Hartje V (2014) Financial costs and benefits of a program of measures to implement a national strategy on biological diversity in Germany. Land Use Policy 36:307–318CrossRefGoogle Scholar
- Yan J, Yoo HI (2014) The seeming unreliability of rank-ordered data as a consequence of model misspecification. MPRA Paper No. 56285. https://mpra.ub.uni-muenchen.de/56285/. Cited 3 Mar 2016
- Yoo HI, Doiron D (2013) The use of alternative preference elicitation methods in complex discrete choice experiments. J Health Econ 32:1166–1179CrossRefGoogle Scholar