Environmental and Resource Economics

, Volume 50, Issue 1, pp 83–110 | Cite as

A Joint Latent-Class Model: Combining Likert-Scale Preference Statements With Choice Data to Harvest Preference Heterogeneity

  • William S. Breffle
  • Edward R. Morey
  • Jennifer A. Thacher


In addition to choice questions (revealed and stated choices), preference surveys typically include other questions that provide information about preferences. Preference-statement data include questions on the importance of different attributes of a good or the extent of agreement with a particular statement. The intent of this paper is to model and jointly estimate preference heterogeneity using stated-preference choice data and preference-statement data. The starting point for this analysis is the belief that the individual has preferences, and both his/her choices and preference statements are manifestations of those preferences. Our modeling contribution is linking the choice data and preference-statement data in a latent-class framework. Estimation is straightforward using the E-M algorithm, even though our model has hundreds of preference parameters. Our estimates demonstrate that: (1) within a preference class, the importance anglers associate with different Green Bay site characteristics is in accordance with their responses to the preference statements; (2) estimated across-class utility parameters for fishing Green Bay are affected by the preference-statement data; (3) estimated across-class preference-statement response probabilities are affected by the inclusion of the choice data; and (4) both data sets influence the number of classes and the probability of belonging to a class as a function of the individual’s type.


Latent class E-M algorithm Choice data Preference statements Likert-scale Preferences Heterogeneity 


E-M algorithm

Expectation-maximization algorithm




Fish consumption advisory


Marginal willingness-to-pay


Stated preference


Revealed preference


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adamowicz W, Louviere J, Williams M (1994) Combining revealed and stated preference methods for valuing environmental amenities. J Environ Econ Manag 26: 271–271CrossRefGoogle Scholar
  2. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automat Contr 19: 716–723CrossRefGoogle Scholar
  3. Aldrich G, Grimsrud K, Thacher J, Kotchen M (2006) Relating environmental attitudes and contingent values: how robust are methods for identifying heterogeneous groups? Environ Resour Econ doi: 10.1007/s10640-006-9054-7
  4. Bartholomew D, Leung S (2002) A goodness of fit test for sparse 2p contingency tables. Br J Math Stat Psychol 55(1): 1–15CrossRefGoogle Scholar
  5. Ben-Akiva M, Morikawa T (1990) Estimation of travel demand models from multiple data sources. In: Koshi M (eds) Transportation and traffic theory. Elsevier, New YorkGoogle Scholar
  6. Ben-Akiva M, Walker M, Bernardino A, Gopinath D, Morikawa T, Polydoropoulos A (2002) Integration of choice and latent variable models. In: Mahmassani H (eds) Perpetual motion: travel behavior research opportunities and application challenges. Pergamon, OxfordGoogle Scholar
  7. Boxall P, Adamowicz W (2002) Understanding heterogeneous preferences in random utility models: a latent class approach. Environ Resour Econ 23(4): 421–446CrossRefGoogle Scholar
  8. Bozdogan H (1987) Model selection and Akaike’s information criterion (AIC): the general theory and its analytical extensions. Psychometrika 52: 345–370CrossRefGoogle Scholar
  9. Breffle W, Morey E, Rowe R, Waldman D, Wytinck S (1999) Recreational fishing damages from fish consumption advisories in the waters of Green Bay. Technical report, Prepared by Stratus Consulting for US Fish and Wildlife ServiceGoogle Scholar
  10. Breffle W, Rowe R (2002) Comparing choice question formats for evaluating natural resource tradeoffs. Land Econ 78(2): 65–82CrossRefGoogle Scholar
  11. Cameron T (1992) Combining contingent valuation and travel cost data for the valuation of nonmarket goods. Land Econ 68(3): 302–317CrossRefGoogle Scholar
  12. Choi A, Papandrea F, Bennett J (2007) Assessing cultural values: developing an attitudinal scale. J Cult Econ 31(4): 311–335CrossRefGoogle Scholar
  13. Colombo S, Hanley N (2007) Modelling preference heterogeneity in stated choice data for environmental goods: a comparison of random parameter, covariance heterogeneity and latent class logit models. EAERE Annual Conference, Thessalonica, Greece, pp 27–30Google Scholar
  14. Cunha-e-Sá M, Madureira L, Nunes L, and Otrachshenko V (2010) Protesting or justifying? A latent-class model for contingent valuation with attitudinal data. Working paperGoogle Scholar
  15. Dempster A, Laird N, Rubin D (1977) Maximum likelihood from incomplete observations. J R Stat Soc Ser B 39: 1–38Google Scholar
  16. Dupont D (2004) Do children matter? An examination of gender difference in environmental valuation. Ecol Econ 49: 273–286CrossRefGoogle Scholar
  17. Eid M, Langeheine R, Diener E (2003) Comparing typological structures across cultures by multigroup latent class analysis - a primer. J Cross Cult Psychol 34(2): 195–210CrossRefGoogle Scholar
  18. Formann A (2003) Latent class model diagnostics—a review and some proposals. Comput Stat Data Anal 41: 549–559CrossRefGoogle Scholar
  19. GAUSS: (2000) Manual. Aptech Systems Inc, Maple Valley, WAGoogle Scholar
  20. Greene W, Hensher D (2003) A latent class model for discrete choice analysis: contrasts with mixed logit. Transp Res B Methodol 37(8): 681–698CrossRefGoogle Scholar
  21. Hensher D, Bradley M (1993) Using stated response choice data to enrich revealed preference discrete choice models. Market Lett 4(2): 139–151CrossRefGoogle Scholar
  22. Hurvich M, Tsai C (1989) Regression and time series model selection in small samples. Biometrika 76(2): 297–307CrossRefGoogle Scholar
  23. Johnson R, Swallow S, Bauer D, Anderson C (2003) Resource economics review. Agric Resour Econ Rev 32(1): 65–82Google Scholar
  24. Kemperman A, Timmermans H (2006) Preferences, benefits, and park visits: a latent class segmentation analysis. Tour Anal 11(4): 221–230CrossRefGoogle Scholar
  25. Kritzberg D, Morey E (2008) It’s not where you do it, but who you do it with? A companion and their relative ability as characteristics in site-specific recreational demand models. Working PaperGoogle Scholar
  26. Lynne G and Rola L (1988) Improving attitude-behavior prediction models with economic variables: farmer actions toward soil conservation. J Soc Psychol 24(1)Google Scholar
  27. Maydeu-Olivares A, Joe H (2005) Limited-and full-information estimation and goodness-of-fit testing in [2. Sup. N] contingency tables: a unified framework. J Am Stat Assoc 100(471): 1009–1021CrossRefGoogle Scholar
  28. McCutcheon A (1987) Sexual morality, pro-life values, and attitudes toward abortion - a simultaneous latent structure analysis for 1978-1983. Sociol Methods Res 16(2): 256–275CrossRefGoogle Scholar
  29. McFadden D (1986) The choice theory approach to market research. Marketing Science 5(4): 275–297CrossRefGoogle Scholar
  30. Morey E, Thacher J, Breffle W (2006) Using angler characteristics and attitudinal data to identify environmental preference classes: a latent-class model. Environ Resour Econ 34(1): 91–115CrossRefGoogle Scholar
  31. Morey E, Thiene M, De Salvo M, Signorello G (2008) Using attitudinal data to identify latent classes that vary in their preference for landscape preservation. Ecol Econ 68(1–2): 536–546CrossRefGoogle Scholar
  32. Morikawa T, Ben-Akiva M, McFadden D (2002) Discrete choice models incorporating revealed preference and psychometric data. In: PH F, Montgomery A (eds) Economic models in marketing, vol 16. Elsevier Science, OxfordGoogle Scholar
  33. Owen A, Videras J (2007) Culture and public goods: the case of religion and the voluntary provision of environmental quality. J Environ Econ Manag 54(2): 162–180CrossRefGoogle Scholar
  34. Patunru A, Braden J, and Chattopadhyay S (2007) Who cares about environmental stigmas and does it matter? A latent segmentation analysis of stated preferences for real estate. Am J Agric Econ 1–15. doi: 10.1111/j.1467-8276.2007.00988
  35. Provencher B, Baerenklau K, Bishop R (2002) A finite mixture logit model of recreational angling with serially correlated random utility. Am J Agric Econ 84(4): 1066–1075CrossRefGoogle Scholar
  36. R Development Core Team (2005) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
  37. Reiser M and Lin Y (1999) A goodness of fit test for the latent class model when expected frequencies are small. Sociol Methodol 81–111Google Scholar
  38. Scarpa R, Thiene M (2005) Destination choice models for rock-climbing in the North-East Alps: a latent-class approach investigating intensity of preferences. Land Econ 81(3): 426–444Google Scholar
  39. Scarpa R, Willis K, Acutt M (2005) Individual-specific welfare measures for public goods: a latent class approach to residential customers of Yorkshire water. In: Koundouri (ed) Econometrics informing natural resource management. Edward Elgar Publisher, AldershotGoogle Scholar
  40. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6: 461–464CrossRefGoogle Scholar
  41. Smith V (2009) Personal communication on combining data types. personal emailGoogle Scholar
  42. Swait J, Sweeney J (2000) Perceived value and its impact on choice behavior in a retail setting. J Retail Consum Services 7(2): 77–88CrossRefGoogle Scholar
  43. Thacher J, Morey E, Craighead E (2005) Using patient characteristics and attitudinal data to identify treatment preference groups: a latent-class model. Depress Anxiety 21(2): 47–54CrossRefGoogle Scholar
  44. Timmins C, Murdock J (2007) A revealed preference approach to the measurement of congestion in travel cost models. J Environ Econ Manag 53: 230–249CrossRefGoogle Scholar
  45. Train K (2003) Discrete choice methods with simulation, 1st edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  46. Vermunt J, Magidson J (2003) Latent GOLD choice. Statistical Innovations, BelmontGoogle Scholar
  47. Vermunt J, Magidson J (2005) Latent GOLD. Statistical Innovations, BelmontGoogle Scholar
  48. Ward K, Stedman R, Luloff A, Shortle J, Finley J (2008) Categorizing deer hunters by typologies useful to game managers: A latent-class model. Soc Nat Resour 21(3): 215–229CrossRefGoogle Scholar
  49. Wedel M, Kamakura W (2000) Market segmentation: conceptual and methodological foundations, second edition. Kluwer, BostonGoogle Scholar
  50. Yang CC, Yang CC (2007) Separating latent classes by information criteria. J Classif 24: 183–203CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • William S. Breffle
    • 1
  • Edward R. Morey
    • 2
  • Jennifer A. Thacher
    • 3
  1. 1.School of Business and EconomicsMichigan Technological UniversityHoughtonUSA
  2. 2.Department of EconomicsUniversity of Colorado-BoulderBoulderUSA
  3. 3.Department of EconomicsUniversity of New MexicoAlbuquerqueUSA

Personalised recommendations