Hierarchical Maximum Likelihood Parameter Estimation for Cumulative Prospect Theory: Improving the Reliability of Individual Risk Parameter Estimates

References

• Abdellaoui M (2000) Parameter-free elicitation of utility and probability weighting functions. Management Sci. 46(11):1497–1512.Link, Google Scholar
• Barberis NC (2013) Thirty years of prospect theory in economics: A review and assessment. J. Econom. Perspect. 27(1):173–195.Crossref, Google Scholar
• Birnbaum MH (1999) The paradoxes of Allais, stochastic dominance, and decision weights. Shanteau J, Mellers BA, Schum DA, eds. Decision Science and Technology (Springer, New York), 27–52.Crossref, Google Scholar
• Birnbaum MH, Chavez A (1997) Tests of theories of decision making: Violations of branch independence and distribution independence. Organ. Behav. Human Decision Processes 71(2):161–194.Crossref, Google Scholar
• Bruhin A, Fehr-Duda H, Epper T (2010) Risk and rationality: Uncovering heterogeneity in probability distortion. Econometrica 78(4):1375–1412.Crossref, Google Scholar
• Camerer CF (1995) Individual decision making. Kagel JH, Roth AE, eds. The Handbook of Experimental Economics (Princeton University Press, Princeton, NJ), 587–703.Google Scholar
• Camerer CF (2004) Prospect theory in the wild: Evidence from the field. Camerer CF, Loewenstein G, Rabin M, eds. Advances in Behavioral Economics (Princeton University Press, Princeton, NJ), 148–161.Crossref, Google Scholar
• Camerer CF, Ho T-H (1994) Violations of the betweenness axiom and nonlinearity in probability. J. Risk Uncertainty 8(2):167–196.Crossref, Google Scholar
• Cavagnaro DR, Gonzalez R, Myung JI, Pitt MA (2013) Optimal decision stimuli for risky choice experiments: An adaptive approach. Management Sci. 59(2):358–375.Link, Google Scholar
• Conte A, Hey JD, Moffatt PG (2011) Mixture models of choice under risk. J. Econometrics 162(1):79–88.Crossref, Google Scholar
• Edwards W (1954) The theory of decision making. Psych. Bull. 51(4):380–417.Crossref, Google Scholar
• Engelmann JB, Tamir D (2009) Individual differences in risk preference predict neural responses during financial decision-making. Brain Res. 1290:28–51.Crossref, Google Scholar
• Farrell S, Ludwig CJH (2008) Bayesian and maximum likelihood estimation of hierarchical response times. Psychonomic Bull. Rev. 15(6):1209–1217.Crossref, Google Scholar
• Fehr-Duda H, Epper T (2012) Probability and risk: Foundations and economic implications of probability-dependent risk preferences. Ann. Rev. Econom. 4(1):567–593.Crossref, Google Scholar
• Figner B, Murphy RO (2010) Using skin conductance in judgment and decision making research. Schulte-Mecklenbeck M, Kuehberger A, Ranyard R, eds. A Handbook of Process Tracing Methods for Decision Research: A Critical Review and User’s Guide (Psychology Press, New York), 163–184.Google Scholar
• Fox CR, Erner C, Walters DJ (2015) Decision under risk: From the field to the laboratory and back. The Wiley Blackwell Handbook of Judgment and Decision Making (John Wiley & Sons, Chichester, West Sussex, UK), 43–88.Crossref, Google Scholar
• Gächter S, Johnson EJ, Herrmann A (2007) Individual-level loss aversion in risky and riskless choice. IZA Discussion Paper 2961, Institute for the Study of Labor, Bonn, Germany.Google Scholar
• Glöckner A, Pachur T (2012) Cognitive models of risky choice: Parameter stability and predictive accuracy of prospect theory. Cognition 123(1):21–32.Crossref, Google Scholar
• Goldstein WM, Einhorn HJ (1987) Expression theory and the preference reversal phenomena. Psych. Rev. 94(2):236–254.Crossref, Google Scholar
• Gonzalez R, Wu G (1999) On the shape of the probability weighting function. Cognitive Psych. 38(1):129–166.Crossref, Google Scholar
• Harless DW, Camerer CF (1994) The predictive utility of generalized expected utility theories. Econometrica 62(6):1251–1289.Crossref, Google Scholar
• Harrison GW, Rutström EE (2008) Risk aversion in the laboratory. Cox J, Harrison G, eds. Risk Aversion in Experiments, Research in Experimental Economics, Vol. 12 (Emerald Group Publishing Limited, Bingley, UK), 41–196.Crossref, Google Scholar
• Harrison GW, Rutström EE (2009) Expected utility theory and prospect theory: One wedding and a decent funeral. Experiment. Econom. 12(2):133–158.Crossref, Google Scholar
• Hey JD, Orme C (1994) Investigating generalizations of the expected utility theory using experimental data. Econometrica 62(6):1291–1326.Crossref, Google Scholar
• Holt CA, Laury SK (2002) Risk aversion and incentive effects. Amer. Econom. Rev. 92(5):1644–1655.Crossref, Google Scholar
• Huettel SA, Stowe CJ, Gordon EM, Warner BT, Platt ML (2006) Neural signatures of economic preferences for risk and ambiguity. Neuron 49(5):765–775.Crossref, Google Scholar
• Ingersoll J (2008) Non-monotonicity of the Tversky-Kahneman probability-weighting function: A cautionary note. Eur. Financial Management 14(3):385–390.Crossref, Google Scholar
• Kahneman D, Tversky A (1979) Prospect theory: An analysis of decision under risk. Econometrica 47(2):263–291.Crossref, Google Scholar
• Kahneman D, Tversky A (2000) Choices, values and frames. Kahneman D, Tversky A, eds. Choices, Values and Frames (Cambridge University Press, Cambridge, UK), 1–16.Crossref, Google Scholar
• Karmarkar US (1979) Subjectively weighted utility and the Allais paradox. Organ. Behav. Human Performance 24(1):67–72.Crossref, Google Scholar
• Knight FH (1921) Risk, Uncertainty, and Profit (Houghton Mifflin Company, Chicago).Crossref, Google Scholar
• Köbberling V, Wakker PP (2005) An index of loss aversion. J. Econom. Theory 122(1):119–131.Crossref, Google Scholar
• Lewandowsky S, Farrell S (2010) Computational Modeling in Cognition: Principles and Practice (Sage, Los Angeles).Google Scholar
• Lichtenstein S, Slovic P (1971) Reversals of preference between bids and choices in gambling decisions. J. Experiment. Psych. 89(1):46–55.Crossref, Google Scholar
• Lichtenstein S, Slovic P (2006) The Construction of Preference (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Loomes G, Sugden R (1995) Incorporating a stochastic element into decision theories. Eur. Econom. Rev. 39(3):641–648.Crossref, Google Scholar
• Lopes LL (1983) Some thoughts on the psychological concept of risk. J. Experiment. Psych. Human Perception Performance 9(1):137–144.Crossref, Google Scholar
• Luce RD (1959) Individual Choice Behavior: A Theoretical Analysis (John Wiley & Sons, New York).Google Scholar
• Luce RD, Raiffa H (1957) Games and Decisions: Introduction and Critical Survey (John Wiley & Sons, New York).Google Scholar
• Luce RD, Suppes P (1965) Preference, utility, and subjective probability. Luce RD, Bush RR, Galante E, eds. Handbook of Mathematical Psychology (John Wiley & Sons, New York), 249–410.Google Scholar
• McFadden D (1980) Econometric models for probabilistic choice among products. J. Bus. 53(3):S13–S29.Crossref, Google Scholar
• Mosteller F, Nogee P (1951) An experimental measurement of utility. J. Political Econom. 59(5):371–404.Crossref, Google Scholar
• Nelder JA, Mead R (1965) A simplex method for function minimization. Comput. J. 7(4):308–313.Crossref, Google Scholar
• Nilsson H, Rieskamp J, Wagenmakers EJ (2011) Hierarchical Bayesian parameter estimation for cumulative prospect theory. J. Math. Psych. 55(1):84–93.Crossref, Google Scholar
• Parducci A (1995) Happiness, Pleasure, and Judgment: The Contextual Theory and Its Applications (Psychology Press, New York).Google Scholar
• Payne JW, Bettman JR, Johnson EJ (1992) Behavioral decision research: A constructive processing perspective. Ann. Rev. Psych. 43(1):87–131.Crossref, Google Scholar
• Pitt MA, Myung IJ (2002) When a good fit can be bad. Trends in Cognitive Sci. 6(10):421–425.Crossref, Google Scholar
• Prelec D (1998) The probability weighting function. Econometrica 66(3):497–527.Crossref, Google Scholar
• Rabin M (2000) Risk aversion and expected-utility theory: A calibration theorem. Econometrica 68(5):1281–1292.Crossref, Google Scholar
• Regenwetter M, Robinson M (2016) The construct-behavior gap in behavioral decision research: A challenge beyond replicability. Working paper, University of Illinois at Urbana–Champaign, Champaign.Google Scholar
• Rieskamp J (2008) The probabilistic nature of preferential choice. J. Experiment. Psych. Learn. Memory Cognition 34(6):1446–1465.Crossref, Google Scholar
• Roberts S, Pashler H (2000) How persuasive is a good fit? A comment on theory testing. Psych. Rev. 107(2):358–367.Crossref, Google Scholar
• Samuelson PA (1938) A note on the pure theory of consumers’ behaviour. Economica 5(17):61–71.Crossref, Google Scholar
• Scheibehenne B, Pachur T (2013) Hierarchical Bayesian modeling: Does it improve parameter stability? Proc. 35th Annual Conf. Cognitive Sci. Soc., Berlin, 1277–1282.Google Scholar
• Scheibehenne B, Pachur T (2015) Using Bayesian hierarchical parameter estimation to assess the generalizability of cognitive models of choice. Psychonomic Bull. Rev. 22(2):391–407.Crossref, Google Scholar
• Schulte-Mecklenbeck M, Pachur T, Murphy RO, Hertwig R (2016) Prospect theory tracks selective allocation of attention. Working paper, Max Planck Institute, Berlin.Google Scholar
• Starmer C (2000) Developments in non-expected utility theory: The hunt for a descriptive theory of choice under risk. J. Econom. Literature 38(2):332–382.Crossref, Google Scholar
• Stevens SS (1957) On the psychophysical law. Psych. Rev. 64(3):153–181.Crossref, Google Scholar
• Stewart N, Chater N, Brown GDA (2006) Decision by sampling. Cognitive Psych. 53(1):1–26.Crossref, Google Scholar
• Stewart N, Chater N, Stott HP, Reimers S (2003) Prospect relativity: How choice options influence decision under risk. J. Experiment. Psych.: General 132(1):23–46.Crossref, Google Scholar
• Stott HP (2006) Cumulative prospect theory’s functional menagerie. J. Risk Uncertainty 32(2):101–130.Crossref, Google Scholar
• Tanaka T, Camerer CF, Nguyen Q (2010) Risk and time preferences: Linking experimental and household survey data from Vietnam. Amer. Econom. Rev. 100(1):557–571.Crossref, Google Scholar
• Toubia O, Johnson EJ, Evgeniou T, Delquié P (2013) Dynamic experiments for estimating preferences: An adaptive method of eliciting time and risk parameters. Management Sci. 59(3):613–640.Link, Google Scholar
• Tversky A, Kahneman D (1992) Advances in prospect theory: Cumulative representations of uncertainty. J. Risk Uncertainty 5(4):297–323.Crossref, Google Scholar
• Varian HR (2006) Revealed preference. Szenberg M, Ramrattan L, Gottesman AA, eds. Samuelsonian Economics and the Twenty-First Century (Oxford University Press, Oxford, UK), 99–115.Crossref, Google Scholar
• Wakker PP (2005) Formalizing reference dependence and initial wealth in Rabin’s calibration theorem. Working paper, Erasmus University, Rotterdam, Netherlands.Google Scholar
• Wakker PP (2010) Prospect Theory: For Risk and Ambiguity (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Wetzels R, Vandekerckhove J, Tuerlinckx F, Wagenmakers EJ (2010) Bayesian parameter estimation in the expectancy valence model of the Iowa gambling task. J. Math. Psych. 54(1):14–27.Crossref, Google Scholar
• Willemsen MC, Johnson EJ (2011) Visiting the decision factory: Observing cognition with MouselabWEB and other information acquisition methods. Schulte-Mecklenbeck M, Kühberger A, Ranyard R, eds. A Handbook of Process Tracing Methods for Decision Research: A Critical Review and User’s Guide (Taylor and Francis, New York), 21–42.Google Scholar
• Willemsen MC, Johnson EJ (2014) Mouselab software. Last accessed November 17, 2016, http://www.mouselabweb.org.Google Scholar
• Zeisberger S, Vrecko D, Langer T (2012) Measuring the time stability of prospect theory preferences. Theory Decision 72(3):359–386.Crossref, Google Scholar
• Zyphur MJ, Oswald FL (2013) Bayesian probability and statistics in management research: A new horizon. J. Management 39(1):5–13.Google Scholar