, Volume 46, Issue 1, pp 23–48 | Cite as

Bayesian analysis of happiness with individual heterogeneity

  • Lei Shi
  • Hikaru HasegawaEmail author
Original Paper


This study applies a new Bayesian univariate ordered probit model to happiness data on Australia, Canada, and the US, with immigration status and religion status reflecting individual heterogeneity in the threshold model. The empirical results show that the models that include individual heterogeneity perform better than those without individual heterogeneity do. Furthermore, the effects of heterogeneity vary between the three countries. Having a religious affiliation affects the thresholds in the US, but shows no evident effects in Canada or Australia. Furthermore, parents’ immigration status can affect the thresholds in Australia, but shows no effects in the US or Canada.


Bayesian analysis Markov chain Monte Carlo (MCMC) Ordered probit model World values survey 

JEL Classification

C11 I31 



The authors appreciate the comments of two anonymous referees, which improved the article greatly. The work of the second author was supported in part by a Grant-in-Aid for Scientific Research (no. 16K03589) from the Japan Society for the Promotion of Science (JSPS).

Supplementary material

41237_2018_59_MOESM1_ESM.pdf (321 kb)
Supplementary material 1 (PDF 322 KB)


  1. Abdel-Khalek AM, Lester D (2009) A significant association between religiosity and happiness in a sample of Kuwaiti students. Psychol Rep 105:381–382CrossRefGoogle Scholar
  2. Albert J, Chib S (1993) Bayesian analysis of binary and polychotomous response data. J Am Stat Assoc 88:669–679MathSciNetCrossRefzbMATHGoogle Scholar
  3. Albert J, Chib S (2001) Sequential ordinal modeling with applications to survival data. Biometrics 57:829–836MathSciNetCrossRefzbMATHGoogle Scholar
  4. Argyle M (2001) The psychology of happiness. Routledge, LondonGoogle Scholar
  5. Bălţătescu S (2007) Central and Eastern Europeans migrants’ subjective quality of life. A comparative study. J Iden Migr Stud 1:67–81Google Scholar
  6. Bartram D (2011) Economic migration and happiness: Comparing immigrants’ and natives’ happiness gains from income. Soc Indic Res 103:57–76CrossRefGoogle Scholar
  7. Blanchflower D, Oswald A (2004) Well-being over time in Britain and the USA. J Public Econ 88:1359–1386CrossRefGoogle Scholar
  8. Brady HE (1985) The perils of survey research: Inter-personally incomparable responses. Polit Methodol 11:269–290Google Scholar
  9. Chib S (1995) Marginal likelihood from the Gibbs output. J Am Stat Assoc 90:1313–1321MathSciNetCrossRefzbMATHGoogle Scholar
  10. Chib S, Jeliazkov I (2001) Marginal likelihood from the Metropolis-Hastings output. J Am Stat Assoc 96:270–281MathSciNetCrossRefzbMATHGoogle Scholar
  11. Clark AE, Lelkes O (2009) Let us pray: religious interactions in life satisfaction. PSE Working Papers n\(^o\) 2009-01Google Scholar
  12. Cohen AB, Johnson KA (2017) The relation between religion and well-being. Appl Res Qual Life 12:533–547CrossRefGoogle Scholar
  13. Diener E, Suh EM, Lucas RE, Smith HL (1999) Subjective well-being: three decades of progress. Psychol Bull 125:276–302CrossRefGoogle Scholar
  14. Diener E, Kesebir P, Tov W (2009) Happiness. In: Leary MR, Hoyle RH (eds) Handbook of individual differences in social behavior. Guilford, New York, pp 147–160Google Scholar
  15. Ellison CG (1991) Religious involvement and subjective well-being. J Health Soc Behav 32:80–99CrossRefGoogle Scholar
  16. Ellison CG, Boardman JD, Williams DR, Jackson JS (2001) Religious involvement, stress, and mental health: findings from the 1995 Detroit Area Study. Soc Forces 80:215–249CrossRefGoogle Scholar
  17. Eluru N, Bhat C, Hensher D (2008) A mixed generalized ordered response model for examining pedestrian and bicyclist injury severity levels in traffic crashes. Accid Anal Prev 40:1033–1054CrossRefGoogle Scholar
  18. Finch B, Kolody B, Vega W (2000) Perceived discrimination and depression among Mexican-origin adults in California. J Health Soc Behav 41:295–313CrossRefGoogle Scholar
  19. Fisher J (2013) Relating with god contributes to variance in happiness, over that from personality and age. Religions 4:313–324CrossRefGoogle Scholar
  20. Fredrickson BL (2002) How does religion benefit health and well-being? Are positive emotions active ingredients? Psychol Inq 13:209–213Google Scholar
  21. Fredrickson B, Cohn M, Coffey K, Pek J, Finkel S (2008) Open hearts build lives: positive emotions, induced through loving-kindness meditation, build consequential personal resources. J Pers Soc Psychol 95:1045–1062CrossRefGoogle Scholar
  22. Frey B, Stutzer A (2002) Happiness and Economics. Princeton University Press, PrincetonGoogle Scholar
  23. Gatina L (2016) Does money buy happiness? Financial and general well-being of immigrants in Australia. J Behav Exp Econ 63:91–105CrossRefGoogle Scholar
  24. Gokdemir O, Dumludag D (2012) Life satisfaction among Turkish and Moroccan immigrants in the Netherlands: the role of absolute and relative income. Soc Indic Res 106:407–417CrossRefGoogle Scholar
  25. Greene W (2007) Limdep version 9.0: reference guide. Econometric Software, PlainviewGoogle Scholar
  26. Greene W, Hensher D (2010) Ordered choices and heterogeneity in attribute processing. J Transp Econ Policy 44:331–364Google Scholar
  27. Hendriks M (2015) The happiness of international migrants: a review of research findings. Migr Stud 3:343–369CrossRefGoogle Scholar
  28. Hwang S-S, Cao Y, Xi J (2011) The short-term impact of involuntary migration in China’s Three Gorges: a prospective study. Soc Indic Res 101:73–92CrossRefGoogle Scholar
  29. Inglehart R (2000) Faith and freedom: traditional and modern ways to happiness. In: Diener E, Helliwell JF, Kahnemann D (eds) International differences in well-being. Oxford University Press, New York, pp 342–368Google Scholar
  30. Inkeles A (1993) Industrialization, modernization and the quality of life. Int J Comp Sociol 34:1–23CrossRefGoogle Scholar
  31. Jeffreys H (1961) Theory of probability. Oxford University Press, LondonzbMATHGoogle Scholar
  32. Joshanloo M, Weijers D (2016) Religiosity moderates the relationship between income inequality and life satisfaction across the globe. Soc Indic Res 128:731–750CrossRefGoogle Scholar
  33. Kapteyn A, Smith J, van Soest A (2007) Vignettes and self-reports of work disability in the United States and the Netherlands. Am Econ Rev 97:461–473CrossRefGoogle Scholar
  34. King G, Murray C, Salomon J, Tandon A (2004) Enhancing the validity and cross-cultural comparability of measurement in survey research. Am Polit Sci Rev 98:191–207CrossRefGoogle Scholar
  35. Kóczán Z (2016) (Why) are immigrants unhappy? IZA J Migr 5:1–25CrossRefGoogle Scholar
  36. Koenig H, McCullough M, Larson D (2001) Handbook of religion and health. Oxford University Press, New YorkCrossRefGoogle Scholar
  37. Kortt M, Dollery B, Grant B (2015) Religion and life satisfaction down under. J Happiness Stud 16:277–293CrossRefGoogle Scholar
  38. Layard R, Mayraz G, Nickell S (2008) The marginal utility of income. J Public Econ 92:1846–1857CrossRefGoogle Scholar
  39. Obuóina O (2013) The patterns of satisfaction among immigrants in Germany. Soc Indic Res 113:1105–1127CrossRefGoogle Scholar
  40. Park C, Slattery J (2012) Spirituality, emotions, and physical health. In: Miller LJ (ed) The Oxford handbook of psychology and spirituality. Oxford University Press, New York, pp 379–387Google Scholar
  41. Powdthavee N, Lekfuangfu WN, Wooden M (2015) What’s the good of education on our overall quality of life? A simultaneous equation model of education and life satisfaction for Australia. J Behav Exp Econ 54:10–21CrossRefGoogle Scholar
  42. Robert C (2001) The Bayesian choice. Springer, New YorkGoogle Scholar
  43. Safi M (2010) Immigrants’ life satisfaction in Europe: between assimilation and discrimination. Eur Soc Rev 26:159–171CrossRefGoogle Scholar
  44. Sellers R, Caldwell C, Schmeelk-Cone K, Zimmerman M (2003) Racial identity, racial discrimination, perceived stress, and psychological distress among African American young adults. J Health Soc Behav 44:302–317CrossRefGoogle Scholar
  45. Stillman S, Gibson J, McKenzie DJ, Rohorua H (2012) Miserable migrants?. Natural experiment evidence on international migration and objective and subjective well-being, IZA Discussion Paper No, p 6871Google Scholar
  46. Taylor J, Turner R (2002) Perceived discrimination, social stress, and depression in the transition to adulthood: racial contrasts. Soc Psychol Q 65:213–225CrossRefGoogle Scholar
  47. Terza J (1985) Ordered probit: a generalization. Commun Stat Theory Methods 14:1–11CrossRefGoogle Scholar
  48. Van Cappellen P, Toth-Gauthier M, Saroglou V, Fredrickson B (2016) Religion and well-being: the mediating role of positive emotions. J Happiness Stud 17:485–505CrossRefGoogle Scholar
  49. Vega W, Rumbaut R (1991) Ethnic minorities and mental health. Annu Rev Sociol 17:351–383CrossRefGoogle Scholar
  50. Vinson T, Ericson M (2014) The social dimensions of happiness and life satisfaction of Australians: evidence from the World Values Survey. Int J Soc Welf 23:240–253CrossRefGoogle Scholar
  51. Werkuyten M, Nekuee S (1999) Subjective well-being, discrimination and cultural conflict: Iranians living in the Netherlands. Soc Indic Res 47:281–306CrossRefGoogle Scholar
  52. Witter RA, Stock WA, Okun MA, Haring MJ (1985) Religion and subjective well-being in adulthood: a quantitative synthesis. Rev Relig Res 26:332–342CrossRefGoogle Scholar

Copyright information

© The Behaviormetric Society 2018

Authors and Affiliations

  1. 1.Graduate School of Economics and BusinessHokkaido UniversitySapporoJapan
  2. 2.Department of EconomicsHokkaido UniversitySapporoJapan

Personalised recommendations