Skip to main content
SpringerLink
Log in

Bayesian Survey Analysis: Introduction

  • Chapter
  • First Online:
Modern Survey Analysis

  • 790 Accesses

Abstract

I previously discussed and illustrated deep analysis methods for survey data when the target variable of a Core Question is measured on a continuous or discrete scale. A prominent method is OLS regression for a continuous target. The target is the dependent or left-hand-side variable, and the independent variables, or features (perhaps from Surround Questions such as demographics), are the right-hand-side variables in a linear model. A logit model is used rather than an OLS model for a discrete target because of statistical issues, the most important being that OLS can predict outside the range of the target. For example, if the target is customer satisfaction measured on a 5-point Likert scale, but the five points are encoded as 0 and 1 (i.e., B3B and T2B, respectively), then OLS could predict a value of −2 for the binary target. What is −2? A logit model is used to avoid this nonsensical result. I illustrated how this is handled in Chap. 5.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Normality does not have to be assumed. This is just convenient for this example.

  2. 2.

    This is based on Haigh (2012, p. 3), although he doesn’t explain how he got his numbers.

  3. 3.

    This is actually an estimate of the probability.

  4. 4.

    I’m assuming, of course, that the deck is thoroughly reshuffled.

  5. 5.

    There is a distinction between data and information. See Paczkowski (2022) for a discussion.

  6. 6.

    See the Wikipedia article on Thomas Bayes at https://en.wikipedia.org/wiki/Thomas_Bayes, last accessed December 27, 2021.

  7. 7.

    Cited by Hajek (2019).

  8. 8.

    If σ is the standard deviation, then the precision is τ = 1∕σ 2.

  9. 9.

    See https://stats.stackexchange.com/questions/20520/what-is-an-uninformative-prior-can-we-ever-have-one-with-truly-no-information?noredirect=1&lq=1. Last accessed January 4, 2022.

  10. 10.

    See https://en.wikipedia.org/wiki/Markov_chain. Last accessed January 3, 2022.

  11. 11.

    See https://en.wikipedia.org/wiki/Monte_Carlo_method#History. Last accessed January 4, 2022.

  12. 12.

    See https://en.wikipedia.org/wiki/Random_walk for a good discussion of random walks as a Markov Chain. Also see https://en.wikipedia.org/wiki/Markov_chain. Both articles last accessed January 3, 2022.

  13. 13.

    As of January 17, 2022.

  14. 14.

    See, for example, the description of SmartRevenue, Inc. at [https://www.linkedin.com/company/smartrevenue/about/](https://www.linkedin.com/company/smartrevenue/about/), last accessed December 7, 2021. SmartRevenue is now defunct.

  15. 15.

    See https://global.nielsen.com/global/en/. Last accessed December 7, 2021.

  16. 16.

    See https://www.sisinternational.com/ as an example market research company using this method. Last accessed December 7, 2021.

  17. 17.

    See the Wikipedia article “Half-normal distribution” at https://en.wikipedia.org/wiki/Half-normal_distribution. Last accessed January 9, 2022.

  18. 18.

    See Rob Hicks’ course notes, which are the basis for this discussion, at https://rlhick.people.wm.edu/stories/bayesian_7.html, last accessed January 16, 2022.

  19. 19.

    Note: the “draw” keyword is not required because it is the first argument to the function.

  20. 20.

    See the pyMC3 and ArviZ documentation.

  21. 21.

    See Hogg and Craig (1970, Chapter 6).

  22. 22.

    For a good explanation of the HDI, see https://stats.stackexchange.com/questions/148439/what-is-a-highest-density-region-hdr. Last accessed January 7, 2022. Also see Hyndman (1996).

  23. 23.

    Be careful how you average. I exponentiated the estimate first for each value in the chains and then averaged these values. You could average the unexponentiated estimates and then exponentiated the average. The latter will produce a smaller value. You need to exponentiate first and then average because each exponentiation is for a separate model.

  24. 24.

    See https://en.wikipedia.org/wiki/Beta_distribution. Last accessed January 22, 2022.

References

  • Andel, J. 2001. Mathematics of Chance. In Wiley Series in Probabilities and Statistics. New York: Wiley.

    Google Scholar 

  • Christensen, R., W. Johnson, A. Branscum, and T.E. Hanson. 2011. Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians. New York: CRC Press.

    MATH  Google Scholar 

  • DeVany, A. 1976. Uncertainty, waiting time, and capacity utilization: A stochastic theory of product quality. Journal of Political Economy 84 (3): 523–542.

    Article  Google Scholar 

  • Eagle, A. 2021. Chance versus randomness. In Stanford Encyclopedia of Philosophy.

    Google Scholar 

  • Feller, W. 1950. An Introduction to Probability Theory and Its Applications. Vol. I. New York: Wiley.

    MATH  Google Scholar 

  • Feller, W. 1971. An Introduction to Probability Theory and Its Applications. Vol. II. New York: Wiley.

    MATH  Google Scholar 

  • Gelman, A. 2002. Prior distribution. In Encyclopedia of Environmetrics, ed. Abdel H. El-Shaarawi, and Walter W. Piegorsch. Vol. 3, 1634–1637. New York: Wiley.

    Google Scholar 

  • Gelman, A. 2006. Prior distributions for variance parameters inhierarchical models. Bayesian Analysis 1 (3): 515–533.

    Article  MathSciNet  Google Scholar 

  • Gelman, A. and J. Hill. 2007. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge: Cambridge University Press.

    Google Scholar 

  • Gelman, A., J. Hill, and A. Vehtari. 2021. Regression and Other Stories. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  • Gill, J. 2008. Bayesian Methods: A Social and Behavioral Sciences Approach, 2nd ed. Statistics in the Social and Behaviorial Sciences. New York: Chapman & Hall/CRC.

    Google Scholar 

  • Haans, H. and E. Gijsbrechts. 2011. “one-deal-fits-all?” on category sales promotion effectiveness in smaller versus larger supermarkets. Journal of Retailing 87 (4): 427–443.

    Article  Google Scholar 

  • Haigh, J. 2012. Probability: A Very Short Introduction. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Hajek, A. 2019. Interpretations of probability. In Stanford Encyclopedia of Philosophy.

    Google Scholar 

  • Hogg, R.V. and A.T. Craig. 1970. Introduction to Mathematical Statistics, 3rd ed. New York: Macmillan Publishing Co., Inc.

    MATH  Google Scholar 

  • Hyndman, R.J. 1996. Computing and graphing highest density regions. The American Statistician 50 (2): 120–126.

    Google Scholar 

  • Kastellec, J.P., J.R. Lax, and J. Phillips. 2019. Estimating state public opinion with multi-levelregression and poststratification using r. https://scholar.princeton.edu/sites/default/files/jkastellec/files/mrp_primer.pdf.

    Google Scholar 

  • Malkiel, B.G. 1999. A Random Walk Down Wall Street, Revised ed. New York: W.W. Norton & Company.

    Google Scholar 

  • Martin, N., B. Depaire, and A. Caris. 2018. A synthesized method for conducting a business process simulation study. In 2018 Winter Simulation Conference (WSC), 276–290.

    Google Scholar 

  • Martin, O.A., R. Kumar, and J. Lao. 2022. Bayesian Modeling and Computation in Python. In Textx in Statistical Science. New York: CRC Press.

    Google Scholar 

  • Mlodinow, L. 2008. The Drunkard’s Walk: How Randomness Rules Our Lives. Vintage Books.

    MATH  Google Scholar 

  • Paczkowski, W.R. 2018. Pricing Analytics: Models and Advanced Quantitative Techniques for Product Pricing. Milton Park: Routledge.

    Book  Google Scholar 

  • Paczkowski, W.R. 2022. Business Analytics: Data Science for Business Problems. Berlin: Springer.

    Google Scholar 

  • Pinker, S. 2021. Rationality: What it is, Why it Seems Scarce, Why it Matters. New York: Viking Press.

    Google Scholar 

  • Santos-d’Amorim, K., and M. Miranda. 2021. Misinformation, disinformation, and malinformation: clarifying the definitions and examples in disinfodemic times. Encontros Bibli Revista Eletronica de Biblioteconomia e Ciencia da Informacao 26: 1–23.

    Google Scholar 

  • SAS. 2018. SAS/STAT 15.1 User’s Guide. In Chapter 7: Introduction to Bayesian Analysis Procedures, 129–166. North Carolina: SAS Institute Inc.

    Google Scholar 

  • Scheaffer, R.L. 1990. Introduction to Probability and Its Applications. In Advanced Series in Statistics and Decision Sciences. California: Duxbury Press.

    Google Scholar 

  • Shonkwiler, R.W. and F. Mendivil. 2009. Explorations in Monte Carlo Methods. In Undergraduate Texts in Mathematics. Berlin: Springer.

    Google Scholar 

  • Todd, M.J., K.M. Kelley, and H. Hopfer. 2021. Usa mid-atlantic consumer preferences for front labelattributes for local wine. Beverages 7 (22): 1–16.

    Google Scholar 

  • Weiss, N.A. 2005. Introductory Statistics, 7th ed. Boston: Pearson Education, Inc.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Data Analytics Corp., Plainsboro, NJ, USA

    Walter R. Paczkowski

Authors
  1. Walter R. Paczkowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Paczkowski, W.R. (2022). Bayesian Survey Analysis: Introduction. In: Modern Survey Analysis. Springer, Cham. https://doi.org/10.1007/978-3-030-76267-4_8

Download citation

Publish with us

Policies and ethics

Search

Navigation