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2022 | OriginalPaper | Buchkapitel

8. Bayesian Survey Analysis: Introduction

verfasst von : Walter R. Paczkowski

Erschienen in: Modern Survey Analysis

Verlag: Springer International Publishing

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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.

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Fußnoten
1
Normality does not have to be assumed. This is just convenient for this example.
 
2
This is based on Haigh (2012, p. 3), although he doesn’t explain how he got his numbers.
 
3
This is actually an estimate of the probability.
 
4
I’m assuming, of course, that the deck is thoroughly reshuffled.
 
5
There is a distinction between data and information. See Paczkowski (2022) for a discussion.
 
6
See the Wikipedia article on Thomas Bayes at https://​en.​wikipedia.​org/​wiki/​Thomas_​Bayes, last accessed December 27, 2021.
 
7
Cited by Hajek (2019).
 
8
If σ is the standard deviation, then the precision is τ = 1∕σ 2.
 
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
As of January 17, 2022.
 
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
See https://​global.​nielsen.​com/​global/​en/​. Last accessed December 7, 2021.
 
16
See https://​www.​sisinternational​.​com/​ as an example market research company using this method. Last accessed December 7, 2021.
 
17
See the Wikipedia article “Half-normal distribution” at https://​en.​wikipedia.​org/​wiki/​Half-normal_​distribution. Last accessed January 9, 2022.
 
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
Note: the “draw” keyword is not required because it is the first argument to the function.
 
20
See the pyMC3 and ArviZ documentation.
 
21
See Hogg and Craig (1970, Chapter 6).
 
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
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.
 
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Metadaten
Titel
Bayesian Survey Analysis: Introduction
verfasst von
Walter R. Paczkowski
Copyright-Jahr
2022
DOI
https://doi.org/10.1007/978-3-030-76267-4_8