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Event sponsored by Affinnova All copyright owned by The Future Place and the presenters of the material For more informa=on about Affinnova visit h>p://www. affinnova.com/
For more informa=on about NewMR events visit newmr.org
Advanced Quant Techniques July 14, 2011
An Introduc4on to Hierarchical Bayes
Ray Poynter, The Future Place
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
An Introduction to Hierarchical Bayes
Ray Poynter The Future Place
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
Why HB?
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
Traditional View To solve a linear equation
y = mx + c 1 unknown, 2 observations
To solve a quadratic y = ax2 + bx + c 2 unknowns, 3 observations
To solve a 2 variable linear equation Y=b0+b1x1 + b2x2
2 unknowns, 3 observations
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
HB?
≈ HB ≈ Magic
e.g. 40 unknowns 12 observations
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
A company has three drivers, Andy, Bob, and Chris. I tell you one of them had a crash today If you had to guess who, you’d have a ⅓ chance
But, if I say Andy and Bob have never had a crash And, Chris has had fiQeen crashes already this year You might start to think it was Chris
With thanks to Rich Johnson at Sawtooth SoQware for the example
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
Introducing Bayes
Reverend Thomas Bayes 1702 -‐ 1761
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
Bayes Theorem
)()(*)|()|(
YPXPXYPYXP =
This is much clearer with an example, based on a nasty disease Bayesi=s, which is fortunately very rare, only 1 in 1000 people have it.
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
Bayesi=s Example
• 1-in-1000 have Bayesitis - chance is just 0.1%
• The test is very reliable: – If you have it the test will be positive in 99% of cases – If you don’t have the it, chance of a negative result is 95%
• You are tested and get a positive result, what is the chance that you have the disease?
Just under 2%
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
Alterna=ve View of Bayesi=s Imagine we have a popula=on of 1 million
Have the disease? P=0.1%
Posi=ve Test? P=99%
Yes, n=990
No, n=10
Posi=ve Test? P=5%
Yes, n=49,5
00
No, n=940,500
50,490 receive a posi=ve result. 990 are real posi=ves, 1.96% of all posi=ve results.
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
Hierarchical Bayes
In the context of choice data
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
Conceptual Guide to HB 2 level model is assumed – the Hierarchy in HB
– Upper level - the part worths for a respondent are drawn from a multivariate normal distribution
– Lower level - the logit assumption that the probability of choosing x is its transformed utility divided by sum of all the utilities
Markov Chain Monte Carlo Simulations – Very computer intensive
Great ability to produce individual level results from choice data
– even with many parameters and relatively few choices
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
Comparison of Hit Rates with Disaggregation
Summary of Six Commercial Studies
Aggregate Logit
Hierarchical Bayes Improvement
Study One 75.8 99.5 23.8Study Two 24.8 79.5 54.7Study Three 60.5 62.6 2.1Study Four 61.2 79.3 18.1Study Five 59.2 78.8 19.6Study Six 71.9 68.1 -3.8
Note, the last study was par=al profile . . . Source: Pinnell (2000)
Does HB Work?
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
Why Did We Need HB?
Allows us to estimate individual utilities for DCM studies
– The missing piece
Opens up other cases where sparcity of data meant individual results not available:
– MaxDiff scaling – Bundled choice modeling
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
HB
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
The Impact of HB on DCM Data If data for a respondent is ‘typical’, the HB contribution to their results is small
– If the respondent was an outlier, the contribution of HB to their solution is more
Data from groups of people who’ve been through the HB are normally good predictors of the group solution
– An individual’s post HB data is not necessarily a good predictor of that individual’s values
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
HB is very useful
But it’s not magic
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
Thank you
Ray Poynter The Future Place
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
Q & A
Ray Poynter The Future Place
Andrew Jeavons Survey Analy=cs
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Speaker Ray Poynter, The Future Place, UK NewMR Advanced Quant Techniques, July 14, 2011
Ray Poynter
Read Ray’s blog @ h>p://thefutureplace.typepad.com/ Follow Ray’s tweets at @ h>p://twi>er.com/raypoynter Connect with Ray on LinkedIn @ h>p://uk.linkedin.com/in/raypoynter Find out about Ray’s book at @ h>p://bit.ly/cmFnbo