Transcript Introducing Bayesian Network in

Introducing Bayesian
Networks in
Neuropsychological
Measures
Presented at 2006 APS Annual Conference
Toshi Yumoto
University of Maryland, Abt Associate
Gregory Anderson
Xtria, Adler School of Professional Psychology
Daisy Wise
University of Maryland
Bayesian Networks
It is very difficult for practitioners to combine this
information objectively
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Bayesian Networks provide an effective way to
combine different sources of information such as:
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Paul Meehl, Clinical versus Statistical Prediction (1954)
Information from distinct domains
Demographic (e.g. gender, race/ethnicity) and Clinical
Information (e.g. previous diagnosis, different type of tests)
It is easy to add new information or modify existing
information
Bayesian Network (2)
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A Bayes Net is suitable for discrete data
 Continuous data needs to be converted into categorical data
Complex models can be divided into several conditionally
independent parts
 Model estimation is easier
 Straightforward to add conditional independent data
Bayesian Network is visual and intuitive
 Class assignments are expressed as a proportion (e.g. percent)
 Provides a prediction for all parameters based on limited (or no)
information
 Allows both subjective and objective evaluation of a network
Microsoft Belief Networks (MSBNx, Kadie, Hovel, Horvitz, 2001)
was used to build a Bayesian Network
Steps in Network Development
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Part I
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Conversion of continuous scores to discrete
categories by Finite Mixture Approach
Part II
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Create Bayesian Network based on hypothesized
model
Estimate conditional probabilities
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This research used a Latent Class Model
Part III
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Examine and Modify model
Measures and Sample
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The ATLAS is a comprehensive assessment for
ADHD containing 7 different sections (Anderson &
Post, 2006). One of the sections is a series of
neuropsychological measures and observations of
performance during testing.
This paper examines three of the major traits of the
neuropsychological measures for ADHD.
Diagnoses of ADHD & LD were gathered from a
parent report.
The sample is around 220 subjects, 8-18 years of
age, from across the nation, gathered in the test
field trials.
Creation of Discrete scores
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The assumption was made that test scores
are from more than one distribution
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Cut scores were established using the
intersection of the distributions
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A Finite Mixture Model was therefore utilized
# of mixture distribution = # of cut scores + 1
A discrete score was assigned based on a
person’s mixture distribution characteristic
For more information contact authors.
Finite Mixture Analysis for Trail A
0.2
Trail A time: Comparison of Observed and Mixture
Distributions
Trail A time: Two Normal Distributions
0.04
0.18
0.035
Observed
0.16
One Normal
0.03
Two Normal
0.14
Three Normal
Normal
0.12
Probability
Proportion
0.025
0.1
0.08
Abnormal
0.02
0.015
0.06
0.01
0.04
0.005
0.02
0
0
10
30
50
70
90
Time in seconds
110
130
150
10
30
50 Cut Score
70
90
Time in Seconds
110
130
150
Hypothesized Model
LD/ADHD
Conditionally Independent Given
Second Order Latent Class
Second Order
Latent Class
Visual Trace
Latent Class
Impulsive/Error
Latent Class
Memory
Latent Class
TAtime
TBtime
DA
TA
DA
Cancel
TAerror
Memory1
Memory3
Forward
Backward
SS
TBerror
CancelO
CancelC
Model Specification
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Three Distinct Domains
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Second Order Latent Class
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Visual Trace/Sequence
 Three Latent Classes
Memory
 Three Latent Classes
Impulsive/Error
 Two Latent Classes
Four Latent Classes
Diagnosis (LD/ADHD)
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Four manifest categories
 Typical, LD, ADHD, and LD/ADHD
Specification of the Bayesian
Network
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For each domain conditional probability of
indicator variables are specified given latent
class membership (for that domain).
These probabilities are first specified based
on the assumption that we have no
information.
These are then updated, given information
such as test scores or clinical observations.
Partial Model: Visual Trace Network
No information known
Partial Model: Visual Trace Network
All item scores known
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Probability of LD/ADHD state given
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Middle Visual Trace level
Middle Memory level
High Impulsive level
SOClass and LD/ADHD states are unobserved
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Proportions are expected class states
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Probability of LD/ADHD state with Six test results
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Trail A time (middle) and error (middle)
Trail B time (middle-low) and error (middle)
Word Memory 1 (low) and Word Memory 3 (low)
Other nodes have expected category distribution
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Highest probability indicates most likely category
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It is easy to combine additional information such as clinical observations and gender
to improve model prediction.
Clinical observation is conditionally independent from other nodes given LD/ADHD
states (i.e. only affect the probability of LD/ADHD node)
Gender has direct effect on LD/ADHD states and Impulsive/Error level, which
indirectly affect second order class states.
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This type of information is harder to add later and should be included from the beginning, if
appropriate.
Summary
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Bayesian Networks provide an effective way to express and
examine hypothesized models.
The model performance can be compared with precision of
prediction (e.g. LD/ADHD diagnoses in this research).
Any statistical procedures estimating expected scores (i.e.
probability of responses) may be used to build a network.
 Bayes Net uses discrete data, therefore latent class model and
latent trait model (with discrete proficiency levels) nicely fit model
development.
Combining additional information is straight forward and relatively
easy
 Understanding of conditional independence is the key
Bayes Net estimates expected probability from available
information
 Makes best possible diagnosis without complete data
Contacts
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Toshi Yumoto
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Gregory Anderson
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[email protected]
[email protected]
Daisy Wise
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[email protected]