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Bayesian Networks in Educational Assessment

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ACED Proficiency Model

ACED Proficiency Model

Graphical Structure

The full ACED proficiency model had three separate branches for arithmetic, geometric and other recursive sequences. Only the middle branch was used in the model. Thus although 'Sequences' is the top node in the model 'Solve Geometric Problems' was treated as if it was the top.

This is a hierarchical breakdown, and a reasonable approximation to this model could be made by reducing the number of levels in each hierarchy.

This was realized in ACED as a Bayesian Network?, where each variable can take on three states: High, Medium or Low. It is a tree structured model where each variable has exactly one parent.

Note that there were a series of tasks tapping the 'Solve Geometric Problems' task that turned out to really be about recognizing geometric sequences. This indicates that there may be a missing node in the model.

Joint probability distribution

Unconditional Probablities

Note that the conditional probability tables were created through a number of "regressions" in which the Math Expert specified the correlation and intercept for the regressions. These are presented below. (I've lost the original numbers and need to back translate them from the conditional probability tables. This is a relatively straightforward process, simply treat it as weighted regression with the conditional probabilities as the weights, but I haven't had a chance to do that yet.)

Conditional Proabilities
SequencesRecognize Sequences
Recognize SequencesDistinguish Types
SequencesSolve Sequence Problems
Solve Sequence ProblemsSolve Geometric Problems
Solve Geometric ProblemsCommon Ratio
Solve Geometric ProblemsExamples Geometric
Solve Geometric ProblemsExtend Geometric
Solve Geometric ProblemsModel Geometric
Solve Geometric ProblemsTable Geometric
Solve Geometric ProblemsVisual Geometric
Solve Geometric ProblemsInduce Rules Geometric
Induce Rules GeometricVerbal Rule Geometric
Induce Rules GeometricAlgebra Rule Geometric
Algebra Rule GeometricExplicit Geometric
Algebra Rule GeometricRecursive Rule Geometric

The complete set of conditional probability tables for this model are given in

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ACED development and data collection was sponsored by National Science Foundation Grant No. 0313202.

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Page last modified on July 20, 2008, at 08:17 PM