Bayesian Network Models for Local Dependence Among Observable Outcome Variables

Author(s):

Almond, Russell G.
Mulder, Joris
Hemat, Lisa A.
Yan, Duanli

Publication Year:

2006

Report Number:

RR-06-36

Abstract:

Bayesian network models offer a large degree of flexibility for modeling dependence among observables (item outcome variables) from the same task, which may be dependent. This paper explores four design patterns for modeling locally dependent observations:

• No Context: Ignore dependence among observables
• Compensatory Context: Introduce a latent variable, Context, to odel task specific knowledge and use a compensatory model to combine this with the relevant proficiencies
• Inhibitor Context: Introduce a latent variable, Context, to odel task specific knowledge and use a inhibitor (threshold) model to combine this with the relevant proficiencies
• Compensatory Cascading: Model each observable as dependent on the previous one in sequence

This paper explores the four design patterns through experiments with simulated and real data. When the proficiency variable is categorical, a simple Mantel-Haenszel procedure can test for local dependence. Although local dependence can cause problems in the calibration, if the models based on these design patterns are successfully calibrated to the data, all the design patterns appear to provide very similar inferences about the students. Based on these experiments, the simpler No Context design pattern appears more stable than the Compensatory Context model, while not significantly affecting the classification accuracy of the assessment. The Cascading design pattern seems to pick up on dependencies missed by the other models, and should be explored with further research.

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Key Word(s):

Bayesian networks / local item dependence / testlets / complex tasks / Mantel-Haenszel test