"i Can Name That Bayesian Network in Two Matrixes!"

Abstract

The traditional approach to building Bayesian networks is to build the graphical structure using a graphical editor and then add probabilities using a separate spreadsheet for each node. This can make it difficult for a design team to get an impression of the total evidence provided by an assessment, especially if the Bayesian network is split into many fragments to make it more manageable. Using the design patterns commonly used to build Bayesian networks for educational assessments, the collection of networks necessary can be specified using two matrixes. An inverse covariance matrix among the proficiency variables (the variables which are the target of interest) specifies the graphical structure and relation strength of the proficiency model. A Q-matrix — an incidence matrix whose rows represent observable outcomes from assessment tasks and whose columns represent proficiency variables — provides the graphical structure of the evidence models (graph fragments linking proficiency variables to observable outcomes). The Q-matrix can be augmented to provide details of relationship strengths and provide a high level overview of the kind of evidence available in the assessment. The representation of the model using matrixes means that the bulk of the specification work can be done using a desktop spreadsheet program and does not require specialized software, facilitating collaboration with external experts. The design idea is illustrated with some examples from prior assessment design projects.