An IRT-based parameterization for conditional probability tables
Russell G. Almond · 2015
In educational assessment, as in many other areas of application for Bayesian networks, most variables are ordinal. Additionally conditional probability tables need to express monotonic relationships; e.g., increasing skill should mean increasing chance of a better performances on an assessment task. This paper describes a flexible parameterization for conditional probability tables based on item response theory (IRT) that preserves monotonicity. The parameterization is extensible because it rests on three auxiliary function: a mapping function which maps discrete parent states to real values, a combination function which combines the parent values into a sequence of real numbers corresponding to the child variable states, and a link function which maps that vector of numbers to conditional probabilities. The paper also describes an EM-algorithm for estimating the parameters, and describes a hybrid implementation using both R and Netica, available for free download.