Models for Conditional Probability Tables in Educational Assessment

Abstract

Experts in educational assessment can often identify the skills needed to provide a solution for a test item and which patterns of those skills pro duce better expected performance. The method described here combines judgements about the structure of the conditional probability table (e.g., conjunctive or compensatory) with Item Response Theory methods for partial credit scoring (Samejima, 1969) to produce a conditional probability table or a prior distribution for a learning algorithm. The structural judgements induce a projection of each configuration of parent skill variables onto a single latent response-propensity $\theta$. This is then used to calculate a probability for each cell in the table.