However, since the skills are not d

However, since the skills are not directly observable, learning therelationships between them is difficult. There is already a method(a combination of two algorithms, Build Pure Clusters (BPC) [17]and MIMbuild [3, page 319]) for discovering causal structure inthe case where the Q-matrix is unknown, but contains many pureitems (i.e. items that load on only one skill, or latent variable).Unfortunately, in our target applications, most test items load onat least two distinct mathematical skills.Instead of assuming we have many pure items, we begin a longerinvestigation into pre-requisite discovery with a simplifyingassumption that we hope to eventually relax: that the Q-matrix isknown. We know of no current method for learning theprerequisite structure among skills in cases where there are veryfew pure items; so although the method we propose here is limitedto cases where the Q-matrix is known, our method solves a novelproblem. There are existing techniques for discovering andrefining a Q-matrix, so there will be many cases where the Q-matrix is known or can be estimated to some approximation.In the following sections, we explain the statistical model and theprerequisite discovery procedure. We then describe our evaluationof the procedure on simulated data, where the Q-matrix and thetrue prerequisite model are known. We conclude by consideringour results in the context of educational technology.