Tree-based approach to proficiency scaling and diagnostic assessment

A method for diagnostic assessment and proficiency scaling of test results for a plurality of tests, each said test having at least one item, each said item having at least one feature, the method using as input a vector of item difficulty estimates for each of n items and a matrix of hypothesized skill classifications for each of said n items on each of k skills, the method comprising the steps of:

• using a tree-based regression analysis based on said vector and said matrix to model ways in which required skills interact with different item features to produce differences in item difficulty, said analysis identifying combinations of skills required to solve each said item, and forming a plurality of clusters by grouping said items according to a predefined prediction rule based on skill classifications;
• and
• using a nonparametric smoothing technique to summarize student performance on the combinations of skills identified in the tree-based analysis, said smoothing technique resulting in cluster characteristic curves that provide a probability of responding correctly to items with specified skill requirements, said probability expressed as a function of underlying test score.