Tree-based approach to proficiency scaling and diagnostic assessment

Abstract

A method for diagnostic assessment and proficiency scaling of test results is provided. The method uses 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 skills. The method includes using a tree-based regression analysis based on the vector and matrix to model ways in which required skills interact with different item features to produce differences in item difficulty. This analysis identifies combinations of skills required to solve each item, and forms a plurality of clusters by grouping the items according to a predefined prediction rule based on skill classifications. A nonparametric smoothing technique is used to summarize student performance on the combinations of skills identified in the tree-based analysis. The smoothing technique results in cluster characteristic curves that provide a probability of responding correctly to items with specified skill requirements. The probability is expressed as a function of underlying test score.