A Matrix Factorization Method for Mapping Items to Skills and for Enhancing Expert-Based Q-Matrices

Uncovering the right skills behind question items is a difficult task. It requires a thorough understanding of the subject matter and of the cognitive factors that determine student performance. The skills definition, and the mapping of item to skills, require the involvement of experts. We investigate means to assist experts for this task by using a data driven, matrix factorization approach. The two mappings of items to skills, the expert on one side and the matrix factorization on the other, are compared in terms of discrepancies, and in terms of their performance when used in a linear model of skills assessment and item outcome prediction. Visual analysis shows a relatively similar pattern between the expert and the factorized mappings, although differences arise. The prediction comparison shows the factorization approach performs slightly better than the original expert Q-matrix, giving supporting evidence to the belief that the factorization mapping is valid. Implications for the use of the factorization to design better item to skills mapping are discussed.