Methods to find the number of latent skills

Identifying the skills that determine the success or failure to exercises and question items is a dicult task. Multiple skills may be involved at various degree of importance, and skills may overlap and correlate. In an eort towards the goal of nding the skills behind a set of items, we investigate two techniques to determine the number of dominant latent skills. The Singular Value Decomposition (SVD) is a known technique to nd latent factors. The singular values represent direct evidence of the strength of latent factors. Application of SVD to nding the number of latent skills is explored. We introduce a second technique based on a wrapper approach. Linear models with dierent number of skills are built, and the one that yields the best prediction accuracy through cross validation is considered the most appropriate. The results show that both techniques are eective in identifying the latent factors over synthetic data. An investigation with real data from the fraction algebra domain is also reported. Both the SVD and wrapper methods yield results that have no simple interpretation.