Methods to Find the Number of Latent Skills

Identifying the skills that determine the success or failure to exercises and question items is a difficult task. Multiple skills may be involved at various degree of importance, and skills may overlap and correlate. In an effort towards the goal of finding 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 find latent factors. The singular values represent direct evidence of the strength of latent factors. Application of SVD to finding the number of latent skills is explored. We introduce a second technique based on a "wrapper" approach. Linear models with different 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 effective 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. (Contains 6 figures and 3 footnotes.) [This project was supported by funding from the MATI institute and by Canada's NSERC discovery program. For the complete proceedings, "Proceedings of the International Conference on Educational Data Mining (EDM) (5th, Chania, Greece, June 19-21, 2012)," see ED537074.]