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. Skills may overlap and correlate. Slip and guess factors affect item outcome and depend on the profile of the student’s skill mastery and on item characteristics. In an effort towards the goal of finding the skills behind a set of items, we investigate two techniques to determine the number of salient 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. A second technique is 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 of simulated data. Finally, an investigation with real data is reported. Both the SVD and wrapper methods yield results that have no simple interpretation, but one interpretation is consistent across the two methods, albeit not well aligned with the assessment of experts.