A comparison of methods for dimensionality assessment of categorical item responses

A spectral clustering method is adopted to assess dimensionality for data following item response theory (IRT) models. Items measuring the same dimension were regarded as a unidimensional manifold hidden in a high-dimensional item response structure. With the information of affinity and tangent space learning through the spectral multi-manifold clustering (SMMC) method, not only the number of dimensions, but also the clusters of items can be identified. Simulation studies were conducted to evaluate the performance in dimensionality assessment of the SMMC method, compared to three popular methods: the parallel analysis (PA) of factor analysis, the Hull method, and the Dimensionality Evaluation to Enumerate Contributing Traits (DETECT). Results showed that the SMMC method performed satisfactorily in many conditions. Among the four methods, the PA was the best when sample sizes were small and correlations among dimensions were low; the DETECT method was the best when sample sizes were large. The SMMC method could supplement these two methods when the number of categories is large. Copyright © 2016 Springer Science+Business Media Singapore.