Detecting Violations of Unidimensionality by Order-Restricted Inference Methods - Heene, Moritz; Kyngdon, Andrew; Sckopke, Philipp (Frontiers in Applied Mathematics and Statistics, 2016)
The assumption of unidimensionality and quantitative measurement represents one of the key concepts underlying most of the commonly applied of item response models. The assumption of unidimensionality is frequently tested although most commonly applied methods have been shown having low power against violations of unidimensionality whereas the assumption of quantitative measurement remains in most of the cases only an (implicit) assumption. On the basis of a simulation study it is shown that order restricted inference methods within a Markov Chain Monte Carlo framework can successfully be used to test both assumptions.