Statistical assessment of latent trait dimensionality in psychological testing.

Assuming a nonparametric item response theory model, a large sample procedure for testing the undimensionality of the latent ability space is proposed. Under the assumption of undimensionality, the asymptotic distribution of the test statistic is derived, thereby establishing an asymptotically valid statistical test of undimensionality. A rigorous mathematical definition of dimensionality proposed as an alternative to the classical item response theory definition of dimensionality.