New techniques for the dimensionality assessment of standardized test data

A new index based on the conditional covariance of item scores given a latent variable is defined and investigated to assess dimensionality in educational and psychological test data. This index successfully detects the test dimensionality in both identifying the number of dimensions present in the test and identifying the items contributing to each dimension by means of cluster analysis. In addition, this index remarkably quantifies lack of unidimensionality in the test data, and the asymptotic behavior of this index under unidimensionality provides theoretical justification.