A multimode direct product model for covariance structure analysis

In the psychometric literature, there is evidence that the modes (facets, dimensions, etc.) in multimode data interact multiplicatively. A basic expression of this idea is that a covariance matrix may then be written as repeated Kronecker product of k , say, parameter matrices, where k is the number of modes. For such a ‘factorial covariance structure’ we give an integrated treatment of ML, WLS and ULS estimators. A modification of the ULS estimator appears to be non‐iteratively computable.