Model based methods for performing multi-way non-symmetric correspondence analysis

Traditionally multiple correspondence analysis involves transforming a contingency table to its indicator or Burt matrix form then performing the classical two-way approach. Alternatively, one may also consider techniques that are more model based such as the partitions associated with the PARAFAC/CANDECOMP models or the Tucker3 model. Traditionally these procedures have proven to be of benefit in studies where the variables are nominally structured. This paper will demonstrate how they can be adapted for ordinal variables by incorporating orthogonal polynomials into the partitions and a graphical description of the association can be obtained by considering correspondence analysis. This paper will also consider the case where the variables of a three-way contingency table are asymmetrically associated.