Visualising grouped three-way data: A common canonical variate analysis biplot

Methods that explicitly incorporate the grouped structure of the data into the construction of graphical displays are not well-developed for three-way data arrays. Moreover, simply matricising the data, to create a wide combination matrix from which an ordinary CVA biplot can be constructed, is problematic in that this can overstate separation between groups. This paper seeks to alleviate these problems by introducing a methodology, based on combining simultaneous diagonalisation and the methods of the two-way CVA biplot methodology, that produces a visual display of three-way data which explicitly incorporates the grouped structure of the data into the construction. This graphical display can be interpreted in the spirit of the two-way CVA biplot. The proposed plot is then applied to simulated data as well as blue crabs dataset studied by Gemperline et al. [13].