Some Issues Connected with a 3d Representation of Multivariate Data Points

The presented considerations complement our former paper (B&Asz) entitled “The augmented biplot and some examples of its use” (Machine Graphics and Vision, 4, 1995, 161–185). Now we consider some topics concerned with a 3D representation of n points–individuals and p points– variables included in a data matrix Xn×p. The representation is displayed in the form of a spinplot called also spinner. Of course, the 3D representation exhibits the true interrelation structure between the displayed points only to some degree of accuracy. We are concerned with the display of two kinds of information: (i) the goodness of the representation of individual points, and (ii) recognizing the mutual position (the out–of–page position) of several points when viewed in a projection plane displaying the flat projection of the whole system which is spinned by performed rotations. Our considerations and needs coming from statistical data analysis problems resulted in a computer program named ASZE (A Slice and siZE displaying plot). We present 3D displays made by this program for the oat varieties data and locations of their growing and the farm production data considered formerly by B&Asz. We show on these examples what a variety of questions can be answered when constructing the spinner with appropriate enhancements.