Trellis display is a framework for the visualization of multivariable databases. Its most prominent aspect is an overall visual design, reminiscent of a garden trelliswork, in which panels are laid out into rows, columns, and pages. On each panel of the trellis, a subset of the data is graphed by a display method such as a scatterplot, curve plot, boxplot, 3-D wireframe, normal quantile plot, or dot plot. Each panel shows the relationship of certain variables conditional on the values of other variables. A number of display methods employed in the visual design of Trellis display enable it to succeed in uncovering the structure of data even when the structure is quite complicated. For example, Trellis display provides a powerful mechanism for understanding interactions in studies of how a response depends on explanatory variables.
Trellis arose from the need to study complex dependencies, in particular, complex interactions among explanatory variables acting on a response. Nascent ideas appeared in 1993 in the book Visualizing Data by Bill Cleveland, where techniques of multipanel conditioning were used extensively, but not for more than two conditioning variables. The extension to many explanatory variables required a new approach to conditioning, and new display technology for multipanel display. Rick Becker and Bill Cleveland teamed up to develop the a framework that evolved through time (1993-1996) and was named "trellis" because the display technology - many panels arrayed into columns, rows, and pages - was reminiscent of a garden trelliswork.
The ideas of Trellis display can be implemented in many data visualization systems. The S/S-PLUS system for graphics and data analysis has a particularly comprehensive implementation.
While the major feature of trellis display is the multipanel conditioning, there are many other display ideas that enhance the ability of the trellis to show structure in data. Here are a few.
Selecting the aspect ratio, or shape, of a graph to maximize the accuracy of our visual decoding of information was an outstanding problem of statistical graphics for decades. The solution, a breakthrough in data display, is an integral part of in trellis display. Banking to 45 degrees chooses the aspect ratio to center the absolute values of the slopes of selected line segments on 45 degrees. Perceptual experiments have shown that this maximizes the accuracy of our visual decoding of the relative values of the slopes.
Trellis displays employs automation methods that save you time by automatically selecting rendering aspects---for example, multipanel layout, line types, plotting symbols, colors, and character sizes---to achieve effective visual perception of the structure of data. These automation methods are tuned to the type of graphics device you are using.
Still, even though our automation methods work well, the basic premise of trellis display is that anything can be drawn in the data region of each panel. The basic notion of trellis is that the details of the layout of the panels does not constrain how the conditioning is done or the plot method of the panel. Of course, in any application you may well connect them but you have the capability to connect in any way you chose.