Conceptual Overviews - Scatter Icon Plots

A scatter icon plot is a scatterplot of point markers which are icons representing for each specific data point (defined by the scatterplot {X,Y} coordinates) the variability within a set of other variables chosen for the icon. Thus, scatter icon plots, in a way, serve the dual purpose of pictorially depicting the variability between two variables (e.g., height and weight) and the variability within a set of other icon variables (e.g., scores of individuals on different questionnaires). The basic idea of using icons (see also the respective discussion of Icon plots) in a scatterplot is to represent individual points as particular graphical objects (rather than point markers) where values of variables are assigned to specific features or dimensions of the objects (icons). The assignment is such that the overall appearances of the objects change as a function of the configuration of values. Thus, the objects are given visual "identities" that are unique for configurations of values and that can be identified by the observer. Examining such icons in the scatterplot may help to discover specific clusters of both simple relations and interactions between variables.

Scatter icon plots vs. Icon plots. Both the Scatter Icon plot and the simple Icon plot capitalize on the human ability to "automatically" spot complex (sometimes interactive) relations between multiple variables if those relations are consistent across a set of instances (in this case "icons"). In both cases, the individual units of observations are represented as particular graphical objects. However, the two types of plots differ in the sense that the individual plot points in the scatter icon plot are represented by icons (star, polygon, Chernoff face, etc.) in the two dimensional space, where axes represent two variables, while in a simple icon plot the individual consecutive observations are represented by (consecutive) icons arranged one-next-to the other, and without any reference to the axes. To be more specific, in the scatter icon plot the two coordinates that determine the location of each point (represented by an icon) correspond to its specific values on the two variables; while the icons in an icon plot are arranged in an array without any significance attached to their location; the function of icons is limited only to representation of individual observations based on a set of variables attached to the features of the respective icons.

Types of Scatter Icon Plots. Most scatter icon plots use one of the two categories of icons: circular (such as star plots, sun ray plots, polygon icons) and sequential (such as column icons, profile icons, line icons). However, it is not uncommon to use pies or Chernoff faces as icons in the scatter icon plot. STATISTICA provides options for using Chernoff faces, Pies, Stars, Sunrays, Polygons, Columns, Lines, or Profiles as icons in the scatter icon plot. See also the description of Icon plots for additional details.

Choice of Icon. The choice of an icon to be used in the scatter icon plot is important and depends on the specific application. For example, the overall shape of the circular type of icon assumes distinctive and identifiable overall patterns, depending on multivariate configurations of values of input variables. Therefore, using this type of icon may help to identify interactive relations between variables of interest that will be used in defining the chosen circular icon (star, sun ray, or polygon). If the aim is to translate overall patterns into specific models (in terms of relations between icon variables) or to verify specific observations about the pattern, then one of the sequential icons (column, profile, or line) may be more appropriate. Pies as icons are more versatile in the sense that they can be used for both types of applications. The use of Chernoff faces as icons is a bit involved, but once their features are appropriately defined by suitably assigning the variables, they can reveal hidden patterns of interrelations between variables.

Additionally, a weight variable can be selected and used to scale the entire icon representing the point. Sometimes the standardization of icon variables may be required to assure within-icon compatibility of value ranges. See also the description of Icon plots for additional details.

Applications. Two-dimensional scatterplots are used to visualize the relationship between two variables (e.g. height and weight). There are many situations where a scatter icon plot can provide information that is beyond the scope of a simple two-dimensional scatterplot. For example, the scatterplot can, no doubt, indicate the lack of homogeneity in the sample by forming distinctive clouds of points in the graph, but the information about other factors that contributed to such clustering can be available if icons (defined by a set of variables) are used in place of point markers, i.e., by creating a scatter icon plot.

Another interesting application of the scatter icon plots is to investigate the nature and causes of outliers in the data. As the icons representing the points are defined by a set of variables, the comparison of icons (corresponding to the outlying observations) with the icons (representing other observations) can suggest the factors (variables) that might have been responsible for the outlying behavior of some observations.

In yet another situation, one may want to explore possible complex relationships between several variables. A scatter icon plot can then be used as a simple icon plot to detect the variables that "go together".

Scatter Icon Plots in STATISTICA. STATISTICA provides a variety of graph types for scatter icon plots including Chernoff faces, Pies, Stars, Sunrays, Polygons, Columns, Lines, and Profiles. Scatter icon plots in STATISTICA can be created from the Graphs menu. Select Scatter icon plot from the 2D Graphs to display the Scatter icon plot dialog in which appropriate selections can be made to create the desired scatter icon plot.