Conclusion on the scales of maps
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The maps presented in this monograph suggest just a few of the numerous ways that demographers can use contour maps to clearly, efficiently, and simultaneously display both persistent global and prominent local patterns in population rates or levels over two dimensions. In particular, contour maps can strikingly reveal the interaction between age, period, and cohort patterns. By using small multiples, computer movies, or ratio surfaces demographers can use the maps to gain access to several dimensions.
Even in cases where some demographic data already have been carefully scrutinized by perceptive analysts who have uncovered most of the interesting patterns, contour maps may be useful in highlighting these patterns. With contour maps, what was before understood now can be seen. Furthermore, the maps, by giving demographers a new perspective on data, may focus attention on some neglected aspects and patterns in even thoroughly studied data.
Beyond efficient description, contour maps can help demographers with exploratory data analysis and with model building. Surfaces can be computed relative to some part of the surface or to another surface; and different surfaces can be placed next to each other and compared. The patterns produced by a model can be displayed for different parameter values as can the fit of the model to some empirical data. If the data are defined over two dimensions, then a contour map can be used to display the residuals, i.e., the differences between the actual values and the values predicted by the model. By scrutinizing the pattern of the residuals, an analyst may glean some clues as to how to improve the model. Tukey (1977) and Mosteller and Tukey (1977) provide clear discussions of the use of residuals in data analysis and model building and several statistical software packages enable users to conveniently plot contour maps of residents.
The resulting contour maps can be displayed not only as printed output but also on a computer monitor. The shades used in most of the maps presented in this monograph range from black to light grey, but the maps can be produced in glowing colors, on a color computer monitor or using a