Component intensities to relate difference by category with difference overall

This article gives methods to analyze the difference between two datasets that describe a mutual set of categories. The methods can analyze classification error between mapped and reference categories, or change between two time points. Previous work showed how to compute difference size as the sum of three components: Quantity, Exchange and Shift. These components exist for difference by category and for difference overall. These components can be challenging to compare when the categories' differences vary by size. To address this challenge, this article introduces equations to compute a component's intensity, which is the size of the component divided by the size of the difference. Component intensities facilitate comparison of each category with other categories and with difference overall. The case study illustrates how to use component intensities to characterize temporal change using remotely sensed data. Results show how an intensive Exchange component can signal possible confusion of two categories with each other. The literature shows that authors could benefit from interpretation of component intensities. Readers can perform the calculations for free by using the diffeR package in R or the PontiusMatrix spreadsheet available at www.clarku.edu/similar to rpontius.