Chapter 5: Change Point Plots: A Graphical Method for Identifying Changes in the Distribution of a Random Variable Over Time

As the size and complexity of available data have grown, massive data sets with both longitudinal and latitudinal characteristics have become more common and problematic. For some of these data sets, large independent samples are collected at several points in time in what may be referred to as serial cross sectional data; for others, a sample is drawn from the same collection of individuals at several points in time in what is commonly called panel data; and frequently, data are collected using a combination of these two methods in what may be called partial or incomplete panel data. When such data are collected, the researcher or analyst is often concerned with whether the data feature a change point—in other words, whether the probability distribution from which these data are drawn has changed over the period under scrutiny. Several mathematically sophisticated methods for identifying a change point exist, but these methods suffer from i) their focus on a single moment of the distribution and ii) the difficulty laypersons experience when trying to understand or interpret the results of a change point analysis. In this research we present a graphical method for identifying changes in the distribution of a random variable over time that we call the Change Point Plot. Change Point Plots, which can be used independent of, as a precursor to, or in support of mathematical change point analyses, provide a means for visual inspection of the changes in the distribution of a variable over several successive time points, thereby allowing for i) focus on all moments of interest for the distribution and ii) the relative ease of understanding and interpretation by laypersons.