Visualizing Complex Data With Embedded Plots

<div><p>This article describes a class of graphs, embedded plots, that are particularly useful for analyzing large and complex datasets. Embedded plots organize a collection of graphs into a larger graphic, which can display more complex relationships than would otherwise be possible. This arrangement provides additional axes, prevents overplotting, and allows for multiple levels of visual summarization. Embedded plots also preprocess complex data into a form suitable for the human cognitive system, which can facilitate comprehension. We illustrate the usefulness of embedded plots with a case study, discuss the practical and cognitive advantages of embedded plots, and demonstrate how to implement embedded plots as a general class within visualization software, something currently unavailable. This article has supplementary material online.</p></div

Letter-Value Plots: Boxplots for Large Data

<p>Boxplots are useful displays that convey rough information about the distribution of a variable. Boxplots were designed to be drawn by hand and work best for small datasets, where detailed estimates of tail behavior beyond the quartiles may not be trustworthy. Larger datasets afford more precise estimates of tail behavior, but boxplots do not take advantage of this precision, instead presenting large numbers of extreme, though not unexpected, observations. Letter-value plots address this problem by including more detailed information about the tails using “letter values,” an order statistic defined by Tukey. Boxplots display the first two letter values (the median and quartiles); letter-value plots display further letter values so far as they are reliable estimates of their corresponding quantiles. We illustrate letter-value plots with real data that demonstrate their usefulness for large datasets. All graphics are created using the R package lvplot, and code and data are available in the supplementary materials.</p

Appendix C. Single-species model summary.

Single-species model summary

Appendix A. Butterfly species categorized by habitat affinity.

Butterfly species categorized by habitat affinity

Appendix B. Mixed-effects model incorporating habitat affinity.

Mixed-effects model incorporating habitat affinity