Multivariate visualization: A Taxonomy and novel visualization methods

While intuitive visualizations for bivariate analyses are numerous and able to be constructed with relative ease, the same is not true for multivariate analyses. Commonly utilized multivariate visualization strategies are often cognitively taxing for readers and there is little guidance for researchers seeking to decide upon the proper visualization for their analysis. In this paper we seek to rectify these limitations by developing a data analysis taxonomy that allows one to easily identify appropriate visualizations. This taxonomy aims to provide guidance to researchers in their decision-making regarding which multivariate visualization strategy best fits their research question. Our taxonomy classifies research questions into five different categories (zero-order effects, conditioning, moderation, mediation, and clustering), providing example research questions and analyses for each. Throughout, we identify tools appropriate for multivariate visualizations, including ghost lines, added variable plots, and paneling. All these tools are freely available in R through the Flexplot package, as well as in the Visual Modeling module in JASP.

Added-variable plots for panel-data estimation

In this article, I extend the theory of added-variable plots to three panel-data estimation methods: fixed effects, between effects, and random effects. An added-variable plot is an effective way to show the correlation between an independent variable and a dependent variable conditional on other independent variables. In a multivariate context, a simple scatterplot showing x versus y is not adequate to show the relationship of x with y, because it ignores the impact of the other covariates. Added-variable plots are also useful for spotting influential outliers in the data that affect the estimated regression parameters. Stata can display added-variable plots with the command avplot, but it can be used only after regress. My new command, xtavplot, is a postestimation command that creates added-variable plots after xtreg estimates. Unlike avplot, xtavplot can display a confidence interval around the fitted regression line.

Flexplot: graphically-based data analysis

The human visual processing system has enormous bandwidth, able to interpret vast amounts of data in fractions of a second (Otten, Cheng, and Drewnowski 2015). Despite this amazing ability, there is a troubling lack of graphics in scientific literature (Healy and Moody 2014), and the graphics most traditionally used tend to bias perception in unintentional ways (Weissgerber, Milic, Winham, and Garovic 2015). I suspect the reason for the underuse and misuse of graphics is because sound visuals are difficult to produce with existing software. While ggplot2 allows immense flexibility in creating graphics, its learning curve is quite steep, and even basic graphics require multiple lines of code. flexplot is an R package that aims to address these issues by providing a formula-based suite of tools that simplifies and automates much of the graphical decision-making. Additionally, flexplot pairs well with statistical modeling, making it easy for researchers to produce visuals that map onto statistical procedures. With one-line functions, users can visualize bivariate statistical models (e.g., scatterplots for regression, jittered density plots for ANOVA/t-tests), multivariate statistical models (e.g., ANCOVA and multiple regression), and even more sophisticated models like multi-level models and logistic regressions. Further, this package utilizes old tools (e.g., added variable plots and coplots) as well as introduces new tools for complex visualizations, including ghost lines, sampling, and jittered-density plots.

Added-variable plots with confidence intervals

An added-variable plot is an effective way to show the correlation between an independent variable and a dependent variable conditional on other independent variables. For multivariate estimation, a simple scatterplot showing x versus y is not adequate to show the partial correlation of x with y, because it ignores the impact of the other covariates. Added-variable plots are especially effective for showing the correlation of a dummy x variable with y because the dummy variable conditional on other covariates becomes a continuous variable, making the relationship easier to visualize. Added-variable plots are also useful for spotting influential outliers in the data that affect the estimated regression parameters. Stata provides added-variable plots after ordinary least-squares regressions with the avplot command. I present a new command, avciplot, that adds a confidence interval and other options to the avplot command.