4 Exploratory Visualizations

The driving goal in everything that we do in the modeling process is to find reproducible ways to explain the variation in the response. As discussed in the previous chapter, discovering patterns among the predictors that are related to the response involves selecting a resampling scheme to protect against overfitting, choosing a performance metric, tuning and training multiple models, and comparing model performance to identify which models have the best performance. When presented with a new data set, it is tempting to jump directly into the predictive modeling process to see if we can quickly develop a model that meets the performance expectations. Or, in the case where there are many predictors, the initial goal may be to use the modeling results to identify the most important predictors related to the response. But as illustrated in Figure 1.4, a sufficient amount of time should be spent exploring the data. The focus of this chapter will be to present approaches for visually exploring data and to demonstrate how this approach can be used to help guide feature engineering.

One of the first steps of the exploratory data process when the ultimate purpose is to predict a response is to create visualizations that help elucidate knowledge of the response and then to uncover relationships between the predictors and the response. Therefore our visualizations should start with the response, understanding the characteristics of its distribution, and then to build outward from that with the additional information provided in the predictors. Knowledge about the response can be gained by creating a histogram or box plot. This simple visualization will reveal the amount of variation in the response and if the response was generated by a process that has unusual characteristics that must be investigated further. Next, we can move on to exploring relationships among the predictors and between predictors and the response. Important characteristics can be identified by examining

  • scatter plots of individual predictors and the response,
  • a pairwise correlation plot among the predictors,
  • a projection of high-dimensional predictors into a lower dimensional space,
  • line plots for time-based predictors,
  • the first few levels of a regression or classification tree,
  • a heat map across the samples and predictors, or
  • mosaic plots for examining associations among categorical variables.

These visualizations provide insights that should be used to inform the initial models. It is important to note that some of the most useful visualizations for exploring the data are not necessarily complex or difficult to create. In fact, a simple scatter plot can elicit insights that a model may not be able to uncover, and can lead to the creation of a new predictor or to a transformation of a predictor or the response that improves model performance. The challenge here lies in developing intuition for knowing how to visually explore data to extract information for improvement. As illustrated in Figure 1.4, exploratory data analysis should not stop at this point, but should continue after initial models have been built. Post model building, visual tools can be used to assess model lack-of-fit and to evaluate the potential effectiveness of new predictors that were not in the original model.

In this chapter, we will delve into a variety of useful visualization tools for exploring data prior to constructing the initial model. Some of these tools can then be used after the model is built to identify features that can improve model performance. Following the outline of Figure 1.4, we will look at visualizations prior to modeling, then during the modeling process. We also refer the reader to Tufte (1990), Cleveland (1993), and Healy (2018) which are excellent resources for visualizing data.

To illustrate these tools, the Chicago Train Ridership data will be used for numeric visualizations and the OkCupid data for categorical visualizations.