16  Data Exploration Toolkit

16.1 Overview

Data exploration is not a single step to complete before analysis; it consists of a set of diagnostic tools applied iteratively across an analytical workflow. In this course, we distinguish –using very non-standard but arguably useful nomenclature– between two complementary phases of data exploration:

  • Ante hoc data exploration: diagnostic checks performed before formal modeling, used to assess data structure, measurement quality, and basic data and model assumptions.
  • Post hoc data exploration: diagnostic checks performed after initial models are fit and used to reassess data in light of model behavior (e.g., leverage, influence, residual structure, convergence failures, factor reduction, or model respecification).

Both phases are essential. Ante hoc exploration helps prevent obvious problems from being baked into models, while post hoc exploration helps identify more subtle issues that only become visible after a model has been fit.

This section introduces a coarse yet practical ante hoc Data Exploration Toolkit, a subset of exploratory tools that should always be considered before formal modeling begins. Post hoc diagnostics are introduced later in the course within the context of formal data modeling.

16.2 The ante hoc Data Exploration Toolkit

In the R exercises used this course, we will repeatedly apply the following steps of the ante hoc Data Exploration Toolkit:

  • Tool #1: Assess potential outliers (univariate and multivariate)
  • Tool #2: Assess the presence of excess zeros
  • Tool #3: Explore interactions and structural relationships
  • Tool #4: Assess potential information redundancy among covariates (e.g., multicollinearity)
  • Tool #5: Decide whether covariate standardization is warranted (this could also be used during post hoc data exploration)

This toolkit is intentionally coarse and non-exhaustive. Its purpose is not to fix the data, but rather to identify critical and fatal issues when they are easiest to diagnose and least costly to address. Skipping these steps often leads to confusion or Paralysis of Analysis during modeling. Many of these are mistakes I have made myself over the years…and learned from the hard way.

This section focuses on the first three most important tools within this toolkit: assessing potential outliers, assessing potential excess of zero values, and assessing potential information redundancy among covariates. The first section –outliers– will be discussed on its own; for the sake of course timing, the other two will be discussed in the tutorial and later in the course.

Most ecological data are far more complex than what simple Analysis of Variance (ANOVA) or linear model frameworks can handle, often involving non-Gaussian dependent variables, hierarchical structures (i.e. nested data), and uneven sampling. In this context, enforcing homogeneity of variance in the classical sense is not required; in face, it is appropriate.

In Generalized Linear Mixed Model (GLMMs) and Generalized Additive Mixed Models (GAMMs), variance is explicitly modeled through the choice of error distribution, link function, and hierarchical structure. As a result, heterogeneity of variance on the response scale is not a violation of assumptions; it is often an expected property of the data.

Takeaway: In GLMMs and GAMMs, variance diagnostics evaluate model adequacy, not whether of not the data meet the homoscedasticity assumption a priori. In other words, you can skip that irrelevant section of Zuur et al. (2010).

16.3 Scope and Next Steps

At this ante hoc stage, the goal is to recognize potential problems, not to resolve them.

In the next sections, we tackle each one of the tools in the toolkit. After focusing on each of these, in turn, we present a hands-on tutorial (discussed in class) that walks through these diagnostics using real data, illustrating how rule-based flags arise and how they should be interpreted responsibly within an analytical workflow.

As a reminder, post hoc data exploration will be introduced later in the course, once models are fitted and can provide additional information about how the data and model interact.