Understanding Multivariate Visualization and Analysis in R: From Parallel Coordinates to PCA

Introduction

The session walks through a wide range of multivariate techniques using the classic iris data set in R. It shows how to move from simple visual checks to sophisticated dimensionality‑reduction methods, emphasizing when and why each tool is appropriate.

1. Parallel‑Coordinates Plot

• Purpose: Visualize many variables (multivariate) on a single plot, each observation drawn as a line across vertical axes representing the variables.
• Implementation: ggparcoord from the GGally package. r ggparcoord(data = iris, columns = 1:4, groupColumn = 5, scale = "globalminmax", mapping = aes(color = Species)) + scale_color_manual(values = c("setosa" = "red", "versicolor" = "green", "virginica" = "blue"))
• Key concepts:
• Grouping – column 5 (species) assigns a colour to each line.
• Scaling – globalminmax rescales every variable to the same 0‑1 range, making patterns comparable.
• Interpretation – clusters appear as bundles of lines; a clear separation of setosa indicates distinct measurements, while versicolor and virginica overlap.

2. Plotting a Single Observation per Species

• Selecting the first row of each species (slice_head(n = 1)) helps newcomers see how a single line is built before adding the full data set.
• The same ggparcoord call with the reduced data produces a clean illustration of the line‑construction process.

3. 3‑D Scatter Plot

• Package: scatterplot3d (install with install.packages("scatterplot3d")).
• Axes: X = Petal.Length, Y = Sepal.Width, Z = Petal.Width.
• Colour: Species converted to numeric for colour mapping.
• Interpretation: The plot confirms the strong positive relationship between petal dimensions and the separation of setosa from the other two species.

4. Multiple Box Plots on One Grid

• Use par(mfrow = c(2,2)) to arrange four box plots (Sepal.Length, Sepal.Width, Petal.Length, Petal.Width) side‑by‑side.
• Each box plot is grouped by species, revealing:
• Setosa has the smallest median values.
• Outliers are visible as individual points beyond the whiskers.
• Reset graphics device with dev.off() when finished.

5. Heat Map of the Correlation Matrix

• Steps:
• Compute correlation matrix (excluding the species column).
• Round to two decimals.
• Melt the matrix with reshape2::melt to long format.
• Plot with ggplot2 using geom_tile() and a diverging colour scale (scale_fill_gradient2).
• Reading the map:
• Red → strong positive correlation (e.g., Sepal.Length ↔ Petal.Length = 0.89).
• Blue → strong negative correlation.
• White → near‑zero correlation.

6. Overview of Multivariate Hypothesis Testing

• One‑sample tests – test a single variable against a known value (e.g., weight of a sugar bag).
• Two‑sample tests – compare two groups (t‑test, Hotelling’s T² for multivariate case).
• ANOVA vs. MANOVA – when >2 groups, ANOVA tests each variable separately; MANOVA tests all dependent variables simultaneously.
• ANCOVA / MANCOVA – include covariates (e.g., initial bird weight) to adjust group comparisons.
• Multiple testing caution – each additional test inflates Type I error; multivariate tests control this by evaluating a vector of outcomes at once.

7. Classification & Clustering Techniques

• Discriminant Analysis – known groups; builds a rule to assign new observations (linear vs. quadratic depending on covariance homogeneity).
• Cluster Analysis – groups are unknown; methods include:
• Hierarchical (agglomerative & divisive) – dendrograms illustrate merging or splitting steps.
• Non‑hierarchical – K‑means, model‑based clustering.
• Practical tip: choose distance metric and algorithm that suit the data domain (e.g., genetics often uses Euclidean distance on expression profiles).

8. Dimensionality Reduction & Factor Models

• Principal Component Analysis (PCA) – transforms many correlated variables into a few orthogonal components that retain most variance.
• Factor Analysis – models latent (unobserved) constructs that explain correlations among observed items (common in psychology, marketing).
• Canonical Correlation – relates two sets of variables (e.g., exercise metrics vs. health outcomes).
• Structural Equation Modeling – extends factor analysis to test complex causal pathways.
• These methods simplify interpretation while preserving essential information.

9. Practical Workflow Recommendations

1. Start simple – explore data with box plots and pairwise scatter plots.
2. Add multivariate visualisations – parallel coordinates or 3‑D scatter to see overall structure.
3. Quantify relationships – correlation matrix → heat map.
4. Test hypotheses – choose univariate or multivariate tests based on the number of outcomes.
5. If groups are unknown, cluster – validate cluster stability (silhouette, gap statistic).
6. When many variables, reduce dimensionality – PCA or factor analysis before modelling.

10. Final Thoughts

The toolbox presented shows how R can move from basic descriptive graphics to advanced multivariate inference. Selecting the right visualisation and statistical test is crucial for communicating clear, actionable insights.

Multivariate visualisation and analysis in R empower you to uncover patterns, test complex hypotheses, and communicate results effectively; start with simple plots, scale up to PCA or MANOVA when needed, and always match the method to the research question.