MVN -

Diagnostic Visualizations

Before relying on numerical test results, it’s essential to visualize data to identify patterns and deviations. We’ll demonstrate a suite of diagnostic plots implemented in MVN.

Example Data

# Load the package:
library(MVN)

We’ll use two numeric variables from the built-in iris dataset:

df <- iris[1:50, 1:2]
head(df)

  Sepal.Length Sepal.Width
1          5.1         3.5
2          4.9         3.0
3          4.7         3.2
4          4.6         3.1
5          5.0         3.6
6          5.4         3.9

We’ll run the Henze–Zirkler test

result <- mvn(data = df)

Multivariate Diagnostics

1. Mahalanobis Q–Q Plot

Compare empirical Mahalanobis distances to theoretical chi-square quantiles:

plot(result, diagnostic = "multivariate", type = "qq")

Points deviating from the line signal departures from multivariate normality.

2. 3D Perspective Plot

Visualize the estimated multivariate density surface:

plot(result, diagnostic = "multivariate", type = "persp")

Rotate and inspect peaks and valleys to detect shape irregularities.

3. Contour Plot

Overlay density contours on the variable space:

plot(result, diagnostic = "multivariate", type = "contour")

Contour levels highlight regions of equal density; distorted shapes indicate non-normality.

Univariate Diagnostics

1. Q–Q Plots

Assess each variable against a theoretical normal distribution:

plot(result, diagnostic = "univariate", type = "qq")

Good normality shows points near the line across variables.

2. Boxplots

Visualize median, quartiles, and potential outliers for each variable:

plot(result, diagnostic = "univariate", type = "boxplot")

Outliers appear as points beyond whiskers; asymmetry suggests skew.

3. Histograms

Combine histograms with fitted normal density curves:

plot(result, diagnostic = "univariate", type = "histogram")

Compare empirical distributions to the smooth normal curve.

4. Scatterplot Matrix

Explore pairwise relationships among variables:

plot(result, diagnostic = "univariate", type = "scatter")

Tip

For interactive exploration, set interactive = TRUE in any plot call to use Plotly-based versions with zoom and hover capabilities.

References

Korkmaz S, Goksuluk D, Zararsiz G. MVN: An R Package for Assessing Multivariate Normality. The R Journal. 2014;6(2):151–162. URL: https://journal.r-project.org/archive/2014-2/korkmaz-goksuluk-zararsiz.pdf