Preface

These notes accompany ISQS 6350 (Multivariate Analysis) at Texas Tech University. They are visual first: most ideas come with a figure, and many figures are interactive (drag a slider, press Play, rotate a 3D plot with the mouse).

The course follows one thread. We observe many variables at once and want to understand why they move together. Chapter 1 sets up the language: the sample we observe, the reduced form (the distribution of the random vector behind the sample) and the structural form (the hidden forces that produce it). Chapter 2 looks at the sample, Chapter 3 at the reduced form, and the remaining chapters present structural models: principal components analysis, multidimensional scaling, factor analysis, cluster analysis, and confirmatory factor analysis and structural equation models.

How to use these notes

  • Code. R code is hidden behind Code buttons; the most important code is shown directly. A figure’s code shows the complete function that draws it.
  • Run it yourself. Each chapter starts with links to its R scripts: a figures script and the shared helpers in _common.R. Save both in one folder, set it as the working directory, and source() the figures script.
  • Slides. The slides used in class are linked at the start of each chapter and at the bottom of the menu on the left. Use the arrow keys to move between slides; figures with a slider or a 3D view are interactive there too.
  • Check your understanding. Each section ends with a few multiple-choice questions; click Answers to check.

The packages used in the notes:

install.packages(c("tidyverse", "plotly", "patchwork", "mvtnorm", "MASS", "GGally",
                   "ggrepel", "palmerpenguins", "lattice"))

Textbook

Everitt, B. S. and Hothorn, T. (2011), An Introduction to Applied Multivariate Analysis with R, Springer. The notes use different examples; each chapter lists the relevant parts of the textbook under Further reading.