Archive for the ‘Biplots’ Category

Multivariate Statistical Analysis: Old School

Monday, February 27th, 2012

Multivariate Statistical Analysis: Old School by John Marden.

From the preface:

The goal of this text is to give the reader a thorough grounding in old-school multivariate statistical analysis. The emphasis is on multivariate normal modeling and inference, both theory and implementation. Linear models form a central theme of the book. Several chapters are devoted to developing the basic models, including multivariate regression and analysis of variance, and especially the “both-sides models” (i.e., generalized multivariate analysis of variance models), which allow modeling relationships among individuals as well as variables. Growth curve and repeated measure models are special cases.

The linear models are concerned with means. Inference on covariance matrices covers testing equality of several covariance matrices, testing independence and conditional independence of (blocks of) variables, factor analysis, and some symmetry models. Principal components, though mainly a graphical/exploratory technique, also lends itself to some modeling.

Classification and clustering are related areas. Both attempt to categorize individuals. Classification tries to classify individuals based upon a previous sample of observed individuals and their categories. In clustering, there is no observed categorization, nor often even knowledge of how many categories there are. These must be estimated from the data.

Other useful multivariate techniques include biplots, multidimensional scaling, and canonical correlations.

The bulk of the results here are mathematically justified, but I have tried to arrange the material so that the reader can learn the basic concepts and techniques while plunging as much or as little as desired into the details of the proofs.

Practically all the calculations and graphics in the examples are implemented using the statistical computing environment R [R Development Core Team, 2010]. Throughout the notes we have scattered some of the actual R code we used. Many of the data sets and original R functions can be found in the file For others we refer to available R packages.

This is “old school.” A preface that contains useful information and outlines what the reader may find? Definitely “old school.”

Found thanks to: Christophe Lalanne’s A bag of tweets / Feb 2012.

Biplots in Practice

Monday, February 27th, 2012

Biplots in Practice by Michael Greenacre.

I was rather disappointed in the pricing information for the monographs on biplots cited in Christophe Lalanne’s Biplots. Particularly since most users would be new to biplots and reluctant to invest that kind of money in a monograph.

With a little searching I cam across this volume by Michael Greenacre, which is described as follows:

Biplots in Practice is a comprehensive introduction to one of the most useful and versatile methods of multivariate data visualization: the biplot. The biplot extends the idea of a simple scatterplot of two variables to the case of many variables, with the objective of visualizing the maximum possible amount of information in the data. Research data are typically presented in the form of a rectangular table and the biplot takes its name from the fact that it visualizes the rows and the columns of this table in a common space. This book explains the specific interpretation of the biplot in many different areas of multivariate analysis, notably regression, generalized linear modelling, principal component analysis, log-ratio analysis, various forms of correspondence analysis and discriminant analysis. It includes applications in many different fields of the social and natural sciences, and provides three detailed case studies documenting how the biplot reveals structure in large complex data sets in genomics (where thousands of variables are commonly encountered), in social survey research (where many categorical variables are studied simultaneously) and ecological research (where relationships between two sets of variables are investigated).

It is available online as well as a print publication.

The R code and other supplemental materials are available at this site.

In terms of promoting biplots, I think this is a step in the right direction.


Monday, February 27th, 2012


A very entertaining and informative account by Christophe Lalanne of his pursuit of biplots from a question about display using Lisp to statistics with R.

Entertaining for professional researchers, who experience the joy of one source unravelling into another on a daily basis.

Instructive for those not yet professional researchers, by demonstrating the riches that await just beyond where most people stop searching.

And not to mention a wealth of pointers to resources on biplots.