Why?

August 16, 2011

Jonathan Rougier – Nomograms for visualising relationships between three variables (useR! 2011)

Filed under: Conferences, R, useR! 2011 — Tags: , , — csgillespie @ 2:19 pm

Background:

Example of Nomogram taken from wikipedia

Donkeys in Kenya. Tricky to find the weight of a donkey in the “field” – no pun intended! So using a few measurements,  estimate the weight. Other covariates include age. Standard practice is to fit:

$\log(weight) = a + b \times \log(heartgirth) + c \times \log(Height)$

for adult donkeys, and other slightly different models for young/old and ill donkeys. What can a statistician add:

• Add in other factors;
• Don’t (automatically) take logs of everything;
• Fit interactions.
Box-Cox suggested that a square-transformation could be a good transformation. Full model has age, health, height and girth. Final model is:

$weight = (-58.9 + 10.2 \times \log(heart) + 4.8 \times \log(height))^2$

We want a simple way of using this model in the field. Use a monogram!

Digression on nomograms

Nomograms are visual tools for representing the relationship between three or more variables. Variations include:
• curved scaled nomograms;
• some others that I missed.
Lots of very nice nomograms from “The lost art of Nomograms”.

Back to donkeys

If we used a log transformation for weight rather than square root we get slightly higher weights for smaller/larger donkeys. Nomograms nicely highlight this.

Summary

Nomograms can be clearer and simpler, but don’t display predictive uncertainty.

References:

1. Full reference for Doerfler’s article:
R. Doerfler, “The Lost Art of Nomography,” The UMAP Journal 30(4), 2009 pp. 457–493.

(The article can be found in pdf form in a link on this page:
http://myreckonings.com/wordpress/2010/04/18/nomography-article-in-the-umap-journal/#more-44)

Ron’s site is at: http://www.myreckonings.com/

His blog: http://myreckonings.com/wordpress/

Comment by efrique — August 16, 2011 @ 11:29 pm

2. Thanks for the references. I’ve added them to the end of the post.

Comment by csgillespie — August 19, 2011 @ 9:03 am