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


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.


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



  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:

    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

    • If you are using Stata instead of R, you may also find this nomogram generator for logistic and Cox regression models useful:


      If you are interested in the topic of nomogram usage in general, you may also find some useful methodological information and graphical examples.

      Comment by Alexander Zlotnik — June 11, 2015 @ 10:47 am

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