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

August 16, 2011

(This article was first published on Why? » R, and kindly contributed to R-bloggers)

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.