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

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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:

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