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

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### Background:

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:

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:

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:

- pynomo for creating nomograms.
- R. Doerfler, “The Lost Art of Nomography,” The UMAP Journal 30(4), 2009 pp. 457–493.
- Ron’s site and blog

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