# Interactive prediction of a child's height - Revisiting a Victorian Era dataset

Jesus M. Castagnetto
2015-07-22

### Background

• I used the dataset GaltonFamilies, in the HistData R package, to create a predictive model for child's height.
• The heights in the dataset were converted to centimenters using the equivalence: 1 inch = 2.54 cm.
• The model predicts a child's height (in cm.), given the father's and mother's heights (in cm.), as well as the child's gender.
• The dataset originates from an 1886 study by Francis Galton (vide infra), in which he concludes that using the average height of the parents (the “mid-parent” height) is a sufficient predictor of his/hers stature.

Galton, F. “Regression Towards Mediocrity in Hereditary Stature”, The Journal of the Anthropological Institute of Great Britain and Ireland Vol. 15 (1886), pp. 246-263, DOI: 10.2307/2841583

### Looking at the correlation

Height variables (in cm.): ch (child), fh (father), mh (mother), and mph (mid-parent). The gender factor: female/male.

The child's height is moderately correlated with the father's, mother's and midparent's heights.

Considering the sample distributions of heights by gender, we observe a distinct difference, so the child's gender is an important factor in any predictive model.

### Picking a linear model

First I used Galton's assumption, considering only the mid-parent's height, resulting in a model with a low $$R^2$$. That is why I tried a couple more models that included the child's gender, as summarized below:

Model Formula Adj. $$R^2$$
1 ch ~ mph 0.1030
2 ch ~ mph + gender 0.6332
3 ch ~ fh + mh + gender 0.6354

Where: fh: father's height, mh: mother's height, mph: midparent's height, ch: child's height, gender: child's gender

The last model gives a slightly better fit, with a reasonable QQ-plot, and is the one I used for the Shiny App.

### Final thoughts

• The Shiny App brings to life in a simple and interactive way, research done in Victorian times :-)
• I did not implement range validation in the serve.R code, so you could put non-sensical values (negative, for example), and you will still get a prediction… Perhaps that could be done in the next version of the app.
• You would think that with genetic data we can now do better predictions of a phenotypical trait such as height, but that is not the case (vide infra), the old Victorian method is not only cost effective, but also more robust.

Go and play with my Shiny App – Read the code @github

Aulchenko, Y.S.; et. al. “Predicting human height by Victorian and genomic methods” European Journal of Human Genetics (2009) 17, 1070–1075, DOI: 10.1038/ejhg.2009.5