The Carlton projectPartial dependence plots on a model of 399 Gedling areas
Train a model, then ask it one question at a time, and check its answers against the raw data.
The learner fetches four Census 2021 tables from Nomis for each of Gedling's 399 output areas. Together the areas hold 51,536 households, and 9,763 of them, 18.94%, had no car or van. A random forest of 500 trees is trained to predict that share for an area from four inputs: population density, the share of one-person households, the share of detached homes and the share of purpose-built flats. Checked by five-fold cross-validation, the forest explains about 73% of the variation between areas it was not trained on (R squared 0.733), against 0.923 on the areas it had seen.
Partial dependence: average predicted no-car share across all 399 areas when one input is fixed, our Python run on Census 2021 data from Nomis| One-person households set to | Average prediction | Detached homes set to | Average prediction |
|---|
| 15% | 14.8% | 0% | 24.5% |
| 20% | 15.8% | 10% | 23.0% |
| 30% | 19.3% | 20% | 20.2% |
| 40% | 24.7% | 40% | 16.1% |
| 50% | 29.2% | 60% | 16.1% |
Read down the left pair of columns. With every other input left as it really is, the forest predicts 15.8% when the one-person share is set to 20% and 24.7% when it is set to 40%, a rise of 8.9 points. The right pair falls from 24.5% to 16.1% as the detached share goes from none to 40%, and then stops moving: the model has learned a curve with a flat end, which a straight-line model could not show. Now compare with the raw data. Areas where 15% to 25% of households are one person average 12.3% without a car; areas at 35% to 45% average 25.9%, a gap of 13.6 points. The raw gap is wider than the partial dependence gap because those two groups differ in other ways as well. In the first group about half of homes are detached (49.8%); in the second, under a quarter (23.2%). The plot holds that difference still, and the raw comparison does not.
There is a catch in holding things still. Setting an area to 50% one-person households while leaving it with mostly detached houses describes a place that barely exists in Gedling, since the two inputs are correlated (minus 0.42). The forest still gives an answer, but it is guessing outside its experience. And in every case the plot reports what the model predicts, not what would happen if households changed. Nothing here shows a cause.
Ages 8 to 11
A recipe game: change only the sugar, taste-score each batch, and draw the line.
Ages 11 to 15
Chart no-car share against one-person share for Gedling areas in Python and describe the pattern.
Ages 15 and up
Train the forest, code partial dependence by hand, and explain why it differs from the raw averages.
Official counts, our model
All household counts are Office for National Statistics Census 2021 data taken from Nomis under the Open Government Licence. The forest, its scores and the partial dependence figures are our calculations and are published nowhere else. They concern areas, never individual households.
