Road distance and travel time for an improved house price Kriging predictor

Figures & data

Figure 1. A comparison of an Euclidean distance matrix versus a drive time distance matrix and a road distance matrix around the center point of Coventry. (a) Euclidean distance buffer from 0 to 4 miles around the centre of Coventry; (b) Travel time distance buffer from 0 to 10 minutes drive time around the centre of Coventry; (c) Road distance buffer from 0 to 4 miles around the centre of Coventry.

Table 1. All restrictions to road network and travel time OSRM calculation from OSM labels.

Restriction type	Description
Barrier	(Rising) bollard, cattle grid, border control, checkpoint, toll booth, sally port, (lift) gate etc.
Restriction	Motor vehicle, vehicle, permissive, designated, destination, private, agricultural, forestry, emergency, parking aisle etc.
Speed profile	Motorway, trunk, primary, secondary, tertiary, ferry, residential, living street, track, unclassified etc.
Surface speeds	Concrete, paved, cement, compacted, paving stones, metal, grass, gravel, unpaved, cobblestone, stone, sand, mud etc.
Tracktype speeds	Grade 1–5, intermediate, bad, horrible, impassable etc.
Maxspeed	Urban, rural, trunk, motorway, single/dual carriageway
U-Turn	Time in seconds
Traffic signal	Time in seconds
Oneway	Boolean, y/n
Route speed	Ferrys, piers, movable bridges

Table 2. Feature name, description and data type in HMLR’s Price Paid dataset.

Feature name	Description	Data type
UID	Unique transaction identifier	Integer
Property type	Flat, terraced, semi-detached, detached	String
Tenure	Freehold or leasehold	Binary
Date of transaction	Transaction date for the property	Date/Time
Address	Full address including postcode	String
Build status	Is the property newly built	Binary

Table

Algorithm 1: Collapsing time distance matrix selection variogram parameter selection spatial interpolation.
Required: , , , maximum likelihood estimator (MLE)
1: Input:
2: Temporal mapping to time :
3:
4: Stratified sampling: Sample across each LSOA
5:
6: for z in {road distance, travel time, linear combination} do
7: =
8: for z in {road distance, travel time, linear combination} do
9:for V in 10-folds, Checkerboard do
10: Variogram selection on vs ← MLE (
11: Ordinary Kriging on  (
12: return
13: Finish

Figure 2. A situation where P3 and P4 are not satisfied.

Figure 3. The goodness of fit value for each Minkowski coefficient tested against the OSRM’s actual road distance calculations, travel time calculations and a linear model of both (here embedded R² = r², and P-Value = p-value). (a) OSRM road distance versus Minkowski p-value goodness of fit graph; (b) OSRM travel time versus Minkowski p-value goodness of fit graph; (c) OSRM linear combination of road distance and travel time versus Minkowski p-value goodness of fit graph.

Figure 4. A streetmap comparing the distances: the road distance, the Euclidean distance, the Manhattan distance and the Minkowski estimated distance.

Figure 5. Spatially aware checkerboard sampling utilized in the validation process to confirm the model is not over fitted.

Table 3. Results for 10-fold cross-validation.

	10-fold cross-validation
Distance matrix	= 1 (Manhattan)	= 1.55	= 1.6	= 1.7	= 2 (Euclidean)
	0.683	0.6847	0.6901	0.6843	0.663
RMSE	57,115	57,000	57,013	57,439	58,913
MAPE	17.92%	17.9%	17.895%	18.01%	18.12%

Table 4. Results for checkerboard holdout.

	Checkerboard stratified validation
Distance matrix	= 1 (Manhattan)	= 1.55	= 1.6	= 1.7	= 2 (Euclidean)
	0.4509	0.4514	0.4558	0.4499	0.4418
RMSE	82,414	82,367	81,940	82,507	82,972
MAPE	24.52%	24.51%	24.40%	24.53%	24.57%

Figure 6. Validation diagrams: (a) the actual versus predicted graph and (b) house price prediction graph with uncertainty bounds both with a Minkowski coefficient of p = 1.6.