Machine learning for inference: using gradient boosting decision tree to assess non-linear effects of bus rapid transit on house prices

Figures & data

Figure 1. Map of Xiamen Island

Figure 2. BRT system in Xiamen Island

Table 1. Descriptions and summary statistics of the predicted and predictor variables

Variable	Description	Mean/Percentage	Standard deviation
Predicted variable
Price per square metre	(unit: 10^4 yuan/m^2)	5.94	1.48
Predictor variables: control variables
Age	-	8.67	5.82
Building height	Number of floors of a building	22.76	11.49
Residential district environment	Dichotomous variable, equals one if a house is located in a residential district (or condominium complex) with a good environment and zero otherwise	0.74	0.44
Population density	(unit: 1000/km^2)	16.93	9.60
Distance to Zhongshan Road	(unit: km)	26.21	11.77
Distance to the sea	(unit: km)	9.99	4.55
Distance to Wuyuan Bay	(unit: km)	14.88	9.97
Distance to the airport	(unit: km)	6.03	1.71
Waterbody	Dichotomous variable, equals one if a house is located within 200 m of a waterbody and zero otherwise (unit: km)	0.11	0.31
Bus access	Number of bus transit stations within 500 m	5.79	4.14
Predictor variables: explanatory variables
Distance to the BRT station	Distance between a house and the closest BRT station (unit: km)	1.05	0.60
Proximity_400 m	Dichotomous variable, equals one if a house is located within 400 m of the BRT corridor and 0 otherwise	0.35	0.48

Table 2. Relative importance of all predictor variables

Variable	Rank	Relative Importance
Control variables
Age	2	21.8%
Building height	3	11.5%
Residential district environment	11	0.3%
Population density	9	1.2%
Distance to Zhongshan Road	5	5.5%
Distance to the sea	1	40.4%
Distance to Wuyuan Bay	6	4.7%
Distance to the airport	4	8.8%
Waterbody	10	0.3%
Bus access	7	3.4%
Explanatory variables
Distance to the BRT station	8	2.0%
Proximity_400 m	12	0.1%

Figure 3. PDP of distance to the BRT station

Figure 4. PDP of proximity_400 m

Figure 5. PDP of age

Table 3. Hedonic regression results

Variable	Coef.	t-stat	p-value
Age	−0.052	−12.35	<0.001
Building height	0.046	8.13	<0.001
Residential district environment	0.206	17.48	<0.001
Population density	0.014	1.16	0.245
Distance to Zhongshan Road	−0.082	−7.51	<0.001
Distance to the sea	−0.128	−16.787	<0.001
Distance to Wuyuan Bay	−0.064	−12.545	<0.001
Distance to the airport	0.063	4.536	<0.001
Waterbody	0.045	4.12	<0.001
Bus access	0.022	13.89	<0.001
Distance to the BRT station	−0.020	−3.38	0.001
Proximity_400 m	−0.046	−3.99	<0.001
Constant	1.961	30.06	<0.001
Performance statistics
R-squared	0.398
Adjusted R-squared	0.396
Log-likelihood	1189.7

Table 4. Comparison of out-of-sample R-squared (10-fold cross-validation)

Model	Out-of-sample R-squared
	Mean	Std.
Hedonic regression (double-log model)	0.035	0.544
GBDT	0.067	0.381