Examining the Bus Ridership Demand: Application of Spatio-Temporal Panel Models

Table 3

Spatial Error Model (SEM) and Spatial Lag Model (SAR) results.

Variable name	Boarding				Alighting
	SEM		SAR		SEM		SAR
	Estimates	t-stat	Estimates	t-stat	Estimates	t-stat	Estimates	t-stat
Constant	2.423	19.260	1.723	172.504	3.084	27.137	2.090	182.354
Stop-level attributes
Headway (Ln of headway)	−0.526	−29.285	−0.403	−3.473	−0.510	−28.956	−0.346	−3.894
Transportation infrastructure around the bus stop
Bus route length in a 600 m buffer	0.307	7.222	0.208	5.502	0.303	7.623	0.208	5.555
Sidewalk length in an 800 m buffer	0.044	5.360	—^2	—	0.058	7.383	—	—
Secondary highway length in a 600 m buffer	0.769	7.047	0.677	36.325	—	—	—	—
Local road length in an 800 m buffer	0.708	10.919	0.528	−16.331	—	—	—	—
Railroad length in an 800 m buffer	—	—	—	—	−0.071	−3.006	—	—
Presence of shelter in a bus stop	0.775	19.904	0.739	39.254	0.553	14.185	0.518	27.966
Built environment around the stop
Land use mix area in an 800 m buffer	0.409	2.712	0.316	3.230	0.628	4.027	0.472	41.242
Household density	—	—	—	—	−0.114	−2.115	—	—
Employment density	−0.016	−2.242	—	—	—	—	—	—
Central business district area distance (km)	−0.110	−5.460	−0.064	−3.920	−0.148	−6.901	−0.055	−3.517
Sociodemographic and socioeconomic variables in census tract
Age 0 to 17 years	0.116	4.685	0.102	1.725	0.100	4.165	—	—
Age 65 and up	−0.106	−5.086	−0.087	−4.737	−0.095	−4.591	—	—
High income (>80 k)	−0.054	−4.122	—	—	−0.067	−5.178	−0.048	−3.941
HH rent	0.051	2.518	—	—	0.065	3.114	0.056	1.741
Spatial and spatiotemporal effect
Temporal lagged variable	0.052	13.320	0.050	0.349	0.051	13.513	0.048	0.344
Spatiotemporal lagged variables in an 800 m buffer	−0.032	−12.685	−0.025	−6.305	−0.027	−11.098	−0.023	−6.087
Spatial autocorrelated term	1.617	39.268	—	—	1.710	104.83	—	—
Spatial autoregressive term	—	—	0.336	174.130	—	—	0.374	200.094

¹We restrict ourselves to spatial random effects model as opposed to developing a spatial fixed effects model for multiple reasons. First, in a spatial fixed effects model, several additional parameters are estimated to account for bus-stop-specific effects. In a dataset with over 3000 stops, this would mean estimating a large number of parameters. The presence of such large number of parameters might lead to overfitting of the data. Second, in the presence of bus-stop-specific fixed effects, the impact of other variables that are common across the system is unlikely to be meaningful. Therefore, the results from such an exercise are not transferable to the future or other locations in any meaningful form. Hence, we have not considered spatial fixed effects models. ²“—“ means insignificant at 90% confidence interval.