. 2019 Nov 8;9:16283. doi: 10.1038/s41598-019-51539-5

Table 1.

The critical point model. All effects are statistically significant at least at the 5% level of statistical significance.

Covariates	Unit	Dependent variables
		Critical accumulation n^* (vehicle km⁻²)		Capacity P^* (vehicle-km h⁻¹ km⁻²)
		β	t-value	β	t-value
Constant n ^* R R × I b _c B	(vehicle km⁻²) (lane-km km⁻²) (lane-km km⁻² × LSA km⁻¹) (−) (bus-km h⁻¹ km⁻²)	−292.73 24.40 −5.34 −140.67 0.307	(−3.46) (15.31) (−2.00) (−4.02) (2.12)	1282.29 18.63 −6.64	(1.56) (18.87) (−5.19)
N Adj. R²		107 0.88		107 0.91
	Elasticity		Hypothesis test: H ₀ : ε = 1
	ε	95% CI	Hypothesis test: H ₀ : ε = 1
∂ log P^/∂ log n^ ∂ log n^*/∂ log R	0.968 0.839	[0.828;1.107] [0.727;0.950]	F(1,40) = 0.20 F(1,40) = 215.60	Prob > F = 0.655 Prob > F = 0.000	not reject reject

The probability that n^* is exogenous is p = 0.000. We cluster standard errors at the city level and weigh observations by a measure of certainty in the critical point estimation. As we cluster standard errors, the test for endogeneity is based on Wooldridge’s robust score test (the equivalent in case of unadjusted standard errors would be the Durbin-Wu-Hausman test). In the Supplementary information, we provide in Tables 2–4 robustness analyses of the model without weights, in a log transformation, and critical density (not accumulation) formulation. The lower part of the table shows elasticity estimates (Delta-method) with the 95% confidence intervals between critical accumulation and capacity as well as road network density and accumulation. For each elasticity, we test the hypothesis of being different from one.