Table 1 Regression results

	Compound vulnerability function	Univariate vulnerability function
\({\boldsymbol{\mu }}\)
Intercept	−4.314	−4.310
	(1.269e−02)	(1.267e−02)
	[2e–16]	[2e–16]
\(\sqrt{{Rv}}\)	−1.536e−03	−1.537e−03
	(2.100e−05)	(2.099e−05)
	[2e–16]	[2e–16]
\({W}^{3}\)	8.587e−06	8.533e−06
	(1.957e−07)	(1.952e−07)
	[2e–16]	[2e–16]
\({P24}^{3}\)	4.558e−07
	(5.445e−08)
	[2e–16]
\({\boldsymbol{\sigma }}\)
Intercept	−2.596	−2.596
	(1.908e−03)	(1.909e−03)
	[2e–16]	[2e–16]
N	203,401	203,401
Number of parameters	5	4
\({R}_{p}^{2}\)	0.0166	0.0165
\({R}_{{CS}}^{2}\)	0.0368	0.0365
Global Deviance	−1,691,833	−1,691,776
BIC	−1,691,772	−1,691,727
RMSE	0.0108	0.0108

This table contains the estimated coefficients, (standard errors), and [p-values] for the compound vulnerability function and univariate vulnerability function for both their predictors for the expected damage ratio \({\mu }_{i}\) and their precision parameters \(\sigma\). The table also reports on two pseudo \({R}^{2}\) indices: \({R}_{p}^{2}\), which is defined as the square of the Pearson correlation coefficient between the dependent variable and the fitted values for the dependent variable and \({R}_{{CS}}^{2}\), which represents the pseudo \({R}^{2}\) as proposed in Cox and Snell⁴⁶. Moreover, the Global Deviance, BIC, and the root mean squared error (RMSE) are also provided, where the RMSE is calculated by taking the square root of the average squared prediction errors of the vulnerability functions.

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