Mathematical pattern of Kessler psychological distress distribution in the general population of the U.S. and Japan

Table 3 Comparison of the fitting of the three models

Model	Data	AICc	BIC	RMSE	R²	Fitting curve
Exponential	NHIS	− 109.9	− 107.4	0.02	0.96	y = 0.1945e^-0.22x
	NSDUH	− 151.8	− 149.3	0.01	0.96	y = 0.2302e^-0.21x
	BRFSS	− 145.2	− 142.7	0.01	0.97	y = 0.2057e^-0.23x
	CSLC	−106.8	− 104.3	0.03	0.94	y = 0.2193e^-0.23x
Quadratic	NHIS	−69.5	−66.6	0.05	0.64	y = 0.0009 × ²–0.03x + 0.23
	NSDUH	− 128.7	− 125.9	0.02	0.91	y = 0.0005 × ²–0.02x + 0.18
	BRFSS	−88.0	−85.2	0.04	0.78	y = 0.0009 × ²–0.03x + 0.23
	CSLC	−68.6	−65.8	0.05	0.60	y = 0.0008 × ²–0.03x + 0.22
Power law	NHIS	− 89.2	− 86.9	0.04	0.91	y = 0.8969x^-1.90
	NSDUH	−98.3	− 96.2	0.03	0.82	y = 0.7778x^-1.68
	BRFSS	− 120.3	− 118.9	0.06	0.93	y = 1.0261x^-1.98
	CSLC	−82.3	−80.3	0.04	0.85	y = 0.945x^-1.91

AICc Corrected Akaike’s Information Criterion, BIC Schwarz’s Bayesian Information Criterion and. RMSE Root Mean Square Error. R² is the coefficient of determination
The independent variable, x, is the K6 total score and the dependent variable, y, is the relative frequency of subjects

ISSN: 1471-244X