Table 3

Goodness of fit of the model with true IQOS introduction months versus placebo models (controlling for household income and seasonality)

Approach	True introduction date model R²	Simultaneous mational-level placebo date models – R² distribution
Approach	True introduction date model R²	Months tested	Mean R²	Top 10%	Top 5%	Max
1	0.9232	47	0.8730	0.9166	0.9183	0.9194
2	0.9215	47	0.8730	0.9166	0.9183	0.9194
3	0.9130	47	0.8676	0.9097	0.9114	0.9123
Approach	True introduction date model R²	Exact permutation test: true model and placebo dates – R² distribution
Approach	True introduction date model R²	True model rank	Permutation count	Significance level	Top 10%	Max
1	0.9232	5	330	1.5%	0.9125	0.9323
2	0.9215	4	55	7.3%	0.9190	0.9262
3	0.9130	2	15	13.3%	0.9130	0.9162

For the simultaneous national-level placebo dates, n=47 (48 months in the dataset minus the first month). The larger the R² value the better the model fits. Ordering the models by the Akaike’s information criteria and Schwarz’s Bayesian information criteria yielded the same results. Month-of-the-year dummies are included in the models to control for seasonality. The regional monthly household income measure is the population-weighted average of the incomes in the prefectures in each region, adjusted for inflation. The Japan Statistical Office is the source for the average monthly household income and monthly inflation data.