Fig. 2
Model specification and testing of model predictions/interpretation in three phases. Schematic representation of the development and testing of the smoking prevalence model given in Eq. (1), see Results for detailed explanation. Logic flows from filled circles to arrow heads. Green rectangles enclose data sets used in this study. Model Specification (blue rectangle): social theory is used to motivate a mathematical model for the dynamics of smoking prevalence. Model predictions are tested in three phases. Phase (i) (red rectangle): the model is fitted to smoking prevalence estimates derived from tobacco use data (see Data subsection in Methods) resulting in good model-data agreement, see Fig. 1 and Fig. A.2 of Additional file 1. Phase (ii) (purple rectangle): the relative conformity parameter a from the model controls the relative contribution of social and individual utilities to total utility, and hence, is interpreted as reflecting the degree of individualism/collectivism in a society. This model prediction is tested by comparing country specific fitted values of a (calculated in Phase (i)) to Hofstede’s IDV, an already established measure of individualism/collectivism. Linear regression of a on IDV confirms that these two quantities are significantly (negatively) correlated, see Fig. 4(a). Phase(iii) (yellow rectangle): the relative conformity parameter a in Eq. (1) plays a central role in determining the rate of the increase/decrease in smoking prevalence. Our interpretation of a in terms of individualism/collectivism therefore predicts a relationship between the average rate of increase in smoking prevalence s x (see Eq. (5)) and IDV, and between the year of peak smoking prevalence t max and IDV. Linear regression of s x on IDV confirms these two quantities are significantly (positively) correlated and linear regression of t max on IDV confirms these two quantities are significantly (negatively) correlated, see Fig. 4(b) and Fig. 6, respectively. Results from Phases (i)-(iii) provide evidence in support of the model proposed in Model specification