Mixture models of delay discounting and smoking behavior

Smokers exhibit an unusually high willingness to forgo a delayed reward of greater magnitude to receive a smaller, more immediate reward. The functional form of such "delay discounting" behavior is central to the discounting-based operationalization of impulsivity, and has implications for theories regarding the basis of steep discounting among smokers and treatment approaches to addiction.

We examined the discounting behavior of current smokers, ex-smokers, and never-smokers to determine whether the functional form of discounting differs between these groups.

Participants completed a 27-item delay discounting questionnaire (25). We used finite mixture modeling in analyzing data as the product of two simultaneous data-generating processes (DGPs), a hyperbolic function and an exponential function, and compared results to a quasi-hyperbolic (QH) approximation, in a relatively large sample (n = 1205).

Consistent with prior reports, current smokers exhibited steeper discounting relative to never-smokers across exponential, hyperbolic, and QH models. A mixture model provided significant support for exponential and hyperbolic discounting in the data, and both accounted for roughly 50% of the participants' choices. This mixture model showed a statistically significantly better fit to the data than the exponential, hyperbolic, or QH functions alone. Contrary to the prevailing view, current smokers were not more likely to discount hyperbolically than nonsmokers, and, thus, were not more prone to time-inconsistent discounting.

The results inform the interpretation of steep discounting among smokers and suggest that treatment approaches could be tailored to the type of discounting behavior that smokers exhibit.