A two‐part mixed effects model for cigarette purchase task data

Abstract

The Cigarette Purchase Task is a behavioral economic assessment tool designed to measure the relative reinforcing efficacy of cigarette smoking across different prices. An exponential demand equation has become a standard model for analyzing purchase task data, but its utility is compromised by its inability to accommodate values of zero consumption. We propose a two-part mixed effects model that keeps the same exponential demand equation for modeling nonzero consumption values, while providing a logistic regression for the binary outcome of zero versus nonzero consumption. Therefore, the proposed model can accommodate zero consumption values and retain the features of the exponential demand equation at the same time. As a byproduct, the logistic regression component of the proposed model provides a new demand index, the “derived breakpoint”, for the price above which a subject is more likely to be abstinent than to be smoking. We apply the proposed model to data collected at baseline from college students (N = 1,217) enrolled in a randomized clinical trial utilizing financial incentives to motivate tobacco cessation. Monte Carlo simulations showed that the proposed model provides better fits than an existing model. We note that the proposed methodology is applicable to other purchase task data, for example, drugs of abuse.

Effect of e‐cigarette advertisement themes on hypothetical e‐cigarette purchasing in price‐responsive adolescents

“…Separate models were used to analyze whether adolescents were price‐responsive and to assess abuse liability indices conditional on being price‐responsive; similar two‐part approaches have been applied to purchase task data previously [44]. Logistic regression assessed odds of being price‐responsive across ad themes.…”

The Demand Curve Analyzer: Behavioral economic software for applied research

“…For example, the DCA does not provide some of the more complex calculations referenced in the literature. For example, the DCA has yet to include methods such as the Extra Sum-of-Squares F-test (Roma, Hursh, & Hudja, 2016), analyses of substitutability (Hursh & Roma, 2013), and mixed-effects demand curve modeling (Zhao et al, 2016). Even further, model selection procedures do not yet exist for recommending one model of demand over another.…”

A model‐based approach for clustering of multivariate semicontinuous data with application to dietary pattern analysis and intervention

“…Failure to do so may result in biased and misleading findings. Methods have been proposed in the literature for modeling and analysis of semicontinuous data, including, perhaps, the most popular two‐part model approach . In essence, the two‐part model incorporates an underlying two‐part structure in which the zero and nonzero observations are modeled separately through distinct (although sometimes overlapping) sets of parameters.…”

“…Methods have been proposed in the literature for modeling and analysis of semicontinuous data, including, perhaps, the most popular two-part model approach. [4][5][6][7][8][9][10][11][12][13][14] In essence, the two-part model incorporates an underlying two-part structure in which the zero and nonzero observations are modeled separately through distinct (although sometimes overlapping) sets of parameters. An excellent overview on the modeling and analysis of semicontinuous data (also of zero-inflated count data, a similar phenomenon) can be found in the works of Neelon et al 15,16 The present research is motivated by the CHEF (Cultivating Healthy Environments in Families with Type 1 Diabetes) study.…”