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

Tingting Zhao, Xianghua Luo, Haitao Chu, Chap T Le, Leonard H. Epstein, Janet L Thomas

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)242-253
Number of pages12
JournalJournal of the experimental analysis of behavior
Issue number3
StatePublished - Nov 1 2016

Bibliographical note

Publisher Copyright:
© 2016 Society for the Experimental Analysis of Behavior


  • cigarette purchase task
  • demand curve
  • mixed effects model
  • nonlinear regression
  • semicontinuous data


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