title: 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.
authors.affiliation: Division of Biostatistics, School of Public Health, University of Minnesota.
authors.forename: Tingting
authors.initials: T
authors.lastname: Zhao
authors.affiliation: Division of Biostatistics, School of Public Health, University of Minnesota.|Masonic Cancer Center, University of Minnesota.
authors.forename: Xianghua
authors.initials: X
authors.lastname: Luo
authors.affiliation: Division of Biostatistics, School of Public Health, University of Minnesota.
authors.forename: Haitao
authors.initials: H
authors.lastname: Chu
authors.affiliation: Division of Biostatistics, School of Public Health, University of Minnesota.
authors.forename: Chap T
authors.initials: CT
authors.lastname: Le
authors.affiliation: Department of Pediatrics, Jacobs School of Medicine and Biomedical Sciences, University at Buffalo.
authors.forename: Leonard H
authors.initials: LH
authors.lastname: Epstein
authors.affiliation: Division of General Internal Medicine, Department of Medicine, University of Minnesota.
authors.forename: Janet L
authors.initials: JL
authors.lastname: Thomas
mesh_terms: D003132:Commerce; D060909:Economics, Behavioral; D005260:Female; D006801:Humans; D008297:Male; D008960:Models, Psychological; D009042:Motivation; D016032:Randomized Controlled Trials as Topic; D012907:Smoking; D062789:Tobacco Products; D055815:Young Adult
keywords: cigarette purchase task; demand curve; mixed effects model; nonlinear regression; semicontinuous data