A common objective of social science and business research is the modeling of the relationship between demographic/psychographic characteristics of individuals and the likelihood of certain behaviors for these same individuals. Frequently, data on actual behavior are unavailable; rather, one has available only the self-reported intentions of the individual. If the reported intentions imperfectly predict actual behavior, then any model of behavior based on the intention data should account for the associated measurement error, or else the resulting predictions will be biased. In this paper, we provide a method for analyzing intentions data that explicitly models the discrepancy between reported intention and behavior, thus facilitating a less biased assessment of the impact of designated covariates on actual behavior. The application examined here relates to modeling relationships between demographic characteristics and actual purchase behavior among consumers. A new Bayesian approach employing the Gibbs sampler is developed and compared to alternative models. We show, through simulated and real data, that, relative to methods that implicitly equate intentions and behavior, the proposed method can increase the accuracy with which purchase response models are estimated.