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Monotonic Regression Based on Bayesian P-splines: an Application to Estimating Price Response Functions from Store-level Scanner Data

出版	Techn. Univ., Sonderforschungsbereich Statistische Analyse Diskreter Strukturen, 2003
URL	http://books.google.com.hk/books?id=0aEoyAEACAAJ&hl=&source=gbs_api

註釋Generalized additive models have become a widely used instrument for flexible regression analysis. In many practical situations, however, it is desirable to restrict the flexibility of nonparametric estimation in order to accommodate a presumed monotonic relationship between a covariate and the response variable. For example, consumers usually will buy less of a brand if its price increases, and therefore one expects a brand's unit sales to be a decreasing function in own price. We follow a Bayesian approach using penalized B-splines and incorporate the assumption of monotonicity in a natural way by an appropriate specification of the respective prior distributions. We illustrate the methodology in an empirical application modeling demand for a brand of orange juice and show that imposing monotonicity constraints for own- and cross-item price effects improves the predictive validity of the estimated sales response function considerably. -- Generalized Additive Model ; Markov Chain Monte Carlo ; Sales Promotion ; Own- and Cross-Item Price Effects ; Asymmetric Quality Tier Competition