文章基本信息

标题：Additive Models with Random Scaling Factors: Applications to Modeling Price Response Functions
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作者：Peter WECHSELBERGER ; Stefan LANG ; Winfried J. STEINER 等
期刊名称：Austrian Journal of Statistics
出版年度：2008
卷号：37
期号：3&4
页码：255-255
出版社：Austrian Statistical Society
摘要：We discuss inference for additive models with random scaling factors. The additive effects are of the form (1+¡ã)f(z) where f is a nonlinear function of the continuous covariate z modeled by P(enalized)-splines and 1 + ¡ã is a random scaling factor. Additionally, monotonicity constraints on the nonlinear functions are possible. Our work is motivated by the situation of a retailer analyzing the impact of price changes on a brand¡¯s sales in its orange juice product category. Relating sales to a brand¡¯s own price as well as to the prices of competing brands in the category, we estimate own- and cross-item price response functions flexibly to represent nonlinearities and irregular pricing effects in sales response. Monotonicity constraints are imposed so that a brand¡¯s own price is inversely related and the prices of competing brands are directly related to the number of items sold, as suggested by economic theory. Unobserved store-specific heterogeneity is accounted for by allowing the price response curves to vary between different stores.
关键词：P-Splines, Monotonicity Constraints, Multiplicative Random Effects, Price Response, Own- and Cross-item Price Effects.