TY - JOUR AU - Wechselberger, Peter AU - Lang, Stefan AU - Steiner, Winfried J. PY - 2016/04/03 Y2 - 2024/03/29 TI - Additive Models with Random Scaling Factors: Applications to Modeling Price Response Functions JF - Austrian Journal of Statistics JA - AJS VL - 37 IS - 3&4 SE - Articles DO - 10.17713/ajs.v37i3&4.307 UR - https://www.ajs.or.at/index.php/ajs/article/view/vol37%2C%20no3%264%20-%204 SP - 255–270 AB - <p>We discuss inference for additive models with random scaling factors. The additive effects are of the form (1+?)f(z) where f is a nonlinear function of the continuous covariate z modeled by P(enalized)-splines and 1 + ? is a random scaling factor. Additionally, monotonicity constraints on the nonlinear functions are possible.</p><p><br />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<br />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.</p> ER -