Sales Promotion Models

Appendix: Variable Definition for the Decomposition in Section 5.4.3

Van Heerde et al. (2004) obtain decomposition Equation (5.14) for price index variables with four types of support (with/without feature, with/without display). To achieve this, they transform the original four promotion variables (PI, FEATONLY, DISPONLY, FEAT&DISP) from the Scan*Pro model into seven new variables: price index with feature-support (PF), price index with display-only support (PD), price index with feature and display support (PFD), price index without support (PWO), plus FWO (Feature without price cut), DWO (Display without price cut), and FDWO (Feature&Display without price cut). Regular price is indicated by a price index with value “1”. A 20% discount would be indicated by 0.8. The PWO, PF, PD, and PFD variables are defaulted to “1” if there is no price discount, but change depending on whether there is a discount and if so how it is supported. The FWO, DWO, and FDWO variables default to “0” and can equal “1” only if there is a feature, display, or both, without a price cut.

To illustrate the transformation, Table A.1contains the four original and seven new variables. In case # 1 there is no promotion, and the original price index (PI) equals 1 while the FEATONLY, DISPONLY, FEAT&DISP are zero, as defined in the Scan*Pro model. Since there is no (supported or unsupported) price discount in case #1, the four new price index variables (PWO, PF, PD, PFD) are all at their nonpromotional value of 1. The FWO, DWO, and FDWO variables are zero since there is no feature or display without a price cut. In case # 2 there is a twenty percent price discount without any support, which shows up in the original variables as a price index of .8 while FEATONLY, DISPONLY, FEAT&DISP remain zero. Since this is a price cut without support, among the new price indices only the price index without support (PWO) variable is decreased to .8. The other three price indices PF, PD, and PFD stay at their nonpromotional level of 1, while the FWO, DWO, and FDWO variables stay at their default value of 0. Case # 3 represents a twenty percent price cut with a feature-only, and hence price index with feature-only support (PF) is lowered to .8 (and again, all other variables are at their nonpromotional levels). Analogously, in cases # 4 and 5 the variables PD and PFD become .8, in turn. In case # 6 there is a feature without a price cut, which can be seen from the original variables since FEATONLY becomes 1 while PI remains 1. Consequently, among the new variables, FWO becomes 1, while DWO and FDWO remain 0, and PWO, PF, PD, and PFD stay 1 since there is no price cut. Cases #7 and 8 show how DWO and FDWO are defined.

Since price cuts tend to be communicated with feature and or display, the four Scan*Pro Variables tend to be highly correlated. The seven new variables, in contrast, describe seven mutually exclusive promotion situations, and they tend to be much less correlated. While the seven new variables are larger in number than the four Scan*Pro variables, a few of them typically do not vary and can therefore be excluded from models (especially the FDWO variable). Researchers who are concerned about multicollinearity in their (store-level) model may consider using the new set of seven variables proposed in this appendix.

Table A.1 Transforming the four scan*Pro variables into seven new variables