By Dennis Fox
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Additional info for Advanced econometric marketing models
5 Model selection Attraction models are often considered for forecasting market shares. It is usually assumed that, by imposing in-sample speciﬁcation restrictions, the out-of-sample forecasting accuracy will improve. Exemplary studies are Brodie and Bonfrer (1994), Danaher (1994), Naert and Weverbergh (1981), Leeﬂang and Reuyl (1984), Kumar (1994) and Chen et al. (1994), among others. A summary of the relevant studies is given in Brodie et al. (2001). A common characteristic of these studies, an exception being Chen et al.
1 − I = H (lc) ln Mt , where H (lc) , with rank I − 1, denotes the transformation matrix corresponding to the log-centering approach. 34) k=1 as H (lc) iI = 0I×I . Due to the reduced rank of H (lc) , the equations, but it only has I − 1 independent equations. 1 ables in the reduced-form model 1 0 ... 0 ln MIt ln M1t 0 1 . . 0 .. .. − . = .. .. . . ln MI−1,t ln MIt 0 0 ... 34) contains I gives as the dependent vari −1 −1 .. ln Mt . 35) 24 Modeling market shares with H (bb) as the relevant transformation matrix.
Given an estimate of σI2 , this relationship can be used to obtain 2 . estimates of σ12 , . . 27) ˜ When taking the square where one should include the appropriate ML estimator for Σ. roots of the diagonal elements of this matrix, one obtains the appropriate standard errors. 2 Modeling market shares Log-centering approach The above estimation routine is based on the reduced-form model, which is obtained from reducing the system of equations using the base-brand approach. An alternative method is the, what is called, log-centering method advocated by Cooper and Nakanishi (1988).
Advanced econometric marketing models by Dennis Fox