If there are m entities with n data elements each, then the model fitted in the log space is lnY=lnA+??M+??+ln??, where Y is a vector of size mn, A is a matrix of [a1 a2 . . . am] (a1 being the base sale for data set 1 and am for data set m), M is the corresponding vector of markdowns, ?? is the shared price sensitivity factor, and ?? is the vector of n shared seasonal indices.