What is a “grid search”? Is it some sort of step-wise regression, or is it just a search which seeks to optimize the lambda by finding the value which minimizes the MSE?
We searched to find the set of lambdas (there are four of them, one for each marketing activity) that minimized MSE (mean square error). This was practical to do because of the fact that we knew the lambdas have to be between zero and one. We looked at several combinations of values for the lambdas and it became clear that the high or low values for detailing and journal advertising, and low values for lambda for DTC and PME, would not be optimal. After looking at several additional combinations, the final values that minimize MSE were lambda = .5 for DET and JAD, and lambda = .9 for DTC and PME. Two simplifications were considered: one would be to assume a lambda of .5; another would be to assume the same lambda for each activity. Neither of these alternatives seemed reasonable, so we went with the grid search approach. Note that this is not a step-wise regression. It was estimated using OLS. The reason we did not use step-wise is that this would exclude variables correlated with othe
