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Mixed Models for Business Decision Making (302442)

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Keywords: ML, REML, Response to TV Ads, Generalized Inference

Practitioners now heavily use Mixed Models for estimating and optimizing the effect of promotional tactics as well as in analysis of data from Clinical Trials. The reason is that in estimating the effect of a covariate by a number of Groups or Subjects using simple regressions yield highly unreliable estimates. The problem is alleviated by using Mixed Models. In Mixed Models, BLUP of group effects are more reliable than regular regression estimates. The BLUPs are a function of variance components, which are traditionally estimated by ML or REML. It is well known that MLE based methods could yield negative (or zero) and/or unreliable estimates for variance components regardless of type of application. As a result, BLUP fails or become highly unreliable, especially in trials involving a few groups and/or small sample sizes. LSE/MLE also has poor performance in estimating location parameters of small magnitude.

To overcome these drawbacks, we propose a generalized estimation method which is substantially superior to MLE in this class of applications. The proposed method also allows one to take advantage of known signs of parameters without taking the Bayesian approach. The utility of the method will be demonstrated using an application involving a problem of optimizing TV ads by market.