Yield Analysis and Mixed Model

• Activity Number: 362
• Type: Contributed
• Date/Time: Wednesday, August 10, 2005 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Eugene Demidenko and Igor Mandel*+
• Companies: Dartmouth University and Media Planning Group
• Keywords: random coefficients ; Hildretch-Houck regression ; mixed model ; variance least squares ; car sales

Abstract

A concept of yield analysis, an approach for estimating an observation-specific prediction of the dependent variable, has been developed. Its relation with Hildretch-Houck regression with random coefficients is established. Two types of estimation are considered: distribution-free based on the variance least squares and weighted least squares and maximum likelihood that uses normal assumption. Special practically important cases of nonnegative and not normally distributed regression coefficients are considered as well. After the fixed-effect coefficients are estimated, the observation-specific predictions are computed as posterior means using the BLUP approach. It is shown that the mixed model implies the yield model when the variance of random coefficients goes to infinity and the design matrix is orthogonal. The results of Monte Carlo simulation are presented proving high efficiency of the models. Case study results are shown, where the application of the proposed technique to car advertisement data demonstrates a high predictability, while standard regression results in a disappointing and weak correlation between cost of ad and car sales.