Response modeling methodology (RMM)—maximum likelihood estimation procedures

Abstract

Response modeling methodology (RMM) is a new approach for empirical modeling. ML estimation procedures for the RMM model are developed. For relational modeling, the RMM model is estimated in two phases. In the first phase, the structure of the linear predictor (LP) is determined and its parameters estimated. This is accomplished by combining canonical correlation analysis with linear regression analysis. The former procedure is used to estimate coefficients in a Taylor series approximation to an unspecified response transformation. Canonical scores are then used in the latter procedure as response values in order to estimate coefficients of the LP. In the second phase, the parameters of the RMM model are estimated via ML, given the LP estimated earlier. For modeling random variation, it is assumed that the LP is constant and a new simple percentile-based estimating procedure is developed. The new estimation procedures are demonstrated for some published data.