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Numerical solution of likelihood equations for a first-order response surface model for mixture paired comparisons
Authors:Tawfik Hassan
Institution:(1) Department of Mathematics, Faculty of Science, Helwan University, Helwa, Cairo, Egypt
Abstract:Summary A simple procedure for numerical solution of the likelihood equations for estimating the regression parameters of a first-order response surface model for the treatment parameters of mixture paired comparison experiments is developed. It is demonstrated that, for defined rotatable designs, those regression parameters are simple functions of the main effect parameters of a corresponding factorial model with no interactions. The maximum likelihood estimators of those main effect parameters, and hence of their corresponding regression parameters, are obtained through using procedures of treatment contrasts, factorial and iterations. A numerical example is given to illustrate applications of the procedures developed in this paper.
Keywords:Paired comparisons  Bradley-Terry model  Springall's response surface model  mixtures  treatment contrasts and factorials  likelihood estimation  solution of likelihood equations
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