Numerical Solution of Likelihood Equations for a First-Order Response Surface Model for Mixture Paired Comparisons | ||||
| The Egyptian Statistical Journal | ||||
| Article 4, Volume 38, Issue 2, December 1994, Page 196-207 | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.1994.314825 | ||||
 View on SCiNiTO | ||||
| Author | ||||
| Tawfik Hassan | ||||
| Abstract | ||||
| 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, factorials 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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