Construction of Saturated D-optimal Designs for Mixture Experiments with a Non Normal Response using an Algorithmic Search Banerjee Rahul1,*, Jaggi Seema2, Varghese Eldho3, Bhowmik Arpan4, Varghese Cini1, Datta Anindita1, Lall Shwetank1 1ICAR-Indian Agricultural Statistics Research Institute, Pusa-110 012, New Delhi, India 2Division of Agricultural Education, ICAR-Krishi Ansuandhan Bhavan-II, Pusa-110 012, New Delhi, India 3ICAR-Central Marine Fisheries Research Institute, Kochi-682 018, Kerala, India 4ICAR-Indian Agricultural Research Institute, Dirpai Chapori, Gogamukh-787 035, Assam, India *Corresponding Author: Rahul Banerjee, ICAR-Indian Agricultural Statistics Research Institute, New Delhi-110 012, India, Email: rahuliasri@gmail.com
Online Published on 15 February, 2024. Abstract Background Mixture experiments belong to the response surface design category, involving the combination of multiple components to create a product. These products are commonly encountered in daily life. In some cases, mixture experiments yield qualitative responses, such as taste in a fruit punch. Qualitative variables often deviate from a normal distribution. Methods To address non-normal responses, a generalized linear model, specifically the logistic model, is employed. This study utilizes logistic models and develops suitable search algorithms to obtain saturated D-optimal designs for mixture experiments. The validation of D-optimality criteria is based on the General Equivalence Theorem. Result For generating locally D-optimal designs, the logistic model is utilized considering non-normally distributed errors. While the procedure remains the same for other nonlinear models, the assumptions regarding error distribution impact the Fisher information matrix (FIM). Top Keywords Candidate set, D-optimality, Fisher information matrix, General equivalence theorem, Logistic Models, Mixture experiments, Modified Fedorov exchange algorithm, Non Normal Response. Top |