The Impact of Using A Linear Model for the Ordinal Response of Mixture Experiments

Syafitri, Utami Dyah (IPB University)
Erfiani, Erfiani (IPB University)
Soleh, Agus M (IPB University)
Wigena, Aji Hamim (IPB University)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 9, No 2 (2025): Zero: Jurnal Sains Matematika dan Terapan

In a sensory test, the response is a Likert scale, which belongs to the ordinal scale. The ordinal response can be analyzed using a linear model approach; however, this approach can be misleading.  This research aims to compare three different methods for ordinal response: the average score, the second-order Scheffe model, and the ordinal logistic model. The case study focused on the response to the taste of cookies resulting from the mixture experiment. The mixture experiment is one type of experimental design which is commonly used for product formulation.  The research involved three ingredients with different lower bonds.  The D-optimal design which also the {3,2} simplex-lattice design was chosen for the experiment. The three methods were conducted, and they all yielded the same results for the optimum composition; however, the ordinal model provided more information about the data's characteristics. The optimal formulation of each ingredient was 10%, 20%, 70%.