Unified multivariate ordinal model for analysis of sensory attributes
Main Article Content
Abstract
Experiments involving sensory analysis of foods and beverages are beneficial for selecting healthy products and assessing the preferences of potential consumers. They are generally planned in incomplete blocks, and their attributes, such as aroma, colour, and flavour, are evaluated using a 9-point hedonic scale, characterizing an ordinal variable response. Also, the generalised logit model with random effects for panellists is one of the appropriate models to relate the multivariate response to the covariates. This study aims to present a method for analysing sensory attributes through a unified multivariate model. Due to the nature of the variable, each separate model already corresponds to a multivariate analysis, so our proposal would incorporate a complete analysis with solely one model. This proposal is based on multivariate methods for categorical data and maximum likelihood theory. Our method was evaluated through a simulation study, in whichwe consider three distinct formulations with two attributes to represent various formulation selection scenarios via mixed discrete models. The simulated results demonstrated overall concordance rates exceeding 80% for the unified model compared to the separate models. Moreover, as motivation is presented a study of 13 prebiotic beverages based on cashew nut almonds added to grape juice, with 130 potential consumers. The attributes evaluated were overall impression, aroma, body, sweetness and flavour, using a 9-point hedonic scale. The selected unified model considering all attributes was the non-proportional odds mixed-effect model. According to this model, the prebiotic beverage formulations most likely to be accepted were: 8% sugar and 40% grape juice (F4), 6% sugar and 44% grape juice (F6), and 9% sugar and 30% grape juice (F13). The results obtained by this approach were according to the analyses for each attribute. However, the unified analysis and computational time showed advantages of this proposal.
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References
1. Aaby, K., Skaret, J., Røen, D. & Sønsteby, A. Sensory and instrumental analysis of eight genotypes of red raspberry (Rubus idaeus L.) fruits. Journal of Berry Research 9, 483–498 (2019). https://doi.org/10.3233/JBR-190387
2. Agresti, A. Analysis of Ordinal Categorical Data (John Wiley & Sons, 2010).
3. Azzalini, A. Statistical Inference: Based on the Likelihood (Routledge, 2017).
4. Borém, F. M., Ribeiro, F. C., Figueiredo, L. P., Giomo, G. S., Siqueira, V. C. & Dias, C. A. Sensory analysis and fatty acid profile of specialty coffees stored in different packages. Journal of Food Science and Technology 56, 4101–4109 (2019). https://doi.org/10.1007/s13197-019-03879-3
5. Chaves, J. B. P. Análise sensorial: glossário Caderno 31. (Editora UFV, Viçosa, MG, 1998). (2025). https://www.editoraufv.ufv.br/produto/analise-sensorial-glossario
6. Christensen, R. H. B. ordinal: Regression Models for Ordinal Data R package version 2015.6-28 (2015). https://CRAN.R-project.org/package=ordinal.
7. Dutcosky, S. D. Análise sensorial de alimentos 5ª, 540–540. (Champagnat - Pucpress, 2019). https://www.pucpress.com.br/wpcontent/uploads/2021/10/Analise_Sensorial_compressed.pdf .
8. Fatoretto, M. B., de Lara, I. A. R., Loro, A. C. & Spoto, M. H. F. Sensory evaluation of dehydrated tomatoes using the proportional odds mixed model. Journal of Food Processing and Preservation 42, e13822 (2018). https://doi.org/10.1111/jfpp.13822
9. Idolo, I. & Marshall, L. J. The effect of ageing temperature on the sensory qualities of Hibiscus sabdariffa (roselle) wine. African Journal of Food, Agriculture, Nutrition and Development 19, 14726–14738 (2019). http://dx.doi.org/10.18697/ajfand.86.17840
10. Johnson, R. A. & Wichern, D. W. Applied multivariate statistical analysis 8. (Prentice hallUpper Saddle River, NJ, 2008).
11. Lemos, T. D. O., Rodrigues, M. D. C. P., De Lara, I. A. R., De Araújo, A. M. S., De Lemos, T. L. G., Pereira, A. L. F. & De Paula, L. V. T. Modeling the acceptability of cashew apple nectar brands using the proportional odds model. Journal of Sensory Studies 30, 136–144 (2015). https://doi.org/10.1111/joss.12145
12. Li, B., Hayes, J. E. & Ziegler, G. R. Interpreting consumer preferences: Physicohedonic and psychohedonic models yield different information in a coffee-flavored dairy beverage. Food Quality and Preference 36, 27–32 (2014). https://doi.org/10.1016/j.foodqual.2014.03.001
13. Marques, J., de Freitas, S. M., de Lara, I. A. R., Nogueira, A. & Dutcosky, S. D. Prebiotics beverages based on cashew nut almond and grape juice: preference analysis by mixed models. Brazilian Journal of Agriculture 98. in Portuguese, with an abstract in English, 196–205 (2023). DOI: 10.37856/bja.v98i3.4341
14. Montgomery, D. C. Design and Analysis of Experiments 8th. (John Wiley & Sons, 2013). https://www.wiley.com/enus/Design+and+Analysis+of+Experiments%2C+8th+Edition-p-9781118146927
15. Nguyen, H. &Wismer, W. V. A comparison of sensory attribute profiles and liking between regular and sodium-reduced food products. Food Research International 123, 631–641 (2019). https://doi.org/10.1016/j.foodres.2019.05.037
16. R Core Team. R: A Language and Environment for Statistical Computing R Foundation for Statistical Computing (Vienna, Austria, 2020). https://www.R-project.org/.
17. Rebouças, M. C., Rodrigues, M. C. P. & Freitas, S. M. Utilization of mathematical models to evaluate the acceptance and physicochemical parameters for the development of a beverage made from cashew nut. International Food Research Journal 25, 684–689 (2018). https://www.researchgate.net/publication/325699101_Utilization_of_mathematical_models_to_evaluate_
the_acceptance_and_physicochemical_parameters_for_the_development_of_a_beverage_
made_from_cashew_nut
18. Rebouças, M. C. Bebida prebiótica à base de amêndoa da castanha de caju: estudos com consumidores em diferentes abordagens para avaliação de fatores sensoriais e externos ao produto PhD thesis (Universidade Federal do Ceará, 2016). https://repositorio.ufc.br/handle/riufc/18214.
19. Rebouças, M. C., Rodrigues, M. D. C., De Freitas, S. M. & Ferreira, B. The physicochemical optimization and acceptability of a cashew nut-based beverage varying in mango juice and sugar: A pilot study. Beverages 2, 23 (2016). https://doi.org/10.3390/beverages2030023
20. Souza, F. L., Lima, C. J. & Almeida, R. M. Consumo de alimentos funcionais e saudáveis: percepção e comportamento do consumidor. Revista Brasileira de Alimentos Funcionais 14. in Portuguese, with an abstract in English, 45–58 (2022) https://www.revistadealimentosfuncionais.com.br/2022/v14n2/consumo-de-alimentos-funcionais-e-saudaveis-percepcao-e-comportamento-do-consumidor
21. Souza, F. L., Lima, C. J. & Almeida, R. M. Consumo de alimentos funcionais e saudáveis: percepção e comportamento do consumidor. Revista Brasileira de Alimentos Funcionais 14. in Portuguese, with an abstract in English, 45–58 (2022) https://www.revistadealimentosfuncionais.com.br/2022/v14n2/consumo-de-alimentos-funcionais-e-saudaveis-percepcao-e-comportamento-do-consumidor
21. Teixeira, L. V. Análise sensorial na indústria de alimentos. Revista do Instituto de Laticínios Cândido
Tostes 64, 12–21. https://www.revistadoilct.com.br/rilct/article/view/70/76 (2009).