Unified Beta Regression Model with Random Effects for the Analysis of Sensory Attributes

João César Reis Alves; Gabriel Rodrigues Palma; Idemauro Antonio Rodrigues de Lara

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arXiv · 2504.05996

Unified Beta Regression Model with Random Effects for the Analysis of Sensory Attributes

João César Reis Alves·Gabriel Rodrigues Palma·Idemauro Antonio Rodrigues de Lara

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Abstract

Studies involving sensory analysis are essential for evaluating and measuring the characteristics of food and beverages, including consumer acceptance of samples. For various products, the experimental designs are generally incomplete block designs, with sensory attributes assessed using hedonic scales, ratings, or scores. Statistical methods such as generalized logits are commonly used to analyze these data but face limitations, including convergence issues due to superparameterization. Furthermore, sensory attributes are traditionally analyzed separately, increasing the complexity of the process and complicating the interpretation of results. This study proposes a unified beta regression model with random effects for simultaneously analyzing multiple sensory attributes, whose scores were converted to the (0,1) interval. Simulation studies demonstrated overall agreement rates greater than 82% for the unified model compared to models fitted separately for each attribute. As a motivational example, the unified model was applied to a real dataset in which 98 potential consumers evaluated eight grape juice formulations for each sensory attribute: colour, flavour, aroma, acidity, and sweetness. The unified model identified the same top-rated formulations as the separately fitted models, characterized by a higher proportion of juice relative to sugar. The results underscore the ability of the unified model to simplify the analytical process without compromising accuracy, offering an efficient and insightful approach to sensory studies.

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João César Reis Alves, Gabriel Rodrigues Palma, Idemauro Antonio Rodrigues de Lara. 2025-04-08. Unified Beta Regression Model with Random Effects for the Analysis of Sensory Attributes. https://arxiv.org/abs/2504.05996

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