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

2025-04-08

AI Summary

In sensory analysis, conventional item-wise modeling suffers from procedural redundancy and poor interpretability, while generalized logit models often encounter convergence issues due to overparameterization. To address these limitations, this paper proposes a unified Beta regression framework that maps Likert-scale ratings onto the (0,1) interval, enabling the first joint modeling of multidimensional sensory attributes—including color, flavor, and aroma. The framework incorporates random effects to capture consumer heterogeneity and inter-product correlations, thereby enhancing robustness and interpretability. Simulation studies demonstrate an overall model consistency exceeding 82%. In an empirical study involving 98 consumers evaluating eight grape juice samples across five sensory dimensions, the model accurately identifies the optimal “high-juice/low-sugar” formulation, achieving prediction accuracy comparable to univariate modeling while substantially improving analytical efficiency and statistical power.

Technology Category

• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Evaluation and Analysis

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Analyze multiple sensory attributes simultaneously using unified model
• Address limitations of traditional separate analysis methods
• Simplify sensory data interpretation without losing accuracy

Innovation

• Unified beta regression model with random effects
• Simultaneous analysis of multiple sensory attributes
• Scores converted to (0,1) interval for comparison