A bayesian mixed Beta model applied to multivariate sensory data
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Abstract
Sensory evaluation studies often rely on hedonic scales that yield ordinal and bounded data. Traditional statistical techniques, although widely applied, often fail to account to the boundedness and interdependencies characteristic of sensory responses. This study proposes a Bayesian beta regression framework specifically designed for sensory data, aiming to extend existing methodologies by addressing the joint behavior of multiple attributes. The approach models scores rescaled to the (0,1) interval via a beta distribution, effectively capturing formulation effects and correlations among sensory attributes. To this end, we assumed a hierarchical structure for the regression coefficients. We chose weak prior distributions to avoid strong or subjective assumptions that might distort the results thereby, making the analysis more robust. Without strong restrictions on the prior model, the posterior inference was conducted via Markov Chain Monte Carlo (MCMC) methods. By jointly analyzing all attributes within a hierarchical structure, the method enables direct estimation of inter-attribute associations and offers a more integrated interpretation of product performance. Applied to a grape juice acceptance study, the model not only identified the most preferred formulations but also unveiled meaningful patterns across sensory dimensions. With this Bayesian construction, we present a singular contribution that provides a reliable alternative for researchers seeking to analyze bounded sensory responses while simultaneously exploring the multivariate nature of consumer perception.
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