Modelo multinomial, Inferência multimodelo e validação cruzada: uma aplicação

Abstract

The constant search for improving the quality of food products requires increasingly sophisticated means and tools. In this context, the human senses assume a strategic role to evaluate and predict the acceptance of a product in the market. The role of Sensometry here involves the application of mathematical and statistical models that address all aspects of data generation and analysis, from the design of experiments to investigate perceptions and preferences, to specific tools to analyze and model the data resulting from these methods giving important tools with applications in product development, quality assurance, market research and consumer behavior. This study seeks, through a statistical approach, to propose a more specific modeling for a set of sensometric data of a particular case of the Likert scale, the hedonic scale, which, as it is an affective variable (reflects acceptance or preference), allows us to assigning a multinomial distribution to the data, an approach that has also been used in few studies in Sensometry. We also sought to evaluate the acceptance of cereal bars to which different amounts of dry jabuticaba flour were added in a randomized block experiment. In the experiment, each consumer (block) classified the appearance, aroma, flavor, texture and overall impression on a hedonic scale as to their degree of satisfaction. These data were reduced to lower-scoring hedonic scales to build more simplified regression models (fewer intercepts). Another relevant factor was that the statistical analyzes of the response variable (global impression), supposedly multinomial, were conducted in the context of Generalized Linear Models, which removes the “strong” assumption of normal distribution for the data and, in the end, the criterion of Akaike information (AIC) for model selection and, here, where we emphasize that it is unprecedented in Sensometry, we used Akaike Weights for multi-model inference. To compare the performances of the “best” model and the multi- model inferential process, performance measures obtained by stratified cross-validation were calculated. Of the main results, it is worth mentioning that the use of the Multimodel Inference methodology presented, in the 1000 (thousand) simulations carried out for cross validation, a greater number of hits and a greater percentage gain than the single model approach, with greater precision when using a decreasing percentage of training data (adjustment for prediction). We also concluded, whenever possible, that for this case we should use Multimodel Inference and that the inclusion of the quadratic term was important in two of the four most substantial models in Multimodel Inference.