Índices de qualidade de ajuste de modelos de equações estruturais considerando repetições e tratamentos com aplicação em análise sensorial de cafés

Abstract

Structural Equation Modeling (SEM) is a multivariate technique that allows studying several relationships simultaneously, including those involving unobservable variables. In general, the structural equation model goodness-of-fit is verified through several indices, which, in short, evaluate the correspondence between the sample covariance matrix and that implied by the model that properly represents the interrelationships among indexes involved in the study. However, none of them considers the repetition between the observed variables. In this sense, this study aims to propose the correction of GFI and AGFI indices considering observed variable repetitions and their application to coffee sensory analysis. Monte Carlo simulation validation was performed under different scenarios, which are represented by different numbers of repetitions, degrees of heterogeneity, and amounts of outliers generated by distributions with symmetry deviations and excess kurtosis. The simulation study showed that improving GFI and AGFI fit-validity indexes were promising since it showed robustness concerning outliers and diagnosed a model as good and bad fitted through degrees of heterogeneity imposed between the sample and hypothesized covariance matrices per model. Given the proposed model for the study of specialty coffees, the information represented in the latent variables production and environmental changes influence the sensory perception of coffees produced in the Serra da Mantiqueira region, and the improvement of indices enhanced model validation due to the inclusion of observed variable repetitions.