Multivariate Methods for Detection of Rubbery Rot in Storage Apples by Monitoring Volatile Organic Compounds: An Example of Multivariate Generalised Mixed Models

This article is a case study illustrating the use of a multivariate statistical method for screening potential chemical markers for early detection of post-harvest disease in storage fruit. We simultaneously measure a range of volatile organic compounds (VOCs) and two measures of severity of disease infection in apples under storage: the number of apples presenting visible symptoms and the lesion area. We use multivariate generalised linear mixed models (MGLMM) for studying association patterns of those simultaneously observed responses via the covariance structure of random components. Remarkably, those MGLMMs can be used to represent patterns of association between quantities of different statistical nature. In the particular example considered in this paper, there are positive responses (concentrations of VOC, Gamma distribution based models), positive responses possibly containing observations with zero values (lesion area, Compound Poisson distribution based models) and binomially distributed responses (proportion of apples presenting infection symptoms). We represent patterns of association inferred with the MGLMMs using graphical models (a network represented by a graph), which allow us to eliminate spurious associations due to a cascade of indirect correlations between the responses.