  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.
