Partial Least Squares for compositional data applied to soil texture and grape composition

Soil texture (i.e. the proportions of different-sized particles in a soil) may affect grape relationships mainly through influence on other soil properties, crucial to plant growth, such, for instance, water infiltration, hydraulic conductivity, water holding capacity. The sum of all soil particles is equal to 100%, thus texture can be considered as compositional data. Compositional data is commonly present in many disciplines. Nevertheless, too often the constant-sum constraint, which each compositional vector presents, is either ignored or improperly incorporated into statistical modeling and a misleading interpretation of the results is given. There are different approaches to incorporate compositional data into a statistical modeling, when it is not realistic to assume a multinomial distribution of the data. Following the approach proposed by Hinkle and Rayens (1995), in this paper we examine the problems that potentially occur when the PLS analysis (Wold, 1966) is performed on two set of compositional data. Up to now, it seems that this approach has never been used in studies pertaining the relationships between physical environmental variables and characteristics of the agricultural production, although many of the physical variables can be regarded as compositional.