Multivariate methods for agricultural research

Agronomic research often involves measurement and collection of multiple response variables in an effort to understand the more complex nature of the system being studied. Multivariate statistical methods encompass the simultaneous analysis of all variables measured on each experimental or sampling unit. Many agronomic research systems studied are, by their very nature, multivariate; however, most analyses reported are univariate (i.e., analysis of one response at a time). The objective of this chapter is to use a hands-on approach to familiarize the researcher with a set of common applications of multivariate methods and techniques for the agronomic sciences: principal components analysis, multiple regression, and discriminant analysis. We use an agronomic data set, a subset of the data collected for the “Yield Challenge” program, established by the Illinois Soybean Association in collaboration with researchers from the University of Illinois in 2010. We provide the reader with a field guide to serve as a taxonomical key, a list of relevant references for each technique, a road map to our work, as well as R code to follow as we explore the data to assess quality and suitability for multivariate analyses. We also provide SAS code. The chapter illustrates how multivariate methods can capture the concept of variability to better understand complex systems. Important considerations along with advantages and disadvantages of each multivariate tool and their corresponding research questions are examined.