Multivariate Analysis: Greater Insights into Complex Systems. (1st March 2015) - Yeater, Kathleen M.; Duke, Sara E.; Riedell, Walter E.
Abstract : Many agronomic researchers measure and collect multiple response variables in an effort to understand the more complex nature of the system being studied. Multivariate (MV) statistical methods encompass the simultaneous analysis of all random variables measured on each experimental or sampling unit. Many agronomic research systems studied are, by their very nature, MV; however, most analyses reported are univariate (analysis of one response at a time). The objective of this review is to outline a statistical foundation of applications of MV methods and techniques for the agronomic sciences. By utilizing two agronomic data sets, both typical in dimension and structure, we discuss three classes of MV techniques based on the research question and characteristics of the data: (i) hypothesis driven, such as MV analysis of variance; (ii) dimension reduction, such as principal components analysis; and (iii) classification and discrimination, which includes canonical discriminant analysis. Several advantages and disadvantages of the MV tools are explained. This review will provide researchers with a beginning framework of MV generalizations of univariate techniques, and methods that are unique to MV dimension analysis. It is important for researchers to capture the concept of variability within a MV data set to better understand the complex system.