Multivariate analysis: greater insights into complex systems

Authors: Yeater, Kathleen; Duke, Sara; Riedell, Walter

Submitted to: Agronomy Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 6/11/2014
Publication Date: 2/25/2015
Citation: Yeater, K.M., Duke, S.E., Riedell, W.E. 2015. Multivariate analysis: greater insights into complex systems. Agronomy Journal. 107:799-810. http://doi:10.2134/agronj14.0017.
DOI: https://doi.org/10.2134/agronj14.0017

Interpretive Summary: Applied multivariate statistical methods arose from the fields of chemistry, psychology, sociology, ecology and climatology – all multi-factor, complex systems with interactions and associations among variables and units. Like these other systems, agricultural systems are equally complex, with multiple-factors driving ecosystem functions and ecological communities. In general, agricultural studies have been and continue to be evaluated based on hypothesis driven experiments and with one response variable analyzed at a time. In contrast, use of multivariate analysis allows evaluation of multiple response variables within a set of experimental results. Agricultural researchers intentionally measure multiple factors based on their subject matter knowledge of the system, presumably with the goal of revealing associations and interrelatedness between and within sets of variables in order to gain greater insight into the system’s function and behavior. We put forth the hypothesis that understanding the complexity of biotic and abiotic systems is better accomplished with multivariate thinking, allowing one to address questions that may otherwise be difficult to conceive by univariate approaches. Our manuscript examines multivariate data and its corresponding analysis options using complex, multidimensional relationships among response variables compared with a univariate analysis which only considers a single response variable. We conclude that the inherent higher dimensionality of MV analyses can be difficult to interpret. Thus, the practical implementation of these approaches may involve the inclusion of several univariate and multivariate analyses to better understand the relationships between variables and their relevance to the complexities that are being researched.

Technical 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 (RV) 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 datasets, both typical in dimension and structure, we will walk the reader through three classes of MV techniques based on the research question and characteristics of the data: 1) hypothesis driven, such as MV Analysis of Variance (MANOVA); 2) dimension reduction, such as principal components (PCA); and 3) classification and discrimination, which includes canonical discriminant analysis (CDA). Several advantages and disadvantages of the MV tools are explained. This review will provide researchers with a beginning framework that will familiarize the reader with 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 dataset to better understand the complex system.