63-1 Multivariate DATA and Analyses in Agriculture.
Multivariate analysis refers to a group of statistical technique used to analyze data that arises from more than one variable (multivariate data). The available information is stored in database tables containing rows (n, individuals) and columns (p variables) variables. Then multivariate analysis can be used to process the information in a meaningful fashion. In agronomy, crop breeding, genetic and genomic, biology and soil science correlated variables are usually collected by researchers and different multivariate analyses have different aims depending on whether inference is required for the individuals (rows) for the variables )columns or for both simultaneously. For example, when a summary of the two-way table is required Factor analyses and/or Principal component analyses reduce dimensions and plot patterns in diagram named biplots where the individuals and variables are referenced by coordinates (factors of principal components). When the objective is to group individuals according to their variables, this type of analyses is called Classification and Discriminant analyses. Find relationships between columns in data tables, find dependencies and interdependencies and find out which columns are important in the relationship. These analyses are called Multiple regression analyses or Partial Least Squares (PLS), depending on the size of the data table. The multivariate normal density is a generalization of the univariate normal density (p≥2) and is a very useful approximation to the true population distribution. In general, data from agriculture experiments are multivariate as several correlated variables are recorded for each individual and or treatment or soil. Commonly measures made in several environments, years, agronomic treatments are multivariate in nature and should be treated accordingly. Several real examples in agronomy, crop breeding, genetic and genomic including genotype × environment interaction will illustrate the use of multivariate analyses of correlated data.