On selecting an appropriate multivariate analysis

Abstract

The broad objective of multivariate data analysis in biology is to summarize associations among species (the dependent or response variables), and to elucidate species responses to one or more environmental factors (the independent or predictor variables). This objective is achieved by reducing the dimensionality of variable space to an efficient, low-dimensional summative model of the underlying data structure that reflects the coordinated response of species to environmental factors. While multivariate methods have proven indispensable for analyzing both experimental and survey data in the biological sciences, considerable confusion persists regarding the selection of appropriate analytical strategies. The selection of an appropriate analytical strategy, which includes important decisions regarding data transformation, variable standardization and methodological approach, should be based on fundamental considerations of statistical appropriateness, data structure, and study objectives. Unfortunately, past and more recent assessments of multivariate analytical strategies have been based largely on empirical models of questionable relevance. This empirical approach has led to misleading recommendations and erroneous generalizations regarding the relative efficacy of the available multivariate methods. This paper dispels these misleading recommendations and provides some general guidelines for selecting appropriate data transformations, variable standardizations and methodological approaches in the multivariate analysis of biological data. Key words: Ordination, canonical analysis, co-inertia analysis, principal component analysis, correspondence analysis, non-metric multidimensional scaling