Principal components analysis (PCA) is an ordination technique used primarily to display patterns in multivariate data. It aims to display the relative positions of data points in fewer dimensions while retaining as much information as possible, and explore relationships between dependent variables. In general, it is a hypothesis-generating technique that is intended to describe patterns, rather than test formal statistical hypotheses. Although PCA was originally developed to analyze continuous variables, it can also be used on ordinal and presence-absence data.
PCA is carried out on the response of dependent variables in a multivariate data set. Consequently it is an unconstrained ordination, in which hypothetical causal independent variables are not explicitly included in the analysis. For example, if the abundance of several species of fish (the response or dependent variables) were measured at a range of different sites with different characteristics such as wave exposure (causal or independent variables), the exposure information would not be explicitly included in the analysis. Patterns recovered in PCA are solely a function of relationships between the dependent variables. For this reason, PCA can also be classified as an indirect gradient analysis, in which hypothetical causal processes such as exposure, moisture, etc., are inferred from patterns in the dependent variables. PCA assumes that the relationships between dependent variables are linear. This implies that PCA should be applied when most dependent variables have nonzero values across most of the samples, and that bivariate scatterplots of each variable against each other variable should be linear or at least monotonically increasing or decreasing. PCA is a very useful analytical tool, and is one of the most widely used ordination methods in ecology.
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