Factor Analysis of Data from an East Devon Heath: A Comparison of Principal Component and Rotated Solutions

Abstract

Since the pioneer work of Goodall (1954) and Dagnelie (1960), rather surprisingly little use has been made of factor analysis* by ecologists. As Professor W. T. Williams and others have emphasized, the name 'factor analysis' embraces a group of methods rather than a single technique. A number of biological applications have made use of 'principal component analysis', which, as Seal (1964) says, is 'intended to achieve a parsimonious summarization of a random sample from a . .. universe of multivariate Normal measurements' in contrast to 'factor analysis' which implies a hypothesis that the observed variables can be explained to a definite extent by a smaller number of underlying 'factors'. Lawley & Maxwell (1963) emphasize another, perhaps more practically important, difference-'that whereas a principal component analysis is variance-orientated, a factor analysis is covariance-orientated'. Principal component analysis is concerned primarily with the distribution of the individuals in relation to the axes of greatest variance in the data; factor analysis is concerned with exploring patterns of relationship among the variables. If there are a few strong overriding directions of variation in a set of vegetation data, these are likely to be reflected strongly and in a relatively simple way in a principal component analysis. But if the pattern of variation is at all complex, much interesting and significant ecological information may be as thoroughly hidden among the later and smaller components as it was in the original data. In such cases, the different questions asked by other factor analysis techniques may elicit more informative answers.