An Operational Approach to Multivariate Classification:with reference to agriculture

Abstract

Social and economic classification schemes have traditionally been administrator constructed, are essentially univariate in nature, and reflect the historical development of a range of structures in society. Advances in multivariate statistical analysis over the last fifty years, together with modern computing power, have made possible the classification of companies, farms, people, families, commodities, or any other entities using data-based polythetic methods. The feasibility of designing an efficient and understandable operational approach to this type of multivariate classification is investigated with reference to agriculture and the results compared with a proposed a priori Farm Typology. The requirement to reduce the size of the variable set employed in an optimization-partition method of cluster analysis suggested the value of principal components or factor analysis as a means of identifying major 'source' dimensions against which to measure farm differences and similarities. Such source dimensions were found to be not unduly sensitive to changes in the sets of either observations or original variables. The need to standardize variables prior to the extraction of factors was, however, confirmed. The Euclidean cluster analysis incorporating the reduced dimensions quickly converged to a stable solution and was little influenced by the initial number or nature of 'seeding' partitions of the data. The most distinctive cluster classes were equally identified in three experimental samples of 500 observations, while the slightly poorer resolution of general mixed farm groups was hopefully eliminated by final classification based on a ten percent sample of some 2200 observations. Although size standardization of most Farm Structure Survey variables has occurred, Classification I using unstandardized component scores still had an important holding size element. Upon standardization, the first two size/technology components have their weight in classification reduced so that an alternative Classification II was produced. The assignment of non-sampled observations from the population to the classes of Classifications I and II was completed using classification functions, stepwise multivariate analysis of variance having indicated the number of useful discriminating variables to be some two-thirds of the total originally included in analysis. The final schemes were found to be both interpretable and meaningful agriculturally and superior in their explanatory power in comparison with the Farm Typology