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Multivariate Statistical Methods and Classification Problems

Multivariate statistical methods are being used increasingly in an effort to clarify problems in psychiatric classification. Numerous references to their application could be given, but it is sufficient here to mention recent publications by Kiloh and Garside (1963), Carney, Roth and Garside (1965) and by Kendell (1968) which have received especial attention (e.g. Eysenck, 1970), as they are concerned with the longstanding controversy about the classification of depressive illness. But there is some confusion, not least amongst the critics, about the particular roles which different multivariate techniques, notably factor analysis, can play in classification problems, and in this paper an attempt is made to clarify the situation. Almost as a trial of the reader's endurance this attempt necessitates some preliminary discussion of the psychometric concept of a ‘unitary trait’ and of the statistical rules involved in defining it. But after this problem has been disposed of attention is confined to a discussion of the main multivariate techniques in question—factor analysis, discriminant function and canonical variate analysis, and finally cluster analysis. The attitude adopted in the paper is admittedly purist, but when controversy arises, as in the case of the classification of depressive illnesses, it is well to be clear about the precise properties and purposes of the statistical models we employ if confusion is to be avoided.