Factor Analysis of Ipsative Measures

lpsative measures are multiple measures, where the data are collected, or are modified, in such a way that all subject totals across the measures are equal. Much has been written about factor analysis with such data, however, no clear consensus has been reached regarding the suitability of ipsative measures for factor analysis. The purpose of the present article is to show analytically the fundamental problems that ipsative measures impose for factor analysis. The expected value of the correlation between ipsative measures is shown to equal - 1/ ( k - I), where k is the number of measures. The rank of the resulting correlation matrix is reduced by one to k - 1, and ipsativity alone produces k - 1 artifactual bipolar factors, which will obscure any actual interrelations among the measures. If the data are known to be ipsative or if the tell-tale signs of ipsativity are seen, factor analysis should not be done.