Factor Analysis of Ipsative Measures

Abstract

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.

The use of a multilevel statistical model to analyze factors influencing land use: a study of the Ecuadorian Amazon

“…Chan and Bentler (1993) provided an algorithm to test if a model is identifiable, while Greer and Dunlap (1997) demonstrated that multiplicative ipsative data are immune to Type I error inflation and loss of power. Studies using ipsative data include Cheung and Chan (2002), Dunlap and Cornwell (1994), Chan and Bentler (1993), Jackson and Alwin (1980). Suppose we have j=1, .…”

A Subcultural Analysis of the Brazilian Knowledge Industry: When Nation, Industry, and Organizational Cultures Collide

“…The resulting response vector has a sum of 200 and each dimension can range from 5 to 20. The ipsative nature of the instrument precludes evaluation using traditional factor analytic techniques (Closs, 1996;Dunlap and Cornwell, 1994) and interitem reliabilities for scales must use Monte Carlo, or enumerative variance estimation techniques to compensate for negative mean intercorrelations. Using alternative reliability computations, scale reliabilities vary from .6 to .9.…”

Ipsative measurement and the analysis of organizational values: an alternative approach for data analysis

“…A fundamental criticism is that scores on a multi-scale measure are statistically interdependent on both item and covariance levels (Meade 2004): true and error scores are contaminated across scales, so reliability is difficult to assess. Because of these features, conventional correlation-based methods-such as factor analysis, regression analysis, and LISREL-are not allowed (Guilford 1952;Cleman 1966;Massy et al 1966;Jackson and Alwin 1980;Chan and Bentler 1993;Dunlap and Cornwell 1994;Cornwell and Dunlap 1994). Also, the interpretation of results may be problematic, since the correlations between constant-sum scales and between ipsative factors often turn out to be spuriously negative (Cleman 1966;Hicks 1970;Johnson et al 1988;Baron 1996;Brown and Bartram 2009).…”