An Index of Fit for Factor Scales

Abstract

An index is defined for each column of a factor matrix to measure the goodness of fit for scale defining items, where the latter are determined in advance by the investigator. Let MS(S), MS(NS), and MS(T) be the mean-square loadings for scale items, nonscale items, and total items, respectively, for a given factor. A measure denoted IFFS (index of fit for factor scales) is defined as the signal-to-signal plus noise ratio: IFFS = 1 - MS(NS)IMS(T). The highest possible value of IFFS is 1.00, with .50 indicating that scale items are no better than nonscale items in defining the construct. An overall measure is also defined. The index is complemented by Kaiser's index of factor simplicity (IFS) as computed for each scale item. Evaluative criteria and examples are presented.