Foundations of factor analysis: Some practical implications

The paper discusses some practical implications of a new approach to factor analysis expounded in Bartholomew (1984). The problem with which it deals may be posed in the following way. Given p variables measured on n individuals, to find one or more functions of these variables which, in some sense, effectively summarize what is common to the larger set. It was shown in the earlier paper that, under fairly general conditions, such a summarization can efficiently be achieved by linear functions of the manifest variables. Here, the consequences of this result are explored in relation to such matters as rotation of axes, factor scores, non‐linear and hierarchical factor analysis. The conclusion reached is that while almost all of the existing numerical methods relating to the estimation of factor models remain relevant, the presentation and interpretation of the results is substantially modified. In particular, the focus is shifted from unobservable factors to observable functions of the data and the distinction between orthogonal and oblique rotations has no significance.