Computational Identification of Confirmatory Factor Analysis Model with Simplimax Procedures

Abstract

Confirmatory factor analysis (CFA) refers to the FA procedure with some loadings constrained to be zeros. A difficulty in CFA is that the constraint must be specified by users in a subjective manner. For dealing with this difficulty, we propose a computational method, in which the best CFA solution is obtained optimally without relying on users’ judgements. The method consists of the procedures at lower (L) and higher (H) levels: at the L level, for a fixed number of zero loadings, it is determined both which loadings are to be zeros and what values are to be given to the remaining nonzero parameters; at the H level, the procedure at the L level is performed over the different numbers of zero loadings, to provide the best solution. In the L level procedure, Kiers’ (1994) simplimax rotation fulfills a key role: the CFA solution under the constraint computationally specified by that rotation is used for initializing the parameters of a new FA procedure called simplimax FA. The task at the H level can be easily performed using information criteria. The usefulness of the proposed method is demonstrated numerically.