TITLE:
Computational Identification of Confirmatory Factor Analysis Model with Simplimax Procedures
AUTHORS:
Jingyu Cai, Henk A. L. Kiers, Kohei Adachi
KEYWORDS:
Confirmatory Factor Analysis, Cardinality of Loadings, Simplimax Rotation
JOURNAL NAME:
Open Journal of Statistics,
Vol.11 No.6,
December
28,
2021
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.