title: Iteration of Partially Specified Target Matrices: Application to the Bi-Factor Case.
abstract: The current study proposes a new bi-factor rotation method, Schmid-Leiman with iterative target rotation (SLi), based on the iteration of partially specified target matrices and an initial target constructed from a Schmid-Leiman (SL) orthogonalization. SLi was expected to ameliorate some of the limitations of the previously presented SL bi-factor rotations, SL and SL with target rotation (SLt), when the factor structure either includes cross-loadings, near-zero loadings, or both. A Monte Carlo simulation was carried out to test the performance of SLi, SL, SLt, and the two analytic bi-factor rotations, bi-quartimin and bi-geomin. The results revealed that SLi accurately recovered the bi-factor structures across the majority of the conditions, and generally outperformed the other rotation methods. SLi provided the biggest improvements over SL and SLt when the bi-factor structures contained cross-loadings and pure indicators of the general factor. Additionally, SLi was superior to bi-quartimin and bi-geomin, which performed inconsistently across the types of factor structures evaluated. No method produced a good recovery of the bi-factor structures when small samples (N = 200) were combined with low factor loadings (0.30-0.50) in the specific factors. Thus, it is recommended that larger samples of at least 500 observations be obtained.
authors.affiliation: a Autonomous University of Madrid.
authors.forename: Francisco J
authors.initials: FJ
authors.lastname: Abad
authors.affiliation: a Autonomous University of Madrid.
authors.forename: Eduardo
authors.initials: E
authors.lastname: Garcia-Garzon
authors.affiliation: b Universidad Iberoamericana.
authors.forename: Luis E
authors.initials: LE
authors.lastname: Garrido
authors.affiliation: c University of Zaragoza.
authors.forename: Juan R
authors.initials: JR
authors.lastname: Barrada
mesh_terms: D003627:Data Interpretation, Statistical; D005163:Factor Analysis, Statistical; D006801:Humans; D015233:Models, Statistical; D009010:Monte Carlo Method; D015999:Multivariate Analysis; D011788:Quality of Life
keywords: Bi-factor rotation; Schmid-Leiman; exploratory factor analysis; target rotation