Rotating Factors to Simplify Their Structural Paths.

Applications of structural equation modeling (SEM) may encounter issues like inadmissible parameter estimates, nonconvergence, or unsatisfactory model fit. We propose a new factor rotation method that reparameterizes the factor correlation matrix in exploratory factor analysis (EFA) such that factors can be either exogenous or endogenous. The proposed method is an oblique rotation method for EFA, but it allows directional structural paths among factors. We thus referred it to as FSP (factor structural paths) rotation. In particular, we can use FSP rotation to "translate" an SEM model to incorporate theoretical expectations on both factor loadings and structural parameters. We illustrate FSP rotation with an empirical example and explore its statistical properties with simulated data. The results include that (1) EFA with FSP rotation tends to fit data better and encounters fewer Heywood cases than SEM does when there are cross-loadings and many small nonzero loadings, (2) FSP rotated parameter estimates are satisfactory for small models, and (3) FSP rotated parameter estimates are more satisfactory for large models when the structural parameter matrices are sparse.

A Sandwich Standard Error Estimator for Exploratory Factor Analysis With Nonnormal Data and Imperfect Models.

This article is concerned with standard errors (SEs) and confidence intervals (CIs) for exploratory factor analysis (EFA) in different situations. The authors adapt a sandwich SE estimator for EFA parameters to accommodate nonnormal data and imperfect models, factor extraction with maximum likelihood and ordinary least squares, and factor rotation with CF-varimax, CF-quartimax, geomin, or target rotation. They illustrate the sandwich SEs and CIs using nonnormal continuous data and ordinal data. They also compare SE estimates and CIs of the conventional information method, the sandwich method, and the bootstrap method using simulated data. The sandwich method and the bootstrap method are more satisfactory than the information method for EFA with nonnormal data and model approximation error.

Target rotation with both factor loadings and factor correlations.

Factor rotation is conducted to aid interpretation in exploratory factor analysis (EFA). Target rotation allows researchers to directly examine the match between the rotated factor loading matrix and their expected factor loading pattern. In some EFA applications, however, researchers have expectations on both the factor loading pattern and the factor correlation pattern. We propose to extend target rotation such that target values can be specified for both factor loadings and factor correlations. We illustrate extended target rotation with a memory study and a personality study with the multitrait-multimethod design. We also explore the statistical properties of extended target rotation using simulated data. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Multiple Local Solutions and Geomin Rotation.

In exploratory factor analysis, factor rotation is conducted to improve model interpretability. A promising and increasingly popular factor rotation method is geomin rotation. Geomin rotation, however, frequently encounters multiple local solutions. We report a simulation study that explores the frequency of local solutions in geomin rotation and the implications of such phenomena. The findings include: (1) multiple local solutions exist for geomin rotation in a variety of situations; (2) ϵ = .01 provides satisfactory rotated factor loadings in most situations; (3) 100 random starts appear sufficient to examine the multiple solution phenomenon; and (4) a population global solution may correspond to a sample local solution rather than the sample global solution.