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

Abstract

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.

Social Well-Being at School: Development and Validation of a Scale for Primary Education Students

“…An EFA was conducted after the validation and reliability analyses (Zhang et al, 2019). Following guidelines given Watkins (2018), first, a testing for normality of distribution using Kolmogorv-Smirnov parameter was carried out.…”

Target rotation with both factor loadings and factor correlations.

“…As comparisons, we also conduct CFA and EFA with regular target rotation. Extended target rotation and target rotation are conducted using the R package EFAutilities (Zhang, Jiang, Hattori, & Trichtinger, 2018); the CFA is conducted using the R package lavaan (Rosseel et al, 2017). We include the R code of conducting EFA with extended target rotation in Appendix B 1…”

“…Extended target rotation incorporates researchers’ substantive knowledge more effectively than other rotation methods. Extended target rotation has been implemented in an R package EFAutilities (Zhang et al, 2018). We demonstrated extended target rotation with an MTMM study and a study of eight cognitive tests.…”

“…1We also prepared a tutorial on the R package EFAutilities (Zhang et al, 2018) to make extended target rotation more accessible. The tutorial is available at the web address https://www3.nd.edu/~gzhang3/Papers/RCPhi/RCPhi.html…”

Local minima and factor rotations in exploratory factor analysis.

“…Later authors (Browne, 2001; Gebhardt, 1968; Hattori et al, 2017; Jennrich, 2004, 2006; Kiers, 1994; Rozeboom, 1992) showed that other rotation criteria were also prone to this phenomenon. Given these findings, it is surprising that few modern EFA programs allow users to initiate factor rotations from different starting values (important exceptions are Bernaards & Jennrich, 2005; Browne et al, 2008; Muthén & Muthén, 2017; Waller, 2020; Zhang et al, 2020). Perhaps this missing option explains, in part, why many applied researchers are seemingly unaware of the prevalence and correlates of LS in EFA.…”