Evaluation and Comparison of SEM, ESEM, and BSEM in Estimating Structural Models with Potentially Unknown Cross-loadings

What are the consequences of ignoring cross-loadings in bifactor models? A simulation study assessing parameter recovery and sensitivity of goodness-of-fit indices

“…These effects are more pronounced when the cross-loadings take larger values (0.20 or more) and the loadings in the group factors are smaller. These findings are congruent with previous research (Zhang et al, 2021a;Wei et al, 2022) and suggest that ignoring moderate and large cross-loadings and forcing them to take zero values will have a negative impact on parameter estimation. Our results of underestimation of the loadings in the group factors may explain the bias of overestimation of the loadings in the general factor and support that the phenomenon of factor collapse may have operated, such that the group factors improperly collapse onto the general factor.…”

“…Our findings of overestimation of the loadings in the general factor and underestimation of the loadings in the group factors are congruent with previous research (Hsu et al, 2014;Zhang et al, 2021a;Wei et al, 2022). These results also reflect that the phenomenon of factor collapse (Geiser et al, 2015;Mansolf and Reise, 2016) may have operated.…”

“…For instance, previous research argues that the problems of the cross-loadings can be overcome by using Exploratory SEM models (ESEM), which integrate EFA and CFA, allowing cross-loadings to be freely estimated rather than being constrained to zero (Asparouhov and Muthén, 2009); and Bayesian SEM (BSEM), where one can postulate cross-loadings not taking zero values and estimate them with reference to a prior distribution (Muthén and Asparouhov, 2012). Wei et al (2022) found that these approaches performed similarly in the case of zero cross-loadings, but SEM performed worse as cross-loadings increased, ESEM exhibited unstable performance in conditions of small factor loadings, and the performance of BSEM depended on the accuracy of the priors for cross-loadings. Thus, future research could be directed to test the effects found here in such models and evaluate whether Shi et al 's (2018) correction for the SRMR index based on communality level works reasonably well to detect model misspecification under these approaches.…”

“…As in the study by Beauducel and Wittmann (2005), they also found that the RMSEA and SRMR indices failed to detect model misspecifications by forcing cross-loadings to zero. More recently, Wei et al (2022) studied the effect of ignoring cross-loadings in SEM models. They considered cross-loading values ranging from 0 to 0.30 and target loadings ranging from 0.55 to 0.95.…”

“…Previous research has addressed these problems in the context of structural equation modeling (SEM) and CFA models (e.g., Beauducel and Wittmann, 2005;Hsu et al, 2014 andWei et al, 2022) but few studies have assessed these issues in the context of confirmatory bifactor models (only the recent study by Zhang et al, 2021a). The present study aims to fill this gap and goes beyond previous research in that it focuses specifically on confirmatory bifactor models and considers a wide range of study conditions to assess the importance of the magnitude of the factor loadings in bifactor models.…”