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

Abstract

Bifactor latent models have gained popularity and are widely used to model construct multidimensionality. When adopting a confirmatory approach, a common practice is to assume that all cross-loadings take zero values. This article presents the results of a simulation study exploring the impact of ignoring non-zero cross-loadings on the performance of confirmatory bifactor analysis. The present work contributes to previous research by including study conditions that had not been examined before. For instance, a wider range of values of the factor loadings both for the group factors and the cross-loadings is considered. Parameter recovery is analyzed, but the focus of the study is on assessing the sensitivity of goodness-of-fit indices to detect the model misspecification that involves ignoring non-zero cross-loadings. Several commonly used SEM fit indices are examined: both biased estimators of the fit index (CFI, GFI, and SRMR) and unbiased estimators (RMSEA and SRMR). Results indicated that parameter recovery worsens when ignoring moderate and large cross-loading values and using small sample sizes, and that commonly used SEM fit indices are not useful to detect such model misspecifications. We recommend the use of the unbiased SRMR index with a cutoff value adjusted by the communality level (R2), as it is the only fit index sensitive to the model misspecification due to ignoring non-zero cross-loadings in the bifactor model. The results of the present study provide insights into modeling cross-loadings in confirmatory bifactor models but also practical recommendations to researchers.

Characterizing the relationship between personality traits and safety motivation among construction workers

“…For instance, Kolar and Zabkar [ 48 ] claimed that the factor loading should be over 0.6 in their study, while a more common threshold was 0.4 by Byrne [ 49 ]. The cross-loading should also be less than 0.3 to discriminate between factors [ 50 ], and the low the better [ 51 ]. In this study, all the factor indicators generally had loading values greater than 0.6, and all cross-factor loadings were less than 0.3.…”

Psychometric Properties of the Albanian Version of the Nursing Self-Efficacy Scale

“…These four factors explained 62.96% of the overall variance. Although some items had cross-loads with similar loads between the factors, overall, this solution demonstrated a good structure [ 40 ]. The factor loadings are shown in Table 3 .…”

Psychometric Validity of the Areas of Work Life Scale (AWS) in Teachers and Healthcare Workers in México

“…Even with this omission of cross-loadings, the overall fit coefficients of the AWS measurement models were not substantially low, and only the introduction of the second model (method factor, CFA-met) was sufficient for the fit to be satisfactory (i.e., statistically non-significant using SRMRu as a criterion). Overall, we can assume an innocuous effect of the potential cross-loadings on the AWS, and that they were not detected with the adjustment indices due to their small magnitude [ 67 ]. On the other hand, the constraints of self-reporting measures and the use of a non-representative sample must also be recognized as limitations, but we believe that the robust estimations used in this study attenuated these limitations to some extent.…”

“…In the global fit, the exact fit tests were χ 2 goodness-of-fit (WLSMV-χ 2 ) and SRMR-unbiased (SRMRu), used as hypothesis testing with confidence intervals [ 64 ]. SRMRu for these decisions has shown to have lower Type I error and has proven to be more robust than different estimation methods [ 64 , 65 , 66 ] on non-normal data, especially with estimators such as WLSMV, and with sensitivity to misspecifications due to omitted cross-loadings [ 67 ]. With SRMRu, the fit was evaluated with an adjusted cutoff point based on the ratio SRMRu/ : × 0.05 ( × 0.05) (=average squared factor loadings, or communality) [ 68 ].…”