Negativity of factor correlations biases the sizes of factor variances in bifactor CFA models

Abstract

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Estimates of factor variances observed together with negative factor correlations in CFA using the bifactor model are explored for specific characteristics. The analysis is conducted on the basis of quantified accounts of common systematic variation achieved by the two group latent variables of the model. It reveals that negative factor correlations tend to be associated with larger factor variance estimates than the zero correlation and positive correlations. Further, it reveals that upper limits to the sizes of factor variances for positive factor correlations corresponding to expectations exist while in negative correlations such limits are missing and allow for overly large factor variance estimates. Results of the analysis based on quantified accounts are supported by the results of a simulation study.

Keywords

• factor variance
• factor loading
• confirmatory factor analysis
• bifactor model
• group latent variable
• group factor