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Measurement Invariance in Longitudinal Bifactor Models: Review and Application Based on the p Factor.

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St Clair, Michelle 
Brodbeck, Jeannette 
Wilkinson, Paul O 
Goodyer, Ian M 


Bifactor models are increasingly being utilized to study latent constructs such as psychopathology and cognition, which change over the lifespan. Although longitudinal measurement invariance (MI) testing helps ensure valid interpretation of change in a construct over time, this is rarely and inconsistently performed in bifactor models. Our review of MI simulation literature revealed that only one study assessed MI in bifactor models under limited conditions. Recommendations for how to assess MI in bifactor models are suggested based on existing simulation studies of related models. Estimator choice and influence of missing data on MI are also discussed. An empirical example based on a model of the general psychopathology factor (p) elucidates our recommendations, with the present model of p being the first to exhibit residual MI across gender and time. Thus, changes in the ordered-categorical indicators can be attributed to changes in the latent factors. However, further work is needed to clarify MI guidelines for bifactor models, including considering the impact of model complexity and number of indicators. Nonetheless, using the guidelines justified herein to establish MI allows findings from bifactor models to be more confidently interpreted, increasing their comparability and utility.



longitudinal bifactor modeling, measurement invariance, p factor (general psychopathology), review, simulation studies

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SAGE Publications
Wellcome Trust (095844/Z/11/Z)
Wellcome Trust (204845/Z/16/Z)
National Institute for Health and Care Research (IS-BRC-1215-20014)
This research was supported by the Cambridge-UCL Mental Health and Neurosciences Network (Wellcome Trust grant 095844/Z/11/Z), the NIHR Collaboration for Leadership in Applied Health Research & Care East of England grant, the NIHR Cambridge Biomedical Research Centre (BRC-1215-20014), the Cundill Centre for Child and Youth Depression at the Centre for Addiction and Mental Health, Toronto, Canada, and the Wellcome Trust Institutional Strategic Support Fund (204845/Z/16/Z).