Why is Measurement Equivalence Important?

QuantFish instructor and statistical consultant Dr. Christian Geiser explains why measurement equivalence (invariance) is important in the context of confirmatory factor analysis and structural equation modeling.
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[@holyw5478]

Great video, helped me read DATA for my annotated bibliography

[@crazystatistician]

Thank you so much for this question. I have a couple of questions about measurement equivalence across times.
1. After I test the configural invariance for the same latent factor, if I obtain poor model fit information from the following fit indices: CFI, TLI, RMSEA, and SRMR, can I explore modification indices and, for instance, add residual covariance based on M.I.? Alternatively, should I refrain from proceeding to calculate the metric invariance model due to the poor model fit of the configural invariance model?
2. If I am allowed to add residual covariances, should I specifically add covariances between residuals belonging to the same latent factor at both time points (time 1 and time 2)?

[@QuantFish]

It definitely does not make sense to proceed to higher levels of invariance (e.g., metric) when the configural model is rejected (when it does not fit your data). One reason for misfit can be shared indicator-specific variance across time. Although this can indeed be modeled by allowing for autocorrelated error variables for the same variables across time, I prefer an approach with residual method (indicator-specific) factors. See my RUclips videos here:
ruclips.net/video/5kv4poKf6Cw/видео.html
ruclips.net/video/qQhmIMFFOns/видео.html
Best,
Christian Geiser