Estabrook and Wu (2016)

[Farideh Alizadeh]

Dear Prof. Rosseel,

I’ll be thankful if you comment on this issue. I was recently introduced to Estabrook and Wu (2016). I think they argue that for testing metric MI, thresholds+loadings must be constrained, and for scalar MI, thresholds+loadings+intercepts must be constrained.

Is my understanding correct?  

Do we have both thresholds and intercepts in ordinal data? Aren’t they the same? 

Doesn’t metric and scalar become the same in this case?

To what extent is their argument accepted by the community?

 The paper was published in 2016.  How has it been received? Has it become a standard practice for ordinal data? Is deviation for this workflow considered wrong? 

Does it really change MI decisions?

Best

Farideh

Wu, H., & Estabrook, R. (2016). Identification of Confirmatory Factor Analysis Models of Different Levels of Invariance for Ordered Categorical Outcomes. Psychometrika, 81(4), 1014–1045. https://doi.org/10.1007/s11336-016-9506-0