Dear all,
I have a question relating to the following paper:
Dubravka Svetina, Leslie Rutkowski & David Rutkowski (2020) Multiple-Group Invariance with Categorical Outcomes Using Updated Guidelines: An Illustration Using Mplus and the lavaan/semTools Packages, Structural Equation Modeling: A Multidisciplinary Journal, 27:1, 111-130, DOI: 10.1080/10705511.2019.1602776
I consider this a very helpful and instructive paper.
However, I was wondering if this approach (and the provided Mplus-/R-syntax) also works for models with correlated residuals?
I am analyzing a well fitting four factor model (19 ordinal indicators) with several correlated residuals (6 "with"-statements in Mplus) to account for method bias (similarly worded items).
So, how do I have to adjust the syntax appropriately to consider those correlated residuals?
Would be very happy for any answer! :)
Kind regards,
Jan
Well, you could re-parameterize the residual covariance as additional orthogonal factors with equal loadings across the two variables involved. Then the generalization is fairly straightforward.
PS Thanks for the alert.
I run in Lavaan to correlate the residuals. I decided to do based on modification indices tests. It suggested a residual relation and I fit the model there with no problem and in fact, the model fit was better.
Have you tried modification indices? It helps to make decisions.
In the Lavaan documents, you can find how to use it.
Regards,
Amalia
Check these articles:
1. Fischer, R., & Karl, J. A. (2019). A Primer to (Cross-Cultural) Multi-Group Invariance Testing Possibilities in R. Frontiers in psychology, 10, 1507. https://doi.org/10.3389/fpsyg.2019.01507
2. Structural Equation Modeling with categorical variables Yves Rosseel Department of Data Analysis Ghent University Summer School – Using R for personality research August 23–28, 2014 Bertinoro, Italy
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