Covariate Effect in Liability Threshold Model

I want to write a script for a GxE-interaction with an ordinal outcome and a continuous moderator and was looking for some scripts that include a covariate effect on an ordinal outcome variable.
In this search I found a [script](https://static1.squarespace.com/static/58b2481a9f7456906a3b9600/t/5d9c0be7b3de004d53e6456b/1570507752071/oneACEoa.pdf) by Hermine Maes where she models the effect of the covariate (age) on the mean of the liability distribution of the outcome variable.
On the other hand, I found a [script](http://ibg.colorado.edu/cdrom2014/rijsdijk/Ordinal/ThreshLiab.pdf) written by Frühling Rijsdijk where she models the effect of the covariate on the thresholds of the outcome variable. So it seems that both approaches are feasible.
My question is what is the different reasoning behind the two approaches? So I'm happy if someone could explain me the idea behind the two approaches or recommend me some literature where I can read something about it.
Thank you very much!
choice is arbitrary
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thank you!
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