Hello,

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 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 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!

As you probably know, the way OpenMx analyzes an ordinal variable is by presuming that such a variable reflects a continuous underlying latent variable that has been discretized into the observed ordinal variable. Because the underlying continuous variable isn't observed, its scaling has to be fixed by some constraint that identifies the liabilty-threshold model. The "location" of the scaling requires that either the latent liability's mean is fixed, or one of its thresholds is fixed. In the case involving regression onto a covariate, the regression intercept needs to be fixed (usually to zero), whether it's the mean or the threshold that's conditioned on the covariate. The choice between conditioning the mean or the threshold on the covariate is arbitrary, so go with whichever you find easier to interpret. Personally, I find it much easier to interpret conditioning the mean on the covariate.

thank you!