Testing diagonal covariance matrix

I have a question regarding testing diagonal covariance matrix (Full and partial block) in a model. Should we do it after adding the covariate effect into the final model, or before the stepwise process (base model)?

Thanks!

there is two schools of thought about this, newer engines like QRPEM would be happy with a full omega and then you can reduce it if you see fit

adding a covariate can reduce the off diagonals ( explain omega correlations) and also the diagonals

see the figure 2 diagmram here (full omega before doing covariate selection)

https://pubmed.ncbi.nlm.nih.gov/23836283/

I typically avoid doing scm (stepwise) there is tons of literature showing that it has major drawbacks:

https://ard.bmj.com/content/77/Suppl_2/5.1

you should look at full model that are plausible and useful to answer key clinical questions

Your detailed answer is really helpful, Thank you Sameer.