Hello Stata users!

I am doing a Latent Profile Analysis with continuous indicators (gsem, lclass option). These indicators are probably not locally independent as some of them are symptoms that are probably dependent on each other (e.g. pain, anxiety, depression) and some are beliefs that relate to these symptoms (e.g. self-efficacy).

I read Canette's 2017 presentation where she states that conditional independence is not necessary with Gaussian variables and that we can include correlations among them.

Does this imply that we can disregard the assumption of local independence, or that we should explicitly relax the assumption for locally dependent variables within a class?
The latter seem to be suggested by others (e.g. by allowing error terms to covary within a class for these variables).

If the latter, how would one identify the locally dependent indicators in Stata, if possible?

Any help would be greatly appreciated.

Best regards,
Martin