Hello there,

It seems that latent variables can be continuous and categorical. Please see attached links

Regards, Witold

https://www.statmodel.com/features2.shtml

https://www.statmodel.com/features1.shtml

Dear Mansour,

Thank you.

Tobi.

Dear Orlik,

Thanks for the contribution and providing the links to Mplus/Statsmodel. I understand that latent variables can be continuous and categorical. Moreover, I am trying to better understand why latent variables in SEM are continuous or assumed to be continuous (Kline, 2011, 2015).

Thanks once again.

 Tobi.

References:

Kline (2011) Principles and Practice of Structural Equation Modeling, Third Edition. Guilford Press.

Kline (2015) Principles and Practice of Structural Equation Modeling, Fourth Edition. Guilford Press.

Hello again,

They are continuous primarily for the reason they are based on numerous observed items (variables). These observed items are often categorical or continuous themselves. For example latent construct of PTSD is based on 30 items with categorical Likert type answer format (1 to 5 range scores for a single item). If you combine them together then the total range is from 0 to 150. Of course in SEM you do not apply total scores as very strong assumptions need to be met (that every single item contributes EQUALLY to the summed score - and this is very unlikely as factor loadings DO differ). In consequence such concept as PTSD is latent, not directly observed. 

To simplify this explanation some researchers agree that categorical is becoming continuous at around 5 answer categories (Likert type!), so with range from 0 to 150 you are dealing with a continuous variable. 

Regards, Witold

Thank you, Witold.

Tobi.

You are very welcome, hope it helped a bit. 

Just take these pieces of information please that are of any use to you. Do not bother about the rest.

Good luck with your research, 

Witold