categorical variable mediation analysis

[Kevin]

Dear all,

I am having a bit of a hard time understanding how exactly lavaan handles ordinal variables in the mediation example https://lavaan.ugent.be/tutorial/mediation.html.

From the model output, it seems that lavaan introduces a new latent variable M and does probit regression for the M ~ X submodel.

However, the documentation is unclear how this is then linked to the Y ~ M model. I get a single coefficient. The documentation suggests that lavaan would treat M as a simple numerical variable in the Y ~ M regression, is that correct?

Thanks!

[Terrence Jorgensen]

The documentation suggests that lavaan would treat M as a simple numerical variable in the Y ~ M regression, is that correct?

No, if M is endogenous and identified as ordered=, it will be treated as an indicator of a normal latent response variable (LRV).  Any equation in the entire system that includes M will be modeling its LRV.  The LRV is linked to the observed discrete M via the thresholds.  These might be helpful:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3162326/

https://doi.org/10.1080/10705511.2015.1062730

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[Guillermo Soto Arias]

I have a similar question. What happens if my mediator variable is a nominal variable with two values ​​without any order? Should I still use the ordered argument or should I recode my variable to dummy?

[Terrence Jorgensen]

nominal variable with two values ​​without any order? 

For binary variables, the distinction between nominal and ordinal is only conceptual.  You can declare it as ordered, where the variable captures the presence or absence (but no intermediary amounts) of some quality.