Comparing different models with covariates

[carolient...@gmail.com]

Hi there,

I want to compare three models but I wonder how to do it the cleanest way. It is a mediator, moderator and independent effects model with two covariates which I specified as follows:

H1 moderator: Model1 <- "

 BAG_z ~ CR_z + gender_beh + age_cen_within
 COG_z ~ CRxBAG_z + BAG_z + CR_z + gender_beh + age_cen_within
"

H2: mediator: Model2 <- "
  BAG_z ~ a*CR_z + gender_beh + age_cen_within
  COG_z ~ b*BAG_z + c*CR_z + gender_beh + age_cen_within

  indirect := a*b
  total    := c + (a*b)
"
H3: independent effects: Model3 <- "
 BAG_z ~  gender_beh + age_cen_within
 COG_z ~ CR_z + BAG_z + gender_beh + age_cen_within
"

I wonder about the covariate specification here, because I only added it to model 3 to make it more comparable to models 1 and 2, but it is actually not NEEDED for the model, because in this model COG_z is the only dependent variable. So I feel like I am including a regression line which is not actually necessary, but without it, I have a different nuisance structure in models 1 and 2 vs. model 3. 

What would you advise? I was also thinking of maybe removing the covariates from all the three models for the moderator/mediator (so for BAG_z) to make it more comparable. Would that be a better option than to include this nonsensical regression in model 3?

I hope my questions are a bit clear. Just for information, I use a bayesian approach in which the models are compared using LOOIC.

Thanks so much for your advise.

Carolien Torenvliet

[Edward Rigdon]

     Against what criterion do you want to compare the models? In terms of chi-square fit, they all appear to be saturated, so any comparison would be uninformative. Do you want to compare variance predicted for COG_z? Then the BAG_z line is irrelevant, as long as covariates are allowed to freely covary.

     You could use the "encompassing principle" strategy where you create one "supermodel" model that encompasses all of these models as special cases and then create testable sets of constraints that reduce the supermodel into each of those special cases. Then you might make comparisons using chi-square differences or Akaike information criterion values. See, e.g.:

https://doi.org/10.1080/00273170701329112

https://doi.org/10.2307/1911313

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[carolient...@gmail.com]

Thanks for your advice. I am sorry to have occupied your time, as I now realize I should have posted this question in the Blavaan group. It is a bayesian set-up. Still appreciate the advice and articles, and I will think it further through!

Op donderdag 4 december 2025 om 16:12:17 UTC+1 schreef edward...@gmail.com: