ROPE or Equivalence Tests for parameters from different regression models?

[emstruong]

Describe the solution you'd like
An extension of equivalence_test() that allows you to pass several models as arguments, then to compare whether a particular named parameter is equivalent across the (2) models.

How could we do it?
I'm not sure. Although, this is related to the frequentist practice of Seemingly Unrelated Regressions.

[mattansb]

You want to test is two estimates from different models are the same? I'm not sure a ROPE analysis is the best fit here - maybe overlap()?

library(rstanarm)
library(bayestestR)

m1 <- stan_glm(mpg ~ wt, data = mtcars, refresh = 0)
m2 <- stan_glm(mpg ~ wt + hp, data = mtcars, refresh = 0)
m3 <- stan_glm(mpg ~ wt + am, data = mtcars, refresh = 0)

wt1 <- insight::get_parameters(m1)[["wt"]]
wt2 <- insight::get_parameters(m2)[["wt"]]
wt3 <- insight::get_parameters(m3)[["wt"]]

(ovrl <- overlap(wt1, wt2))
#> # Overlap
#> 
#> 26.0%

plot(ovrl)

(ovrl13 <- overlap(wt1, wt3))
#> # Overlap
#> 
#> 85.0%

plot(ovrl13)

[emstruong]

My understanding of the problem has changed since I first opened this issue.

I suspect this might not be such a good idea to automate because I'm pretty sure that if you don't fit everything in one model, then you won't have modelled the covariance between the parameters. Or at least that's my understanding of SUR.

https://mc-stan.org/docs/stan-users-guide/regression.html#seemingly-unrelated-regressions

I think I should close this issue.