I'm following-up on this great answer. Essentially, I was wondering how could misspecification of random-effects bias the estimates of fixed-effects?

So, can the same set of fixed-effect coefficients become biased if we create models that only differ in their random-effect specification?

Also as conceptual matter, can we say in mixed-effect models, the fixed-effect coef is some kind of (weighted) average of the individual regression counterparts fit to each individual cluster and that is why fixed-effect coefs in mixed models can prevent something like this Simpson's Paradox case from happening?

A possible R demonstration is appreciated.

I'm following-up on this great answer. Essentially, I was wondering how could misspecification of random-effects bias the estimates of fixed-effects?

So, can the same set of fixed-effect coefficients become biased if we create models that only differ in their random-effect specification?

Also as a conceptual matter, can we say in mixed-effect models, the fixed-effect coef is some kind of (weighted) average of the individual regression counterparts fit to each individual cluster and that is why fixed-effect coefs in mixed models can prevent something like this Simpson's Paradox case from happening?

A possible R demonstration is appreciated.

I'm following-up on this great answer. Essentially, I was wondering how could misspecification of random-effects bias the estimates of fixed-effects?

So, can the same set of fixed-effect coefficients become biased if we create models that only differ in their random-effect specification?

A possible R demonstration is appreciated.

I'm following-up on this great answer. Essentially, I was wondering how could misspecification of random-effects bias the estimates of fixed-effects?

So, can the same set of fixed-effect coefficients become biased if we create models that only differ in their random-effect specification?

Also as conceptual matter, can we say in mixed-effect models, the fixed-effect coef is some kind of (weighted) average of the individual regression counterparts fit to each individual cluster and that is why fixed-effect coefs in mixed models can prevent something like this Simpson's Paradox case from happening?

A possible R demonstration is appreciated.