Jonathan Horowitz

Dear Everyone:

Multilevel models, random intercept/effects models, hierarchical models, and mixed models are all the same thing. Any differentiation of them is nominalism.

Also, growth models are just special cases of the above. Or a special case of structural equation models, but since all regression methods are special cases of structural equation models, that's not so exciting.

If you disagree, you can try to prove me wrong. But I doubt you can.

Sincerely,
Me

#sociodon

Dec 22, 2022 at 4:38pmWeb
Show threadJonathan HorowitzDec 22, 2022
By the way, Andrew Gelman agrees with me:
https://statmodeling.stat.columbia.edu/2019/09/18/all-the-names-for-hierarchical-and-multilevel-modeling/
All the names for hierarchical and multilevel modeling | Statistical Modeling, Causal Inference, and Social Science

Show threadNathaniel D. PorterDec 22, 2022
@jonathanhorowi1 I wish we taught stats this way so each discipline understood how their methods are connected (really all just different specifications or reporting approaches) to others. Andy Field does a pretty good job of calling attention to this in his intro stat texts too.
Show threadJonathan HorowitzDec 22, 2022

@ndporter
It's funny, I was taught these were all the same thing. BUT

I was at an informal job interview for a rather prestigious R1, where the interviewer (who taught graduate statistics) seemed to think they were all different. I said, "You realize those are all the same things, right?" As you might guess, I did not get invited for an on-campus interview.

(It's fine, my job is amazing, I can't complain, I would take this one over that one anyway)

Show threadGiuseppe A. VeltriDec 22, 2022
@jonathanhorowi1 I support you 100%. In the social sciences, we love to be fractal in labels.
Show threadOmar LizardoDec 22, 2022
@jonathanhorowi1 Seems like mixed effects is what you want to call them to balance precision and inclusiveness. "Multilevel" or "hierachical" is too specific because it implies nested levels (people within classrooms or obs within people) and leaves out crossed (non-nested) effects. Same for growth which as you note is even more specific (time-ordered obs within units).
Show threadAndrew Heiss Dec 22, 2022
@jonathanhorowi1 @philipncohen evergreen (via @chelseaparlett)
Show threadPeter EllisDec 23, 2022
@jonathanhorowi1 I was always taught (and read) that these are the same, or rather that multi level and hierarchical models are special cases of mixed effects.