Adding to the confusion is the different ideas disciplines have about what "fixed effects" are. Statisticians think of _parameter_ fixed effects (as opposed to something that is "inside" a distribution), while soc scientist think of sets of parameters for each category/value.
So in general that within- and between-person associations can deviate often has to do with confounding and I think that’s what people usually think of when they talk about Simpson’s paradox.>
However I think the example from the text is a bit different (if you reframe it causally, it’s the immediate effect of exercise on heart rate vs the accumulated effects of repeated past exercise. Which, I guess, one could construe as a confounder here)
I know it's getting boring when I keep posting easystats-stuff, but here's an example (vignette) how to "tweak" mixed models (demeaning) to get unbiased estimates: https://easystats.github.io/parameters/articles/demean.html
I wouldn't call it "tweaking mixed models", because FE do the same. It rather about data...
...preparation - in case heterogeneity bias is present, you need person-mean centering. FE regression (or packages like feisr/lfe) just do this automatically, if I understand right.
I guess it will provide some relieve to you that in many fields people share your concerns regarding standard multilevel models 😂? In psych, there’s some consensus that for many research questions, the random intercepts aren’t sufficient.>
Appropriate standard errors are sometimes explicitly used as a justification for multilevel modeling, but I think that’s mainly because psychologists are literally unaware that alternative solutions exist.
Between you and @stephenjwild.bsky.social I don't think I will ever run out of interesting methods papers to read. I only worry I will end up like the guy in the Twilight Zone whose glasses break once he finally has time to read them all!
Curious about all this and frustrated that abstracts aren't anywhere near as useful as tweet (bleet, skeet, whatever) summaries. Since when do random effects not control for stuff, anyone have a summary for me?
If you’re coming from the SEM angle, random intercepts on both sides *that are allowed to correlate* work fine (that’s probably why you’re asking?). If you do a standard multilevel model, you only put a random intercept on the outcome, and that’s not sufficient to remove between-unit differences.
Do you know Raudenbush's work on adaptive centering (a powerful general method for "tweaking" RE models)? I love this paper: https://doi.org/10.1162/edfp.2009.4.4.468
Yes, if the unit is a person, that would be between-person differences. And to analyze the design in a manner that does indeed isolate the within-subject differences, it’s necessary to analyze the data appropriately (ie, a regular multilevel model usually isn’t sufficient)
I haven't followed the developments in multi-level modeling.
A paired t-test would do, or is there some deeper issue here. Sorry, but somethings methodologists go on and on about some things that have no practical relevance.
A paired t-test would do if you only have two occasions 😅 the generalization for more measurements would usually be concerned a multilevel model; but that doesn’t by default isolate the differences (as the paired t-test does).>
The appropriate generalization would be the fixed effects model (which is rare in psych), but it’s also possible to modify a multilevel model to do the trick.
From where does that belief come from? I guess i am glad that I rapidely came across the paper of Enders and Tofighi (2007) when learning about multilevel regression - truely an amazing paper imo
I’d guess it comes from not reading many methods papers to begin with 🤗 and rather just copying what you see others do, which may explain why this is heavily clustered by literature
Comments
I wouldn't call it "tweaking mixed models", because FE do the same. It rather about data...
I do love my correlated random effects / Mundlak devices / between-within models, so I guess I'm... a tweaker.
https://bsky.app/profile/stephenjwild.bsky.social/post/3l3jfholtwq2p
https://doi.org/10.1017/pan.2020.41
https://doi.org/10.1162/edfp.2009.4.4.468
https://link.springer.com/article/10.1007/s11135-018-0802-x
https://www.annualreviews.org/content/journals/10.1146/annurev-psych-020821-103525
Don't within-subject designs control for these because we compare a person to themselves?
A paired t-test would do, or is there some deeper issue here. Sorry, but somethings methodologists go on and on about some things that have no practical relevance.