Timeline for Fixed vs. random effect meta regression
Current License: CC BY-SA 4.0
23 events
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| May 2, 2023 at 17:17 | vote | accept | user352188 | ||
| May 1, 2023 at 9:10 | comment | added | Christian Hennig | Nice added example. I have added something to my answer that addresses this. | |
| S Apr 30, 2023 at 10:03 | history | bounty ended | CommunityBot | ||
| S Apr 30, 2023 at 10:03 | history | notice removed | CommunityBot | ||
| Apr 23, 2023 at 15:56 | comment | added | Sextus Empiricus | The additional random interaction effect of individuals on intercept improves the standard error of the slope but not of the main intercept effect. In your case of meta regression it is like that, you are adding a random intercept and this makes the standard error of the intercept increase. | |
| Apr 23, 2023 at 15:46 | comment | added | Sextus Empiricus |
Also note that in your example the standard error of the intercept improves because of it's correlation with the slope. The addition of the random intercept only improves the estimate of the slope and not really the intercept parameter. If you do the same with first centering the age variable Orthodont$age = Orthodont$age-mean(Orthodont$age) then the difference between the two models is that the intercept has a smaller standard error for the intercept, in comparison to the model with the additional random effect.
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| Apr 23, 2023 at 15:45 | history | edited | user352188 | CC BY-SA 4.0 |
Removed misunderstanding
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| Apr 23, 2023 at 15:31 | comment | added | Sextus Empiricus | @user352188 I gave a line of code for this move from a fixed effect for subject to a random effect for subject. The standard error does not increase. | |
| Apr 23, 2023 at 15:27 | comment | added | user352188 | @SextusEmpiricus maybe that's where my confusion is coming from then. Adding a random effect as opposed to completely ignoring clustering will reduce the error variance and give lower standard errors, but when moving from a fixed effect for subject to a random effect for subject, the standard error will increase. | |
| Apr 23, 2023 at 15:25 | comment | added | dipetkov | Not sure the linear mixed model example helps. Age is a fixed effect in the LMM while in a random-effects meta-analysis the treatment effect is random. (There are differences in how the variances are modeled too.) Your intuition that meta-analysis is just like any other regression analysis may be misleading you. | |
| Apr 23, 2023 at 15:21 | comment | added | Sextus Empiricus |
In your code example you are comparing two models with a different number of effects. When you compare fixed effects versus random effects while keeping the number of effects the same, then the random effects has not a smaller standard error. Compare for example with summary(lm(distance~age+Subject,data=Orthodont)) which gives the same standard error of $0.06161$ for the age coefficient. So the smaller standard error is due to adding an effect and not due to turning a fixed effect model into a random effect model (the same smaller standard error can be achieved with a fixed effects model).
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| Apr 23, 2023 at 14:58 | history | edited | user352188 | CC BY-SA 4.0 |
added 550 characters in body
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| Apr 23, 2023 at 14:13 | comment | added | user352188 | @dipetkov I can't find a source that says using random effects will shorten the confidence intervals of the fixed effects. I may be mistaken. But if it is the case that they can in some cases do this, then I'm curious about why the article in the original post says definitively that in meta analysis the confidence intervals will get wider when random effects are used. I'm trying to figure out if there's something I'm missing about meta regression that makes it different than any other regression analysis. | |
| Apr 23, 2023 at 13:12 | comment | added | dipetkov | I agree that always is not a word that accords well with the practice of statistics. Then on the other hand, "I've seen implied many times" is not exactly convincing either. Do you have any references at hand? | |
| Apr 23, 2023 at 12:41 | comment | added | user352188 | @dipetkov the contradiction is what my question is about; something I have seen implied many times is that random effects models will lower the standard errors of the estimates compared to a fixed effects model. I am aware that this is not ALWAYS the case, but to read now that with respect to meta analysis, the standard errors will always INCREASE when using random effects versus fixed effects is extremely surprising as I've never heard that said about random effects models outside of meta analysis. As far as I'm concerned a meta regression is no different from any other regression? | |
| Apr 23, 2023 at 12:34 | comment | added | dipetkov | Thanks for the clarification; you might want to edit your question to highlight this. Furthermore, the claims "the random effects model will give larger standard errors" and "we use random effects models to gain power" contradict each other. The fixed effects analysis should be more powerful; the question would be whether it's justified. See more here: Justifications for a fixed-effects vs random-effects model in meta-analysis. | |
| Apr 23, 2023 at 12:32 | comment | added | user352188 | @dipetkov the former is what I had in mind. | |
| Apr 23, 2023 at 11:49 | comment | added | dipetkov | In your question would you like to assume that, to do the meta analysis, you have access only to the summary statistics from multiple studies with their standard error estimates & sample size info? Or you assume that you have the original patient measurements from all the studies? | |
| Apr 23, 2023 at 11:16 | answer | added | Christian Hennig | timeline score: 1 | |
| Apr 23, 2023 at 10:37 | answer | added | Sextus Empiricus | timeline score: 1 | |
| S Apr 22, 2023 at 8:37 | history | bounty started | user352188 | ||
| S Apr 22, 2023 at 8:37 | history | notice added | user352188 | Draw attention | |
| Apr 19, 2023 at 20:11 | history | asked | user352188 | CC BY-SA 4.0 |