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Post by NullModelBestModel on Jun 5, 2016 9:08:31 GMT
Greetings all ye damned in statistics hell, here's a question:
We have ML and REML for estimating the parameters for the mixed effects model, right?
To summarize, ML is negatively biased but usually has lower MSE. REML, on the other hand, is approximately unbiased, but you end up with larger variability in the estimates.
So far so good, but: did Prof. Alonso cover during his lectures when to use which? Or is it a matter of taste and/or resulting fit?
~ Alex
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Post by Karel on Jun 5, 2016 10:58:38 GMT
Yes!
You can only use REML if the fixed (main) effects in the model are the same. ML works for both changed and unchanged fixed effects. ML needs high enough observations (sample large enough) while REML does reasonably well with a small n. But all that is on slide 53, no?
So NEVER embark on ruling in or out of main predictors in your model/comparing models with different predictors if you've used REML. You're dead in the water if you do.
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Post by NullModelBestModel on Jun 5, 2016 12:34:55 GMT
Yes! You can only use REML if the fixed (main) effects in the model are the same. ML works for both changed and unchanged fixed effects. ML needs high enough observations (sample large enough) while REML does reasonably well with a small n. But all that is on slide 53, no? So NEVER embark on ruling in or out of main predictors in your model/comparing models with different predictors if you've used REML. You're dead in the water if you do. Thanks for the reply! Slide 53 eh? Thanks for alerting me to the fact I was using the outdated slides. D: Anyway, I have one follow-up question: So if I understand it right, REML is only to be used to estimate the parameters in two models that have the same fixed effects. This is because comparisons between two or more models with differing fixed effects, that have been estimated through REML are useless. And I guess the reason for the comparison being useless is connected to the fact that REML takes into account the number of fixed effects parameters when calculating the likelihood. And one obvious example where REML can be used to estimate the parameters is when comparing two models that share the same fixed effects but differ in their variance structure (heterosc. vs homosc. models). The follow-up question concerns what counts as the "same fixed effects" ? Say I have two models that share the structure: Y = B0 + B1XNow, one of the models uses random effects in both slope and intercept, while the other one only models random effects in the slope. The structure of the fixed effects remain the same, with only one predictor X in each model, but B0 and B1 will obviously behave differently between the two models. So, they differ in the random effects, while keeping the amount of predictors constant — does this disqualify using REML for estimation and comparison? ~ Alex |
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Post by Karel on Jun 5, 2016 13:04:01 GMT
I think that qualifies for REML.
The reason why the fixed effects have to be constant for REML is that fact that you orthogonally transform the fixed-effects-matrix (X) first when you do REML (A'X=0). This transformation is applied on the matrix with the fixed effects only (so meddling with random and variances is no problem). However, if you start throwing stuff out of X (dropping (or adding) fixed effects) then your transformation is no longer valid. That's how I understood it :-)
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Post by NullModelBestModel on Jun 5, 2016 13:15:11 GMT
I think that qualifies for REML. The reason why the fixed effects have to be constant for REML is that fact that you orthogonally transform the fixed-effects-matrix (X) first when you do REML (A'X=0). This transformation is applied on the matrix with the fixed effects only (so meddling with random and variances is no problem). However, if you start throwing stuff out of X (dropping (or adding) fixed effects) then your transformation is no longer valid. That's how I understood it :-) Thanks, I understand it all better now! ~ Alex |
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Post by Carlos on Jun 6, 2016 10:11:10 GMT
Hot topic this one! The latter issue mentioned also sparked another question with me: I noted down that, if you use REML, you can't use p-values by anova anymore, which makes sense I guess since we've been told over and over that anova builds up the model along the way, so X changes. But then what about the summary() method? I didn't note anything down for that method and don't remember Alonso saying anything about it, but I'm kind of inclined to say it is also not okay to use that. On one hand, it tests H0: beta = 0 vs H1: beta != 0 for a certain parameter, so you could say that X is left unchanged. But on the other hand, if you would allow THAT, I was thinking that anova would also not be a problem: just formulate it as "I'm not going to change X, I'm just going to change a decreasing number of beta-values to 0". Anyone have a thought? Am I completely wayward?  |
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