Slightly off topic, but related :-) [Design Issues]

posted by PharmCat  – Russia, 2019-12-22 02:12 (1613 d 16:26 ago) – Posting: # 21013
Views: 5,783

Hi ElMaestro!

❝ This. I think, is around the "effective zero" for fits in R at default settings on 64- and 32-bit systems.

Anyway residual "can't" be zero.

❝ Is this a fact? How do we actually know this? Do you have a reference I coud learn from (not Pinheiro and Bates, I don't understand a word of it).

For ML: Yes, it's a fact. ML biased always "by definition". proof

For REML: this is a more difficult question. We can see following:

* link 1
* link 2
* link 3
* link 4
* link 5
* link 6

Some links behind the paywall, but this problem can be solved with sci-hub.

What can we say: "REML does effectively reduce bias.", "The REML estimates are typically less biased than the ML methods."

REML does not always eliminate all of the bias in parameter estimation, since many methods for obtaining REML estimates cannot return negative estimates of a variance component. However, this source of bias also exists with ML, so REML is clearly the preferred method for analyzing large data sets with complex structure.

Hm... I understand that REML not always unbiased. May be I'm wrong, but all above make me think this.

❝ Does "less biased" apply to both the fixed effects and to the variance components?

Mmm. If we call model coefficients as fixed effects - they are unbiased, no problems with them. Variance component in LM if say strictly is a model error. LM have analytical solution and ubiased estimator of variance. But model should be fitted correctly: each level of any factor should have at least 2 observations.

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