[R-sig-ME] Testing Random Effects--On the Boundary

[Ben Bolker]

On 13-11-21 02:47 PM, AvianResearchDivision wrote:
> Hi all,
> 
> I've read multiple times that using LRT to test the significance of random
> effects terms in mixed models yields conservative p-values and that one way
> to correct this is to divide the p value in half.  Is this a hard fast rule
> or is there a script for R that gives an actual corrected value?
> 
> Thank you,
> Jacob

  It's not hard and fast.  Fabian Scheipl's RLRsim package gives a fast
stochastic algorithm for getting the correct null distribution in these
cases, but it only works for a subset of models.  I *believe* (but may
misremember) that for the simple case of a single, scalar random effect
(i.e. a single blocking factor with an intercept effect only, ~ ... +
(1|block)) that the null distribution is provably 0.5*chi^2(0) +
0.5*chi^2(1) (i.e., you should divide by 2), but (1) this might only
hold for LMMs (not GLMMs) and (2) it might only hold asymptotically and
(3) it definitely doesn't hold for more complex random-effects models.
Pinheiro and Bates 2000 discuss this (as referenced in
http://glmm.wikidot.com/faq#random-sig ; I believe the ur-reference is
Stram and Lee (1994), it's also discussed briefly in Bolker (2008) p 250:

http://ms.mcmaster.ca/~bolker/misc/Bolker_2008_p250.pdf

P&B incorporated simulation machinery in nlme (?simulate.lme -- note
that simulate.lme *predates* the more general simulate() accessor in
base R, and works differently); this sort of functionality can be
replicated pretty easily with lme4, but it will be slow.


Stram, Daniel O, and Jae Won Lee. 1994. “Variance Components Testing in
the Longitudinal Fixed Effects Model.” Biometrics 50 (4): 1171–1177.
http://links.jstor.org/sici?sici=0006-341X%28199412%2950%3A4%3C1171%3AVCTITL%3E2.0.CO%3B2-H.