[R-sig-ME] Fwd: same old question - lme4 and p-values

[Andrew Robinson]

On Sun, Apr 06, 2008 at 10:15:09AM -0500, Douglas Bates wrote:
> On Sat, Apr 5, 2008 at 5:10 AM, Reinhold Kliegl
> <reinhold.kliegl at gmail.com> wrote:
> > Here is a section that worked in Kliegl, Risse, & Laubrock (2007, J
> >  Exp Psychol:Human Perception and Performance, 33, 1250-1251).
> >
> >  "Analysis
> >      Inferential statistics are based on a linear mixed-effects model
> >  (lme) specifying participants and items as crossed random effects.
> >  This analysis takes into account differences between participants and
> >  differences between items in a single sweep and has been shown to
> >  suffer substantially less loss of statistical power in unbalanced
> >  designs than traditional ANOVAs over participants (F1) and items (F2;
> >  see Baayen, in press, Pinheiro & Bates, 2000; Quen? & van den Bergh,
> >  2004, for simulations).
> >     We used the lmer program (lme4 package; Bates & Sarkar, 2006) in
> >  the R system for statistical computing (R Development Core Team, 2006)
> >  and report regression coefficients (b; absolute effect size in ms),
> >  standard errors (SE), and p-values for an upper-bound n of denominator
> >  degrees of freedom computed as n of observations minus n of fixed
> >  effects. As these p-values are potentially anti-conservative, we
> >  generated confidence intervals from the posterior distribution of
> >  parameter estimates with Markov Chain Monte Carlo methods, using the
> >  mcmcsamp program in the lme4 package with default specifications
> >  (e.g., n=1000 samples; locally uniform priors for fixed effects;
> >  locally non-informative priors for random effects). Both procedures
> >  yielded the same results.
> >     Finally, we also computed post-hoc power statistics for the
> >  preview and lexical status main effects and for the interaction effect
> >  on first fixation durations (with effect sizes similar to those
> >  reported earlier, e.g., Kliegl, 2007), and using lme estimates of
> >  between-participant, between-item, and residual variances (Gelman &
> >  Hill, in press). For the observed proportion of random loss of items,
> >  power estimates based on 1000 simulations each were around .85 for
> >  word n and n+2 and .59 for word n+1 (due to the higher skipping
> >  rate)."  (page 1251)
> >
> >  Power statistics were included in response to a reviewer request. I am
> >  not much in favor of post-hoc power statistics; but note that here
> >  they are restricted to the use of estimates of random effects. For
> >  reviewers, we also included traditional F1- and F2-ANOVA tables; they
> >  are not part of the article. In other articles, it has also been
> >  acceptable to report coefficients, their standard errors, and their
> >  ratio, and to say that coefficients larger than 2 SE are interpreted
> >  as significant (e.g., Kliegl, 2007, J Exp Psychol: General, 136,
> >  530-537), that is, it is possible to leave out p-values completely.
> >
> >  Corrections and improvements of the above sentences are highly welcome
> >  for future articles. In perspective, I think the p-value problem will
> >  simply go away.
> >
> >  Best
> >  Reinhold
> >
> >  PS: Would it be useful to have a site where peer-reviewed articles
> >  using lme4 for statistical inference are listed and, possibly,
> >  retrievable versions are provided?
> 
> Thanks for the suggestion, Reinhold.  I would be delighted to provide
> a page on http://lme4.r-forge.r-project.org/ to list such references.
> 
> May I ask for a volunteer to maintain such a listing?  I am rather
> overextended at present trying to get lme4_1.0-0 out and writing a
> book about what it does.  All that is required is to obtain a R-forge
> login, decide how to organize the pages and then update the pages as
> new references are submitted.

I'm happy to do that, Doug.  I've registered.

Andrew

-- 
Andrew Robinson  
Department of Mathematics and Statistics            Tel: +61-3-8344-6410
University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
http://www.ms.unimelb.edu.au/~andrewpr
http://blogs.mbs.edu/fishing-in-the-bay/