[R-sig-ME] Fwd: same old question - lme4 and p-values
A.Robinson at ms.unimelb.edu.au
Sun Apr 6 23:02:19 CEST 2008
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.
Department of Mathematics and Statistics Tel: +61-3-8344-6410
University of Melbourne, VIC 3010 Australia Fax: +61-3-8344-4599
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