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

[Douglas Bates]

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; Quené & 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.