[R-sig-ME] lmer and p-values

Ben Bolker bbolker at gmail.com
Mon Mar 28 23:18:08 CEST 2011

On 03/28/2011 01:04 PM, Iker Vaquero Alba wrote:
>    Ok, I have had a look at the mcmcsamp() function. If I've got it
> right, it generates an MCMC sample from the parameters of a model fitted
> preferentially with "lmer" or similar function.
>    But my doubt now is: even if I cannot trust the p-values from the
> ANOVA comparing two different models that differ in a term, is it still
> OK if I simplify the model that way until I get my Minimum Adequate
> Model, and then I use mcmcsamp() to get a trustable p-value of the terms
> I'm interested in from this MAM, or should I directly use mcmcsamp()
> with my Maximum model and simplify it according to the p-values obtained
> with it?
>    Thank you. Iker

  Why are you simplifying the model in the first place?  (That is a real
question, with only a tinge of prescriptiveness.) Among the active
contributors to this list and other R lists, I would say that the most
widespread philosophy is that one should *not* do backwards elimination
of (apparently) superfluous/non-significant terms in the model.  (See
myriad posts by Frank Harrell and others.)

  If you do insist on eliminating terms, then the LRT (anova()) p-values
are no more or less reliable for the purposes of elimination than they
are for the purposes of hypothesis testing.

> --- El *lun, 28/3/11, Ben Bolker /<bbolker at gmail.com>/* escribió:
>     De: Ben Bolker <bbolker at gmail.com>
>     Asunto: Re: [R-sig-ME] lmer and p-values
>     Para: r-sig-mixed-models at r-project.org
>     Fecha: lunes, 28 de marzo, 2011 18:27
>     Iker Vaquero Alba <karraspito at ...> writes:
>     >
>     >
>     >    Dear list members:
>     >
>     >    I am fitting a model with lmer, because I need to fit some nested
>     > as well as non-nested random effects in it. I am doing a split plot
>     > simplification, dropping terms from the model and comparing the
>     models with or
>     > without the term. When doing and ANOVA between one model and its
>     simplified
>     > version, I get, as a result, a chisquare value with 1 df (df from
>     the bigger
>     > model - df from the simplified one), and a p-value associated.
>     >
>     >    I was just wondering if it's correct to present this chisquare and
>     > p values as a result of testing the effect of a certain term in
>     the model. I am
>     > a bit confused, as if I was doing this same analysis with lme, I
>     would be
>     > getting F-values and associated p-values.
>     >
>       When you do anova() in this context you are doing a likelihood ratio
>     test, which is equivalent to doing an F test with 1 numerator df and
>     a very large (infinite) denominator df. 
>       As Pinheiro and Bates 2000 point out, this is
>     dangerous/anticonservative
>     if your data set is small, for some value of "small".
>        Guessing an appropriate denominator df, or using mcmcsamp(), or
>     parametric
>     bootstrapping, or something, will be necessary if you want a more
>     reliable p-value.
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