[R-sig-ME] Confidence interval around random effect variances in place of p-value
Ben Bolker
bbo|ker @end|ng |rom gm@||@com
Sat Apr 3 02:15:40 CEST 2021
I'm not sure that the bootstrapped CIs *wouldn't* work; they might
return the correct proportion of singular fits ...
On 4/2/21 8:12 PM, Jack Solomon wrote:
> Thank you all very much. So, I can conclude that a likelihood ratio test
> and/or a parametric bootstrapping can be used for random effect variance
> component hypothesis testing.
>
> But I also concluded that the idea of simply using a bootstrapped CI for
> a random-effect variance component [e.g., in lme4;
> confint(model,method="boot",oldNames=FALSE) ] by definition can't be
> used for significance testing, because it requires the possibility of
> seeing sd = 0 which can't be "strictly" captured by such a CI from a
> multilevel model (at least not easily so).
>
> I hope my conclusions are correct,
> Thank you all, Jack
>
> On Fri, Apr 2, 2021 at 6:51 PM Ben Bolker <bbolker using gmail.com
> <mailto:bbolker using gmail.com>> wrote:
>
> Sure. If all you want is p-values, I'd recommend parametric
> bootstrapping (implemented in the pbkrtest package) ... that will avoid
> these difficulties. (I would also make sure that you know *why* you
> want p-values on the random effects ... they have all of the issues of
> regular p-values plus some extras:
> http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#testing-significance-of-random-effects
> <http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#testing-significance-of-random-effects>
>
> )
>
> On 4/2/21 7:37 PM, Jack Solomon wrote:
> > Thanks. Just to make sure, to declare a statistically
> NON-significant
> > random effect variance component, the lower bound of the CI must be
> > EXACTLY "0", right?
> >
> > Tha is, for example, a CI like: [.0002, .14] is a
> > statistically significant random-effect variance component but
> one that
> > perhaps borders a p-value of relatively close to but smaller than
> .05,
> > right?
> >
> > On Fri, Apr 2, 2021 at 6:19 PM Ben Bolker <bbolker using gmail.com
> <mailto:bbolker using gmail.com>
> > <mailto:bbolker using gmail.com <mailto:bbolker using gmail.com>>> wrote:
> >
> > This seems like a potential can of worms (as indeed are all
> > hypothesis tests of null values on a boundary ...) However,
> in this
> > case
> > bootstrapping (provided you have resampled appropriately -
> you may need
> > to do hierarchical bootstrapping ...) seems reasonable,
> because a null
> > model would give you singular fits (i.e. estimated sd=0) half
> of the
> > time ...
> >
> > Happy to hear more informed opinions.
> >
> > On 4/2/21 6:55 PM, Jack Solomon wrote:
> > > Dear All,
> > >
> > > A colleague of mine suggested that I use the bootstrapped CIs
> > around my
> > > model's random effect variances in place of p-values for them.
> > >
> > > But random effect variances (or sds) start from "0". So,
> to declare a
> > > statistically NON-significant random effect variance
> component, the
> > > lower bound of the CI must be EXACTLY "0", right?
> > >
> > > Thank you very much,
> > > Jack
> > >
> > > [[alternative HTML version deleted]]
> > >
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