Confidence interval around random effect variances in place of p-value
Well, how about concluding so: If a (say 2-level) model gives a singular fit (even though perhaps there is a "tol" that is small but not exactly "0" for that warning to show up), that would mean we have a "practically" non-significant random-effect variance component.
On Fri, Apr 2, 2021 at 7:15 PM Ben Bolker <bbolker at gmail.com> wrote:
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 at gmail.com
<mailto:bbolker at 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:
<
)
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 at gmail.com
<mailto:bbolker at gmail.com>
> <mailto:bbolker at gmail.com <mailto:bbolker at 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]]
> >
> > _______________________________________________
> > R-sig-mixed-models at r-project.org
<mailto:R-sig-mixed-models at r-project.org>
> <mailto:R-sig-mixed-models at r-project.org
<mailto:R-sig-mixed-models at r-project.org>> mailing list
> >
>
> _______________________________________________
> R-sig-mixed-models at r-project.org
<mailto:R-sig-mixed-models at r-project.org>
> <mailto:R-sig-mixed-models at r-project.org
<mailto:R-sig-mixed-models at r-project.org>> mailing list
>