[R-sig-ME] Confidence interval around random effect variances in place of p-value

[Patrick (Malone Quantitative)]

Jack,

As Ben said, testing a hypothesis at the boundary of the parameter space is
a can of worms. I think the usual approach is to use difference (likelihood
ratio) tests for the variances, testing a model with the variance
constrained to zero against the original model.

Pat

On Fri, Apr 2, 2021 at 7:37 PM Jack Solomon <kj.jsolomon using gmail.com> 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> 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
> > >
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-- 
Patrick S. Malone, Ph.D., Malone Quantitative
NEW Service Models: http://malonequantitative.com

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