[R-sig-ME] LMM reduction following marginality taking out "item" before "subject:item" grouping factor

[Jake Westfall]

Maarten,

I think it's fine. I can't think of any reason to respect a principle of
marginality for the random variance components. I agree with the feeling
that it's better to remove higher-order interactions before lower-order
interactions and so on, but that's just because of hierarchical ordering
(higher-order interactions tend to explain less variance than lower-order
interations), not because of any consideration of marginality. If in your
data you find that hierarchical ordering is not quite true and instead the
highest-order interaction is important while a lower-order one is not, then
it makes sense to me to let your model reflect that finding.

Jake

On Wed, Nov 28, 2018 at 12:18 PM Maarten Jung <
Maarten.Jung using mailbox.tu-dresden.de> wrote:

> Dear list,
>
> In a 2 x 2 fully crossed design in which every participant responds to
> every stimulus multiple times in each cell of the factorial design the
> maximal linear mixed model justified by the design (using the lme4 syntax)
> should be:
> y ~ A * B + (1 + A * B | subject) + (1 + A * B | item)  + (1 + A * B |
> subject:item)
>
> Within a model reduction process, be it because the estimation algorithm
> doesn't converge or the model is overparameterized or one wants to balance
> Type-1 error rate and power, I follow the principle of marginality taking
> out higher-order interactions before lower-order terms (i.e. lower-order
> interactions and main effects) nested under them and random slopes before
> random intercepts.
> However, it occurs that the variance components of the grouping factor
> "item" are not significant while those of the grouping factor
> "subject:item" are.
>
> Does it make sense to remove the whole grouping factor "item" before taking
> out the variance components of the grouping factor "subejct:item"?
>
> A reduced model would f.i. look like this:
> y ~ A * B + (1 + A | subject) + (1 | subject:item)
>
> I'm not sure whether this contradicts the principal of marginality and, in
> general, whether this is a sound approach.
>
> Any help is highly appreciated.
>
> Best regards,
> Maarten
>
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