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

[Maarten Jung]

Hi Jake,

Thanks for your thoughts on this.

I thought that Bates et al. (2015; [1]) were referring to this principle
when they stated:
"[...] we can eliminate variance components from the LMM, following the
standard statistical principle with respect to interactions and main
effects: variance components of higher-order
interactions should generally be taken out of the model before lower-order
terms nested under them. Frequently, in the end, this leads also to the
elimination of variance
components of main effects." (p. 6)

Would you agree with me that this is referring to the principle of
marginality? And if so, can you think of a reason why they suggest to
follow this principle other than "higher-order interactions tend to explain
less variance than lower-order interations"?

Best regards,
Maarten

[1] https://arxiv.org/pdf/1506.04967v1.pdf

On Wed, Nov 28, 2018 at 7:24 PM Jake Westfall <jake.a.westfall using gmail.com>
wrote:

> 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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>>
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