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

[Jake Westfall]

Maarten,

No, I would not agree that the Bates quote is referring to the principle of
marginality in the sense of e.g.:
https://en.wikipedia.org/wiki/Principle_of_marginality

Bates can chip in if he wants, but as I see it, the quote doesn't hint at
anything like this. It simply says that "variance components of
higher-order interactions should generally be taken out of the model before
lower-order terms nested under them" -- which I agree with. The reason this
is _generally_ true is because hierarchical ordering is _generally_ true.
But it looks like it's not true in your particular case.

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"?


No.

Jake

On Wed, Nov 28, 2018 at 12:53 PM Maarten Jung <
Maarten.Jung using mailbox.tu-dresden.de> wrote:

> 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
>>>
>>>         [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
>>> R-sig-mixed-models using r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>

	[[alternative HTML version deleted]]