[R-sig-ME] LMM reduction following marginality taking out "item" before "subject:item" grouping factor
M@@rten@Jung @ending from m@ilbox@tu-dre@den@de
Wed Nov 28 21:33:28 CET 2018
thanks for this insight.
So, regarding this issue, there is no difference between taking out
variance components for main effects before interactions within the same
grouping factor, e.g. reducing (1 + A*B | subject) to (1 + A:B | subject),
and taking out the whole grouping factor "item" (i.e. all variance
components of it) before "subject:item"?
And, I would be glad if you could answer this related question:
Do all variances of the random slopes (for interactions and main effects)
of a single grouping factor contribute to the standard errors of the fixed
main effects and interactions in the same way?
On Wed, Nov 28, 2018, 20:03 Jake Westfall <jake.a.westfall using gmail.com wrote:
> No, I would not agree that the Bates quote is referring to the principle
> of marginality in the sense of e.g.:
> 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"?
> 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; ) 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,
>>  https://arxiv.org/pdf/1506.04967v1.pdf
>> On Wed, Nov 28, 2018 at 7:24 PM Jake Westfall <jake.a.westfall using gmail.com>
>>> 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.
>>> 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
>>>> should be:
>>>> y ~ A * B + (1 + A * B | subject) + (1 + A * B | item) + (1 + A * B |
>>>> Within a model reduction process, be it because the estimation algorithm
>>>> doesn't converge or the model is overparameterized or one wants to
>>>> Type-1 error rate and power, I follow the principle of marginality
>>>> out higher-order interactions before lower-order terms (i.e. lower-order
>>>> interactions and main effects) nested under them and random slopes
>>>> 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
>>>> 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,
>>>> general, whether this is a sound approach.
>>>> Any help is highly appreciated.
>>>> Best regards,
>>>> [[alternative HTML version deleted]]
>>>> R-sig-mixed-models using r-project.org mailing list
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