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

[Maarten Jung]

Hi Jake,

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"?
>
>
> I think that if you have strong evidence that this is the appropriate
> random effects structure, then it makes sense to modify your model
> accordingly, yes.
>

 This makes sense to me.

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?
>
>
> No -- in general, with unbalanced datasets and continuous predictors, it's
> hard to say much for sure other than "no." But it can be informative to
> think of simpler, approximately balanced ANOVA-like designs where it's much
> easier to say much more about which variance components enter which
> standard errors and how.
>
> The standard error for a particular fixed effect is proportional to the
> (square root of the) corresponding mean square divided by the total sample
> size, that is, by the product of all the factor sample sizes. So examining
> the mean square for an effect will tell you which variance components enter
> its standard error and which sample sizes they are divided by in the
> expression.
>

Your app is very useful, too. Just to double-check if I get this right: the
entries in each cell of the table are the numbers by which the variance
components are divided in the equation of the noncentrality parameter. Is
this correct?


Regards,
Maarten

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