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

Maarten Jung M@@rten@Jung @ending from m@ilbox@tu-dre@den@de
Wed Nov 28 19:17:32 CET 2018

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 |

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,

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