I have a crossed and implicitly nested design and am trying to validate the correct ‘maximal’ model (including all linear and pairwise interactions of the variables) for use in
lmer(). I intend to use this as the starting point for some kind of backward stepwise regression, possibly making use of the function
mixed() in the
This a linguistics study. We have 20
Subjects, each speaking 180 utterances, amounting to 3600 observations in total. Each utterance is initiated via prompting, and an associated Response Time is measured. Log Response Time is the dependent variable.
Conditions & Blocks
The Response Time for the utterances is affected by 3
Conditions (coded 1 to 3). Each
Condition is implemented by prompting the
Subject to recite 1 of 4
Blocks of utterances (coded 1 to 12).
Words & Tones
Block brings about its associated
Condition via 15-utterance repetition of 3 carefully chosen
Words. There are a total of 12
Words used in the experiment (coded 1 to 12). The
Words within each
Block can also be categorized by
Tone (coded 1 to 2). There are 6
Each of the 20
Subjects utter all 12
Blocks of 15 utterances each. In doing so, they repeatedly utter all 12
Words (15 utterances per
Word), and thereby use both
Tones (90 utterances per
I would like to consider
Subject as random effects, and
Tone as fixed.
I think the model can be written in the following way…
RT_log ~ Condition*Tone + (Condition*Tone|Subject) + (Condition|Word) + (Tone|Block)
1. Is this the 'maximal' model (with linear plus pairwise interactions) appropriate for my experimental design?_
2. There is correlation between
Condition (there are only 4 possible blocks - out of the total 12 - for each
Condition). There is, similarly, correlation between
Tone. Is it 'okay' to leave this correlation in the model? I don't see a good way of removing it.
3. How will lme4 handle implicit nesting: I.e., the blocks, which are implicitly nested in the 3 conditions (i.e., only 4 blocks are applicable to each of the 3 conditions, even though the blocks are coded from 1 to 12), and the words, which are implicitly nested within the 2 tones (only 6 words are applicable to each tone, even though words are coded from 1 to 12)?
Words of only a single
Tone, whereas other
Blocks utilize words of both
Tones. Will that cause problems for the
(Tone|Block) term in the model? It will only make sense for certain values of Block.
5. It has been suggested by some that we might need a "Subject:Word" grouping (random effect). Why might we need this grouping?