[R-sig-ME] specifying random intercepts for repeated measures mixed factorial design

[Schulze, Anna]

Dear mixed-models experts,

I�m struggling to specify the correct random effect structure to analyze the data of a virtual reality experiment we conducted with
a patient and a healthy control group. I�ve read (and learned) a lot in the last months, but still struggle to apply this to my data
structure, therefore I would be very grateful for every hint.


Shortly to our paradigm:

Participants were asked to read out the same 9 questions (asking for advice or support) in the same order consecutively to 8 different

avatars (first, all questions are asked to the first avatar, then to the second, etc., 72 trials in total). The answers of the avatars differed

with regard to social acceptance and rejection and whether the avatars explained their response or not. Therefore, the answers can be

characterized on the two factors 1) reaction (rejection=0/acceptance=1) and 2) explanation (no=0/yes=1), (with 18 trials for each of the

four combinations).

                                    --> 2 (within) x 2 (within) x 2 (between) repeated measures design

Participants were asked to assess the avatar�s benevolence towards them after each answer by adjusting a slider on a scale
(=dependent variable). The slider started in the middle of the scale at the beginning of each of the eight conversations and
did not jump back between trials, but remained at the height set.

Among the avatars, the number of answers that were rejecting or accepting as well as with and without explanations was balanced.
The frequencies, combined occurrences, and sequence of all four types of answers were also evenly distributed across all avatars.
The response pattern assigned to each avatar remained consistent across participants, assigning a distinct �personality� to each
avatar. The presentation order of the avatars was randomized.

The dataset looks like this:

Subj.   Group             Avatar          Question        Reaction         Explanation       Rating

1          HC                  1                      1                      1                     0                      9
1          HC                  1                      2                      0                     1                      8
�        �                    �                    �                    �                    �                    �
32        BPD                8                      9                      0                     1                      10

In short, we are interested in whether and how the groups differ in their ratings dependent on the experimental factors,
so my fixed effects look like this: rating ~ group * reaction * explanation

Regarding the random intercepts, I assume
1) repeated measures on both experimental factors and
2) a crossed random factor structure (multiple observations per subject due to multiple rated answers, multiple observations per answer due to multiple subjects).
In addition, since our virtual characters all had their specific answer pattern, appearance and voice, the slider did not jump back
to the middle after each rating and also the specific nature of the nine questions asked might influence the ratings,
we wanted to include the contextual factors �avatar� and �question�.

For point 1), I�ve seen two different approaches:
a) (1 | subject/reaction/explanation)
b) (1 | subject) + (1 | reaction:subject)+ (1 | explanation:subject)

Since I assume reaction and explanation are crossed, I would have guessed the second one is correct, but in this case the df�s for the
3-way interaction explode to 4319 � I understand that df�s in mixed models are complicated estimations, but 4319 looks suspicious for
64 subjects and I�m afraid that the dependencies in our data were not correctly accounted for � do exploding df�s indicate a problem?

For point 2), is a direct specification of a by-answer intercept (1-72) or indirect specification via random intercepts for combination
the contextual factors avatar (1-8) and question (1-9) or a combination of answers, avatars and questions correct?
a) (1 | avatar) + (1 | question)
b) (1 | avatar / question)
c) (1 | avatar) + (1 | question) + (1 | answer)
d) (1 | avatar / question) + (1 | answer)

Was there anything useful in my combinations or might the solution be something completely different? Thank you very much in advance, especially for reading this rather long mail!


Best,


Anna Schulze

Psychologist

Central Institute for Mmental Health Mannheim

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