[R-sig-ME] glmmTMB: repeated measure design and ar component

[Sara D'Amario]

Dear all,
I am trying to implement a mixed model that takes into account the
repeated measure design of my study.

My study consists of a 2 parts ("part 1" and "part 2") x 2 takes ("take
1" and "take 2") x 2 target ("NOT AT ALL" and "MOST") x 2 mode ("UNISON"
and "CANON") x 15 participants (i.e. participants number from P01 to
P15).  Part, take, target, mode and participant number are fully
crossed.


For each condition resulting from the above fully crossed combinations,
I also have an autoregressive component (time).


I would like to investigate the fixed effects of: 
- target (a categorical variable, with 2 levels)
- mode (a categorical variable, with 2 levels)
- tuning (a continuous variable)

 on:
- wrist_position (a continuous variable) - the response variable

I am a bit familiar with glmmTMB, but I am not sure:
1) how to account for the repeated measure design
2) how to specify the ar1 component

For a simple model without the repeated measure design I would have done
something like:

m_simple <- glmmTMB(wrist_position ~  tuning  + mode + target +
	(1|participant),
        data = tuning_wrist, na.action = na.exclude)


However, my study is much more complex than that and includes a repeated
measure design and an autoregressive component for the data resulting
from these fully crossed variables. 
I would really appreciate your input in this respect.


How can I account for the repeated measure design?
How can I enter the ar1 component with the conditions resulting from
this fully crossed design?


Thanks a lot for you feedback.
 
Best,
Sara D'Amario


-----
Dr Sara D’Amario
Postdoctoral Research Associate
Department of Music Acoustics – Wiener Klangstil
University of Music and Performing Arts Vienna
Anton-von-Webern-Platz 1
1030 Vienna, Austria
 
Ad majora semper
 
https://www.mdw.ac.at/iwk/fwf-togetherness/ 


Recent publications:
- D’Amario, S. & Bailes, F. (2021). Ensemble timing and synchronization,
in R. Timmers, F. Bailes, & H. Daffern (Eds.), Together in Music:
Coordination, expression, participation (139-147), Oxford University
Press. DOI: 10.1093/oso/9780198860761.001.0001.
- Daffern, H. & D’Amario, S. (2021). Understanding expressive ensemble
singing through acoustics, in R. Timmers, F. Bailes, & H. Daffern
(Eds.), Together in Music: Coordination, expression, participation
(129-138), Oxford University Press. DOI:
10.1093/oso/9780198860761.001.0001.