I've got longitudinal data from a psychological experiment and try to model the data using R package lme4. My dependent variable y is continuous and is measured at eleven occassions. Each subject is randomly allocated to a treatment or control condition (treatment/control) in the beginning of the experiment. There are two hypothesis I would like to test with my model.
H1: Participants in the experimental group will have an increased value in the dependent variable y in contrast to participants in the control group at each subsequent point of measurement.
H2: The effect of the intervention is stronger for male than for female.
At the moment my model is only specified for hypotheses H1:
m1
I recommend
http://www.rensenieuwenhuis.nl/r-sessions-16-multilevel-model-specification-lme4/
https://juancarloscastillo.github.io/jc-castillo/documents/diplomado_multinivel/bibliografia/finch%20et%20al%202014%20multilevel%20modeling%20using%20R.pdf
All of this should have been part of the design phase. Now you expect someone to sort this all out. Well as the old song from the 1920's said "and Fisher can always allow for it" but Fisher died in the 1960's. however he did say something that applies here and that was (to paraphrase) call a statistician at design phase not the analysis phase, because he knew there is often no solution to these problems. Most of us will have no clue what the solution is or how to fix this mess up. What we know about experiments is largely in this book, : https://www.bing.com/search?FORM=U528DF&PC=U528&q=Montgomery+D+C+design+and+Analysis+of+experiments. Thus you are asking us to solve a brand new statistical research problem for a one-time use. Salvage jobs are usually no fun. Here is a possible reference:
https://www4.stat.ncsu.edu/~davidian/st732/notes.html. Prof Davidian invented a lot of this. May the Force Be with YOU
D. Booth PS Hearty shout out to @Henning Teickner for pointing some this out in detail. Say Max where is your advisor in all of this. Did s/he approve this design? If so then that's the person to ask.
Hello,
Christian Ramos-Vera, thank you for the recommendations.
Henning Teickner, thanks a lot for the helpful remarks on the topic.
These resources should help
http://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/repeated-measures.pdf
http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#multipleresp
https://www.pilesofvariance.com/
Quite naturally in these models I would have a random intercept and an allowed to vary random slope associated with time. The covariance is a key term, if positive it suggests that the variation between individuals is increasing over time, if negative , this between variance id decreasing. I think it is good to start with an unconditional model with time in the fixed part to pick up the trend and in the random part. This will give you a good idea of what needs to be explained. You can then add in fixed part terms first as main effects than as interactions. The usual rule is that you must have a main effect before an additional interaction is included.
For the sort of thing I am suggesting, see my longer answer to this question:
https://www.researchgate.net/post/What_is_the_best_alternative_to_ANCOVA_in_longitudinal_RCT
the point being that you learn from your models if you fit them in an informative sequence.
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