Dear Yoann

I expecte that you can use ANOVA ONE WAY to compare between methods.

I have no idea what your question is. However if you have two raters it seems to me that the best you can do is compare the two raters. A longitudinal model is what you use when you believe there might be a change over some condition, eg. time. Why do you think the rater's ability would change.? Further, 2 raters is a pretty small sample. Even if you had a hypothesis I can't see how with 2 raters you could test it. Further, you would be confounding the rater's ability with the method used. My advice: Back to the drawing board. Good luck, D. Booth

I am more hopeful and see it as a multilevel problem, specifically as a multivariate (ie multiple response) repeated measures design.

http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#multipleresp

I see it possibly as a 3 level structure - at the top, level 3 is the individual being measured (there are the fewest of these , say n people). They are rated by two individuals , so that there are 2 by n observations, these form level 2 of the structure. Level 1 is the repeated measure on each rater and there 2 by n by t of these measurements. The model will allow the calculation of the means, and the variances and covariances at each level so you can look at differences sources of variability and you could see how this changes over time. You can also include predictors to try and account for this variation. If you could provide some data given this structure, I would be willing to help as it might be a little tricky to set up. Indeed it would be good to experiment with an alternative structure: individuals at level 3 being repeatedly measured at level 2 by 2 raters at level 1.

The reason that I am more hopeful is because of what is possible with twins

https://www.researchgate.net/post/What_kind_of_statistical_analysis_is_appropriate_for_evaluation_of_continuous_dependent_variables_between_twins_independent_variable

Multitrait Multimethod approach of scale validation. It's available in lavaan or psy packages in R.

Does the mm method take account of the dependence due to the repeated measures, as I do not know.