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I have an ordinal variable (11 cat), measured twice a day (morning and evening, not at the same time) for about a thousand living objects for several months.

What's a sensible way to analyse change over time for this time-series? Particularly, I am interested whether there is significant change after the first week (some procedure changed).

Things I considered (using R):

  1. Fitting an ordinal GAM with some correction for autocorrelation, and taking the derivative. Plotting it. However, I'unclear whether I should run this separately for morning and evening or incorporate the grouping variable into the GAM.

  2. Just plotting daily averages by morning and evening.

  3. Calculating weekly averages and taking the difference from week 1. Calculating CIs, plotting it by morning and evening.

Based on the sketch of the data and my considerations, what would be the most sound approach to analyse this?

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"taking the difference from week 1" - doing this may mean your data is not long on the original units, so I am not sure this is the best approach. However, you could do 3) without taking this difference. What are you rationale for taking the difference? I think it is worth doing all 3 steps if these are relevant to the problem investigated.

  1. Fitting an ordinal GAM with some correction for autocorrelation, and taking the derivative. Plotting it. However, I'unclear whether I should run this separately for morning and evening or incorporate the grouping variable into the GAM. **you can do this: fit using morning and evening and include the grouping variable as the random effects. Then visualise the splines for morning and evening separately. This is preferable as each variable is adjusted against each other. **

  2. Just plotting daily averages by morning and evening. do this as an initial hypothesis formulating step or an initial descriptive analysis of the problem

  3. Calculating weekly averages and taking the difference from week 1. Calculating CIs, plotting it by morning and evening. as explained previously

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