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):
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.
Just plotting daily averages by morning and evening.
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?