# Compare dependent categories over time?

I have a dataset with 50 individuals. 25 are exposed to a substance on low concentration, 25 are exposed to a substance on high concentration over time.

I have 4 categories that represent different states of an individual. e.g. "searching", "doing sth", "doing sth else", "dead" over time.

At the beginning all individuals are in the category "searching".

Then I investigate over time and the two factors (low concentration, high concentration) how the distribution of my categories changes over time. I am interested in the effect of time and effect of the concentration factor on the distribution of my categories.

Because my data is not independent as individuals stay the same over time, I think something like Dirichlet Regression is not appropriate here?

Additionally, I have a correlation structure in my categories, because obviously if an individual is dead it cannot be in another state other than death at the next time point.

Is there a way to statistically model how the distribution of my categories changes along time and differs for the two concentrations and taking into account the facts that (1) I have the above mentioned dependencies in my 4 categories, and (2) my datapoints are not independent, because I always investigate the same 50 individuals over time always exposed to the same concentration (either low or high).

• Can you give some more details? How many observations for each person? All observed at the same times, or when there is a transition? ... Maybe a Markov chain for each person is possible, with a common (or one for each group) transition matrix? Jul 8 '20 at 1:15
• thanks for your help. there are distinct time points at which the system is observed (0, 12,24,36,48 hours after the start of the experiment). All individuals are checked for their state at these timepoints only. Markov chain sounds interesting would love to hear more about this approach. Thanks again Jul 8 '20 at 6:23
• Does this go into this direction? This sounds very interesting: [link] (datacamp.com/community/tutorials/…) Jul 8 '20 at 7:01
• Could be. 50 observations could be few for such an analysis ... maybe start with some graphical representation? Jul 17 '20 at 1:45