I would like to see whether there is an association between an existing ordinal response scale and a newly devised continuous response scale. I have unbalanced longitudinal data and I would like to know what is the best way to go about this. These scales used to measure a patient's sickness and I would like to see if there is an association between the two scales.
For example, my dataset in long form looks like this:
ID ContinuousVar CategoricalVar Week
1 7.6 Good 0
1 5.5 Good 3
1 8.6 OK 6
1 2.1 Bad 9
2 2.4 OK 0
2 4.7 OK 2
2 7.1 Good 7
3 6.1 Good 0
3 3.3 OK 3
3 1.5 Bad 7
3 4.6 OK 8
Here, ID represents each patient, so all the observations with the same ID comes from the same patient. I would like to take that into account in my analysis.
Each patient goes through treatment for several weeks and we measure their status at each time point using two scales; the existing one is the categorical variable, and a new one is the continuous variable. I would like to see if the new scale is associated with the old one. (Eg. Are the values in the new scale high when the old scale values are "Good", and low when the old scale values are "Bad"?)
I would also like to take into account any effect of time, which denoted as Week in the table above. (Eg. Do the two scales tend to agree more at the beginning of the treatment compared to near the end of the treatment?)
Would a linear mixed effects model be what I'm looking for? If so, how would the set up look like? If not, what would you suggest?
Thanks in advance.
Edit: The way I was thinking of going about this is to regress one of the scale variables against the other scale variable as well as time, using a linear mixed effects model/generalized linear mixed effects model. Like this:
ContinuousVar ~ CategoricalVar*Week
Or
CategoricalVar ~ ContinuousVar*Week
But since CategoricalVar and ContinuousVar are both time-dependent, I am not sure if this is the correct way of doing it.