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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.

Sheep
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  • I am off to catch a flight, so I will write more later, but yes, you could use either a mixed effects model or you could use the method of Generalized Estimating Equations. But first to questions: are you interested in the associations or effects of the individuals in your study or are you primarily concerned with the population as a whole? Also, which of the variables that you have listed is considered your dependent variable and which are your independent variables? – StatsStudent Oct 20 '15 at 16:14
  • Hi StatsStudent, thanks for your feedback. I would like to take into account that some of the observations come from the same individual, so yes I am interested in the effects of individuals in my study. (I'm also concerned about the population.) For example, subject A can have "OK" in the categorical response and 5.2 in the continuous response, but subject B could have "Bad" in categorical but also 5.2 in the continuous response. cont' – Sheep Oct 20 '15 at 16:29
  • This difference between the two subjects could be due to the fact that subject A tends to have low levels in the continuous response but subject B tends to have high levels in the continuous response. I would not be able to see this if I did not account for an individual effect. – Sheep Oct 20 '15 at 16:29
  • I would consider both CategoricalVar and ContinuousVar as responses since they are both some measurement of patient status at each time point. I would like to see if the two measurements are associated. The independent variable would be Week, but I am not sure how to incorporate the time effect. – Sheep Oct 20 '15 at 16:32
  • Possible duplicate of [Correlations between continuous and categorical (nominal) variables](https://stats.stackexchange.com/questions/102778/correlations-between-continuous-and-categorical-nominal-variables) – kjetil b halvorsen May 21 '17 at 12:44

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