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I would like to perform logistic regression of skin damage by use of some drugs(all subjects will be applied with the same drug) with clinical change as ordinal categorical variable. Clinical change could be 'worse','stationary','slight improvement' and 'marked improvement'.

This clinical change=$x$ is ordinal categorical variable. I cold definitely choose scoring scheme to label them by $x=1,2,3,4,5$, $x=0,3,4,5,6$ or ...

How do I tell which labeling scheme is appropriate? There is no obvious reason that $x=1,2,3,4,5$ is correct. The book choose $x=-1,0,1,2,3$ as scoring scheme. However, the book says on pg 189, 'A much larger sample is needed to determine color scoring is most appropriate' for a different data set. So there is implication that larger data set will choose some scoring scheme. How and why this would be the case?

Ref. Categorical Data Analysis by Agresti pg 181.

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