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Are there some variables where it can be difficult to assess whether they are purely categorical?

For example:

To assess the level of pain that a patient is in, you use a scale between 1 and 10.I wouldn't consider pain score to be a categorical variable here, just discrete; this is because it is a measurement (even if it is subjective).

Conversely if I have something such as tumour stage, it is still a discrete variable between say 1 and 4, however I am more tempted to say these are categories. The thing is, increasing value in the Tumour stage does actually have meaning: more likely to have aggressive disease. For categories such as hair colour, or gender, there is no numerical relationship between the categories!

The only thing I can really see is that in discrete variables, each step increase has the same meaning (thus increase of 1-2, 5-6 and 9-10) is the same. Whereas with tumour stage va the step sizes don't mean the same thing : 1-2 is different than 2-3 and 3-4 because the tumour aggression is probably not linear.

This has implications when running logistic regression models, where you could treat categorical variables differently (names you code them differently).

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  • $\begingroup$ I don't get this question. To me, discrete and categorical mean the same thing: you have labeled categories, that's all. There's a subset of categorical/discrete variables called "ordinal" variables, where the categories have a well-defined ordering. For any two numbers on the pain scale, and for each individual, the greater number means greater pain (although one could argue that a pain of 3 for one person may be another person's 5). Likewise, with tumor progression, the greater number means the more serious condition. Is this question about terminology, really? $\endgroup$ – StasK Aug 31 '12 at 17:35
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You can have ordered or unordered factors. The equivalent of a logistic model for these variable types are the ordered logit and multinomial logit. For the ordered logit you can have known or unknown cut points.

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  • $\begingroup$ If I have several variables, and only one of them is ordinal, would I still need to use ordered logit (if I were perfomring a multiple regression)? In R I can usually account for categorical variables using as.factor, is that insufficient or is it necessary to use ordered logit or multinomial logit whenever you have ordinal variables? $\endgroup$ – user4673 May 15 '12 at 23:30
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    $\begingroup$ Whether to use ordinal logistic regression (or whatever kind of regression) depends on the nature of the dependent variable, not the independent variables. $\endgroup$ – Peter Flom - Reinstate Monica May 16 '12 at 0:24
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    $\begingroup$ In addition to @Tristan's answer, I just want to add that ordered and unordered factors can also be referred to as ordinal and nominal variables $\endgroup$ – jthetzel May 16 '12 at 1:15
  • $\begingroup$ My concern isn't so much between ordinal and nominal variables so much as ordinal and discrete variables. Age is a discrete variable, which we would not consider ordinal. Tumour stage is also a discrete variable, but we would consider it ordinal. The only difference between these examples is that a 1-unit increase in age always means the same thing (1 year); but a one unit increase in tumour stage doesn't translate to the same thing (tumour aggression is exponential, not linear). Is step size the determining factor? Otherwise pain score, which I mentioned is an ordinal variable. $\endgroup$ – user4673 May 16 '12 at 17:23

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