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I'm currently writing a .NET library to handle various statistical/classification tasks and I am currently writing the structures to represent nominal and ordinal data.

In doing so, I've been debating whether or not the structures that handle ordinal data should derive from the structures that handle nominal data.

My thought is that yes, all ordinal data is nominal data; even though it means huge (or infinite) sets, each of them is an attribute that while being able to compared to another attribute for rank (for lack of a better term, which implies ordinal) can still be compared to for equality and is still a label (nominal).

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  • $\begingroup$ I know this is old but going to leave a comment anyway in case future people see this. #1: Don't write this code. Someone else who has researched the area more has already written it so you should import their stuff instead. #2: Yep, the data-structure you are considering is correct. You could look at Ord for a nice well-thought-out tree of the standard ⊂ for statistical data types. $\endgroup$ May 5, 2015 at 3:21
  • $\begingroup$ @isomorphismes If someone else has written this code for .NET would you point it out? Ord looks nice, but it's for Haskell, and the question clearly indicates this is for .NET. $\endgroup$
    – casperOne
    May 6, 2015 at 12:06

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I would definitely make the distinction between discrete ordinal variables and continuous ordinal variables. For the second case, in practice there never is any sense in comparing values for equality.

I don't see a sound reason to state that continuous ordinal variables are in fact nominal: what would be the gain?

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    $\begingroup$ The design of the object oriented program would be nicer. $\endgroup$
    – xmjx
    Oct 9, 2011 at 9:17
  • $\begingroup$ Well, not if it doesn't reflect reality. You're going to get stuck somewhere down the line... $\endgroup$
    – Nick Sabbe
    Oct 9, 2011 at 12:17
  • $\begingroup$ @xmjx hit the mark with the intent and the gain; Nominal dervies from Ordinal. Discrete ordinals and continuous ordinals can be derivations of Discrete ordinals when I get to that point. Another example, Nominal types can do two things, say if they are equal to another nominal type, and tell if they are missing; these characteristics/methods are shared with all ordinal ordinal values. $\endgroup$
    – casperOne
    Oct 9, 2011 at 14:04
  • $\begingroup$ How could you have a continuous ordinal variable? $\endgroup$ May 5, 2015 at 3:19

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