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I am learning about the difference between categorical, ordinal and numerical variables.

From what I understand:

  • Categorical variables have 2+ categories without any intrinsic order.
  • Ordinal variables have clear ordering but the intervals are not necessarily equally spaced.
  • Numerical variables are ordered with equally-spaced intervals.

I am stuck on trying to classify these two situations:

1. What level of commitment are you prepared for?

  • Multiple times per week
  • Once per week
  • A couple times per month
  • No more than once per month
  • Level of commitment is not a factor.

2. What level of commitment are you prepared for?

  • 9-11 times per month
  • 6-8 times per month
  • 3-5 times per month
  • 0-2 times per month
  • Level of commitment is not a factor.

My guess would be #1 is ordinal and #2 is numerical. However, the "Level of commitment is not a factor" is throwing me off. Can anyone help clarify this for me?

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    $\begingroup$ Modeling that as a missing value might work well for algorithms that treat it separately like most decision tree impls. You could model as yes/no commitment is a factor and if so, the value as well as a separate feature. $\endgroup$ – Sean Owen Aug 25 '20 at 21:29
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The responses to both of those questions can be treated as categorical, as although they mention numbers you can’t fully encode the information in them as a number. You could obviously number them, e.g. “I’ll call 9-11 times per month response 1”, but the number 1 doesn’t reflect the value of the response.

These types of categorical “buckets” representing a range of values are often used when the value we want to measure is continuous and the range of possible values is large.

If you wanted numerical variables you could recode the responses. For example you could represent answers to question 2 as two numerical variables, min_times and max_times.

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Simply give each category in the response a score.

5- more than 15 times a month 4 - between 10-15 times a month 3- 7-10 times a month 2 - 3-7 times a month 1- less than thrice a month

And use those scores as encodings.

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