# Can categorical variables be treated as count data?

In a questionnaire study, I asked for the frequency of certain behaviors using a 5-point scale.　Originally, I planned to treat it as categorical, however, distribution of the answers (N=1000) turns out to be more like zero-inflated Poisson. In fact, data fit well with zero-inflated Poisson regression model. Would it be justifiable to treat categorical data as counts in such case?

It seems like the data could be seen as count information, as I asked number of behaviors (anchor of the 5-point scale was as follows: 0=never, 1=less than once a week, 2= two to three times a week, 3=almost every day, 4=everyday).

Thank you very much for your insights!

• What is it that you want to do with this variable? Is it intended as an explanatory variable or a response variable? What are your goals in this study? Commented Jan 4, 2015 at 16:26

## 2 Answers

For a variable that was simply ordinal, it could be done; the better question is whether it should. I see several problems, starting with what is probably the most critical:

1) ordered categories are ordinal, not interval nor ratio (while the Poisson is for count data which is ratio)

2) the Poisson has non-zero probability of exceeding 5, while your variable doesn't.

However, your data consist of discretized frequencies (and that's not actually a count). You might be able to use the actual definitions of your categories to get intervals of frequencies per week, though the vagueness of category 3 is a problem; if you can argue that category 3 actually covers the territory between "more than 3 times per week but less than 7 times per week" then this variable could be handled essentially as what's effectively a set of interval-censored categories.

As such I generally still wouldn't use a Poisson model (because the content of the intervals that the categories contain don't correspond to the category labels - the weekly frequency covered by "4" isn't four times as often as the weekly frequency covered by "1", for example), but I might use something that attempted to use more of the information than treating it as a purely ordered-categorical variable.

Technically, you can of course do this if the variables are ordered.

The question is what your result will be useful, but that is hard to predict...

In your case, you make the differences 1-0 (less than once a week vs. never ever) the same as 4-3 (almost every day vs. every day). I'm not convinced that this is the same difference...

This problem is quite well known in the context of Likert items. I believe the modern evaluation of such data does not use the numerical values, even when the users were asked to "rate on a scale of 1 to 5" etc. because there is a lot of psychological bias in the way you choose options (prefer extremes, central tendencies, etc.) most likely, this also applies to your data. E.g. when would a user say "every day" and not "almost every day"? After such correction, you may end up with only three values: 0 and 1 = low, 2 = medium, 3 and 4 = high. And even though these are still ordered, it may yield better results to treat these as categories.