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I'm aware that using a count variable as a regressand in an OLS model is a no-no and know how to deal with that.

My question is, is it ok to use count variables without transformation as covariates in OLS, 2SLS, Heckman, etc type of models?

Ferdi
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financial theory
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    Why wouldn't you? – Tim Oct 27 '17 at 09:52
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    Why is this a no-no? In my experience it is fine to use count variables are independent variables in regression. Depending on the number of values and the specific application you can enter it as a continuous or as a categorical covariate. – Knarpie Oct 27 '17 at 09:53
  • No-no for having the count variable on the left hand side in OLS. – financial theory Oct 27 '17 at 09:54
  • I guess I'm wondering if count data would violate any distributional assumptions regarding explanatory variables (if there are such assumptions). – financial theory Oct 27 '17 at 09:57
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    The quick answer is "no," using integer valued features does not violate any assumptions of OLS regression. There have been many, many threads on this topic on CV since its inception, e.g., http://stats.stackexchange.com/questions/16381/what-is-a-complete-list-of-the-usual-assumptions-for-linear-regression?rq=1 – Mike Hunter Oct 27 '17 at 10:05

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As long as you can reasonably assume the response to be commensurate with the count data, e.g., the difference in $y$ between $x=1$ and $x=3$ to be twice that between $x=1$ and $x=2$, there is no problem whatsoever. Your regression doesn't care whether the regressor is discrete or is only observed discretely (as it is in any data analysis situation).

And if that assumption does not make sense, you can always transform your count variable (e.g., using splines). Just as for (nominally) continuous data.

As an example, it often makes sense to run a so-called "additive model" for the influence of certain single nucleotide polymorphisms (SNPs) on the susceptibility for some disease. Here you would encode whether someone had 0, 1 or 2 copies of the risk alleles.

Stephan Kolassa
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