# Modeling low-cardinality dependent variable continuous linear regression

What problems, if any, would exist if I were to treat a dependent variable with relatively low cardinality (e.g. 10 distinct values) as continuous versus binary (the latter requiring that I create some threshold to "binarize" the column)?

For example, I have a dependent variable consisting of points assigned to answers on a survey. There are several thousand respondents in my survey and for this particular variable the points are distributed somewhat uniformly, if not somewhat right-skewed.

Does this warrant a different type of regression, e.g. Poisson?

• There are many problems with using linear models in that context, as discussed at length elsewhere on this site. Use a methods that is dedicated to ordinal response data, e.g. the proportional odds ordinal logistic model, which is a generalization of the Wilcoxon test. See my RMS book and course notes for more. Jan 27 '20 at 21:28

As a rating is an ordinal response, (i.e. an ordered categorical response variable) the function MASS::polr should be more appropriate; it implements the proportional odds logistic regression routine. Simplifying things a bit: through a proportional odds model instead of modelling the probability of response in a particular category (as we would do if we simply assumed a multinomial response without any ordering), we model the cumulative probability that the response is not greater than a chosen category. This is also the core point behind the proportional odds assumption that this model relies one; i.e. that the estimated "rate of change" across two response levels is the same regardless of which pair of outcomes we consider. Particular to the case mentioned, the "right-skewness" of the data is not a problem either. Ananth & Kleinbaum (1997) Regression models for ordinal responses: a review of methods and applications is a very accessible paper on the matter. A&K point to some example in SAS but a very comprehensive tutorial on the analysis of ordinal response variables using R can be found in the UCLA Stats consulting pages: here; I strongly recommend it as it offers a step-by-step explanation with code examples.