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I am currently trying to predict the outcomes of a search site for purchases. The three outcomes have value: 0 (no click) 1 (click and no purchase) 10 (click and purchase)

It seems that the data is not ordinal (exact values matter), so it must be continuous. But regression models always produce a significant spread in the target variable, so there will often be illegal values (like 4.58).

How does one try to fit a model for such a target variable? And how would I evaluate such a model?

Daniel

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  • $\begingroup$ This data seems like it could be treated as ordinal to me, but it definitely doesn't really fit the description of numerical data. The numbers are just placeholders for the three different outcomes, which kind of have an inherent order, i.e. ordinal. If you don't want to model it as ordinal, I would suggest looking into a multinomial logistic regression. It is an extension of a logistic regression that can handle more than a binary outcome. It is typically possible to fit these models in any statistical software (SPSS, R, etc.) $\endgroup$
    – sjp
    Commented Jan 18, 2021 at 20:56
  • $\begingroup$ But I want click and purchase to be much more valuable than just click. Going from purchase to no click should be treated as an error 10x worse than going click to no click $\endgroup$
    – Daniel Kagan
    Commented Jan 18, 2021 at 22:07

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I'm going to respond to your comment as an answer because the comment would be too long.

I understand that the difference between your levels is not equal, and it shouldn't be. The thing with the methods commonly used to model ordinal data is that the distance between levels is not assumed to be equal. Let's say we had four categories: "strongly disagree", "somewhat disagree", "somewhat agree", and "strongly agree". The "mental distance" for people responding to the survey question for "somewhat disagree" and "somewhat agree" may be much bigger than the difference between "somewhat agree" and "strongly agree". This is taken into account in ordinal regression and is why we shouldn't treat ordinal data as numerical.

I'd recommend these papers on ordinal data:

Liddell, T. M., & Kruschke, J. K. (2018). Analyzing ordinal data with metric models: What could possibly go wrong?. Journal of Experimental Social Psychology, 79, 328-348.

Bürkner, P. C., & Vuorre, M. (2019). Ordinal regression models in psychology: A tutorial. Advances in Methods and Practices in Psychological Science, 2(1), 77-101.

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