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I have a planned study to conduct in few weeks. As it is my first time to deal with a 'count' dependent variable, I have been searching on this website what statistics tools I should use.

I have two independent variables - both binary (0 or 1).

The main dependent variable is a count variable that range from 0 to 3. To be more specific, participants rank 6 independent options that are given. If they have all three options - Option A, Option B, and Option C - in the highest rank of three, I assign them with a score of 3. If they have only two of them in the highest rank, I assign, 2, and so on until 0.

From what I read from this website, it seems both "poisson count model" and "negative binomial model" can be used for my study.

I am familiar with the ordinary linear regressions but not with either of the two. I believe that the Poisson model would be a better choice, since I have read that Negative binomial is used for more 'outstretched' data.

I would like to hear your thoughts on this!

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    $\begingroup$ Please edit the question to say more about what the "count" outcomes represent. Might that be the number of "correct" outcomes out of 3 trials, or a ranking of something on an integer scale from 0 to 3, or something else? The way to proceed can depend on the specific process that leads to your "count" outcome. Neither Poisson nor negative binomial might end up the best choice. Please edit your question to provide that information, as comments are easy to overlook and can be deleted. $\endgroup$
    – EdM
    Mar 11, 2022 at 13:39
  • $\begingroup$ Thanks, @EdM! Thats a good point. I just edited to make the description of my dependent variable more precise. Thanks for letting me know to make direct edits to the content - I am new here, so I would have gone for just leaving comments if not your comment! $\endgroup$
    – Ted
    Mar 12, 2022 at 23:51
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    $\begingroup$ This appears to be an ideal situation for an ordinal semiparametric model. See here for resources. $\endgroup$
    – Frank Harrell
    Mar 13, 2022 at 14:36
  • $\begingroup$ @FrankHarrell Thanks for your input! I will look into this more! $\endgroup$
    – Ted
    Mar 22, 2022 at 21:24

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participants rank 6 independent options that are given. If they have all three options - Option A, Option B, and Option C - in the highest rank of three, I assign them with a score of 3. If they have only two of them in the highest rank, I assign, 2, and so on until 0.

This is probably best handled by viewing the outcomes as ordered, with integer outcome values ranging from 0 through 3, and performing an ordinal logistic regression. The UCLA website has links to implementation of that type of regression in each of 5 statistical software packages.* With only 2 binary predictors you might not have much discrimination in your model. You probably should include an interaction term between those 2 predictors so that the effect of one predictor can depend on the value of the other.

A Poisson model wouldn't be a good choice, as that implicitly assumes that there is no upper limit to the number of "counts" even if large numbers of counts are improbable. Here, you have a fixed upper limit of 3 "counts."

*While I was writing this answer, Frank Harrell made a similar suggestion in a comment. As his course notes and book explain, that approach can be useful even with continuous outcomes. Review the resources to which he links for more background.

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  • $\begingroup$ Thanks! I will look in to the ordinal logistic regression and ordinal semiparametric model more. I guess they are two separate analyses methods! $\endgroup$
    – Ted
    Mar 22, 2022 at 21:24

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