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I need to test some hypotheses for a social sciences dissertation. In my description below, I refer to the independent as the Xs and the dependent variables as the Ys.

I am expecting a straight linear relationship between the Xs and Ys, like Y = mX + C. The Xs are a "continuous" variable that will be the average of four questions from a 5-point Likert scale. The Ys are both Count variables that can take the values 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

I am assuming that as that as that as my Ys are count variables, I will need to use something like a Poisson model or a Zero-Inflated Poisson model. However, as my the Ys have an upper bound, would that complicate matters?

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Ordinal regression can be a good choice for such data. It makes no assumptions about the distribution or limits of the outcome values, just that the outcomes are rank ordered. Frank Harrell outlines the concepts on this page. The lrm() function in his rms package is suitable for a small number of outcome levels like yours. A UCLA web page explains another implementation in R. Do pay attention to details of the implementation you use, as some software models the odds of moving into a higher outcome level as a function of the predictors while others model the odds of going into a lower level

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  • $\begingroup$ thank you, is the ordinal regression still suitable even though my dependent variables have a lower and upper bound? $\endgroup$ Commented Jan 23 at 17:09
  • $\begingroup$ @NutellaMonster yes. It's most frequently used for situations like yours with a few ordered categories, which necessarily means that there's a lower and an upper bound. The actual outcome values don't matter, just the order. $\endgroup$
    – EdM
    Commented Jan 23 at 18:29

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