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I'm using interrupted time series analysis to estimate the impact of an intervention in the same group. However, my target variable is a satisfaction index that goes from -1 to 1.

How can I model a dependent variable that is bounded between -1 and 1?

The distribution of the dependent variable looks like this:

enter image description here

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    $\begingroup$ Perhaps you could rescale to [0, 1] and use logistic regression? $\endgroup$
    – Scriddie
    Commented Dec 4, 2023 at 22:47
  • $\begingroup$ Please clarify the structure of your data. Do you have a big N, small T panel or just a single time series? $\endgroup$
    – dimitriy
    Commented Dec 4, 2023 at 23:33
  • $\begingroup$ Beta regression is also an option $\endgroup$
    – Alex J
    Commented Dec 5, 2023 at 0:39
  • $\begingroup$ Call this variable $Y$' then $(Y + 1)/2 =: y$ is as @Scriddie advises within $[0, 1]$ and is fit for logistic regression. More at e.g. journals.sagepub.com/doi/10.1177/1536867X0800800212 $\endgroup$
    – Nick Cox
    Commented Dec 5, 2023 at 0:49

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You could rescale to $[0,1]$ and then use Beta Regression (Wikipedia) which is designed for response data that lies between $[0,1]$. Also, see this answer to a similar question which talks in a little more detail about the pros and cons of simply using logistic regression for this.

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  • $\begingroup$ Thanks! But how do I interpret the coefficients afterwards? Do I need to scale back? For example, the interruption coefficient (based on a binary variable on whether there was interruption or not) is -0.2133 — does this mean that the index decreases by 0.213 with the intervention? Or do I have to scale the -0.213? $\endgroup$
    – Carolina
    Commented Dec 5, 2023 at 16:18
  • $\begingroup$ Also, how can I perform diagnostic checks on the beta regression? Two of my coefficients (time since intervention and time*intervention) are not significant $\endgroup$
    – Carolina
    Commented Dec 5, 2023 at 16:20
  • $\begingroup$ Perhaps this would help: cran.r-project.org/web/packages/betareg/vignettes/betareg.pdf $\endgroup$
    – blooraven
    Commented Dec 6, 2023 at 3:10
  • $\begingroup$ The seminal resource for beta regression is *A Better Lemon Squeezer& by Smithson and Verkullen. $\endgroup$
    – Peter Flom
    Commented Jan 27 at 22:20

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