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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:

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Carolina
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    Perhaps you could rescale to [0, 1] and use logistic regression? – Scriddie Dec 04 '23 at 22:47
  • Please clarify the structure of your data. Do you have a big N, small T panel or just a single time series? – dimitriy Dec 04 '23 at 23:33
  • Beta regression is also an option – Alex J Dec 05 '23 at 00:39
  • 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. https://journals.sagepub.com/doi/10.1177/1536867X0800800212 – Nick Cox Dec 05 '23 at 00:49

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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.

blooraven
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  • 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? – Carolina Dec 05 '23 at 16:18
  • Also, how can I perform diagnostic checks on the beta regression? Two of my coefficients (time since intervention and time*intervention) are not significant – Carolina Dec 05 '23 at 16:20
  • Perhaps this would help: https://cran.r-project.org/web/packages/betareg/vignettes/betareg.pdf – blooraven Dec 06 '23 at 03:10
  • The seminal resource for beta regression is *A Better Lemon Squeezer& by Smithson and Verkullen. – Peter Flom Jan 27 '24 at 22:20