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A model is supposed to predict a value that represents proportion, namely, the predicted value should be in [0,1]. However, model is just a linear regression, producing confidence intervals violating the boundaries of [0,1]. Of course it is not an adequate model. However, what is the statistical term to describe such symptom of a model, Namely, confidence interval violating physical boundaries of objects being modeled? If you could provide a reference, it would be highly appreciated!

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    $\begingroup$ Even when the model is perfectly correct, confidence intervals can cover invalid values of the parameter: that's an issue with the confidence interval procedure rather than the model. Since obviously you cannot do any worse by restricting the procedure's output to the set of valid values, nobody ever (knowingly) uses the kind of procedure you describe. $\endgroup$ – whuber Nov 12 '14 at 19:24
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    $\begingroup$ For percentage outcome you may consider beta regression. $\endgroup$ – Penguin_Knight Nov 12 '14 at 20:37
  • $\begingroup$ For Whuber:Thank you. But could you please provide an example whereupon the model is perfectly correct but the confidence interval still cover invalid values of the parameter? $\endgroup$ – John Zi Nov 13 '14 at 2:41
  • $\begingroup$ Hi, Penguin_Knight, thank you very much. I am not the one who built that model, I am only the one who serves as commentator/grader. I know beta regression is a much better choice but what I am trying to get is the technical term for the symptoms of this model. $\endgroup$ – John Zi Nov 13 '14 at 2:45
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    $\begingroup$ There are many examples, even in simple situations. Consider the "Normal approximation confidence interval" for a Binomial proportion. When the estimate $\hat p$ is within $Z^2/(n+Z^2)$ of $0$ or $1$, this interval will lie beyond the valid range $[0,1]$. This is taught in the elementary textbooks--along with caveats that urge against its application in situations for which, as it turns out, this interval will cover invalid values. $\endgroup$ – whuber Nov 13 '14 at 4:02
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I don't think there is any term for the specific problem you are asking about. You could say something like:

One piece of evidence that this is the wrong model is that the confidence interval includes impossible values.

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  • $\begingroup$ I'm not sure this is entirely correct, the problem could be with the method used to construct CI, nor with the model itself. A CI constructed by inverting a Likelihood ratio test would not have the problem, even if the model was at least somewhat wrong. $\endgroup$ – kjetil b halvorsen May 5 '19 at 16:33

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