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In the data that I am working on, my response is a proportion ranging between 0 and 1. I learnt that beta regression is probably the best choice to model such data, but is there a suitable alternative in GLM or even in OLS where I can make the boundary between 0 and 1 rather than negative-infinity to positive-infinity?

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    $\begingroup$ If you know that beta regression is appropriate for your problem, why are you looking for alternatives? $\endgroup$ – Roland Feb 8 '16 at 16:40
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    $\begingroup$ Because beta regression results are not easy to explain to the business. $\endgroup$ – Raj Feb 9 '16 at 5:23
  • $\begingroup$ Logistic quantile regression. See the lqr R package. $\endgroup$ – Christian Eduardo Galarza Mar 1 '18 at 13:56
  • $\begingroup$ You should spell out what you mean by GLM. Many people have different meanings for this acronym. Some see this as "general linear model," while others might read "generalized linear model." Others in realiability might read this as "Generalized Life Model." $\endgroup$ – StatsStudent Feb 10 '19 at 21:13
  • $\begingroup$ @Raj Do you need to explain the particulars of the loss function you used to business partners? Business people are usually concerned with how well you predict what you say you're predicting, and the economic impact of using those predictions for whatever task is at hand. The statsy stuff is better to keep to the data scientists. $\endgroup$ – Matthew Drury Feb 10 '19 at 21:49
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Some of the other commenters have posted good questions, so you should try to answer their questions when determining how to model your data. But I'll also offer another idea. Have you considered using a regular transformation of your data and then just using ordinary linear regression or weighted least squares?

An often suitable transformation for least squares for proportions can be given by:

\begin{eqnarray*} Y^{\prime} & = & 2arcsin\sqrt{Y} \end{eqnarray*}

So, you can essentially perform this transformation on your response variable to obtain $Y^\prime$ and then attempt to perform least squares regression on $Y^\prime.$ That being said, this should be used with caution. Although the transformation is found in many regression texts, some have argued against it.

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Logistic regression (which is a glm with a logit link function) can be used to model outcomes between 0 and 1, not just binary outcomes.

But I do second the comment. If beta is the right choice, use beta regression.

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  • $\begingroup$ do you know an R package that can do this logistic regression for continuous 0-1 outcomes? Does this include exact ones and zeros? $\endgroup$ – spore234 Mar 2 '16 at 12:12

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