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I have proportion data (percentage viewership of TV programs) that i'd like to model as a function of various demographics (age, sex etc.) and time (year). After surveying options for appropriate multiple regression models, I'm debating between the following two strategies:

1) fit a beta regression model after dividing the percentage data by 100 and adjusting the range slightly so that values of zero and one do not occur.

2) fit an OLS model after logit transforming the percentage data (again, divided by 100 and adjusted slightly) so that the dependent variable is mapped to the Real line.

One key consideration is that i'd like to make the results as intuitive as possible to a non-statistical audience. So, interpretations such as "for a one unit change in X we get a percent change in Y", or something like that, would be most welcome.

Can anyone outline pros and cons of these two approaches in this regard?

It seems to me that using beta regression with a logit link, and then calculating odds ratios may lead to nice "percent change" explanations. The coefs from the OLS model would also be on the ln(odds) scale, so I assume I could also do the same for that model. My data are too large to share, but I ran both models in R and there are only minor differences in the coefs.

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    $\begingroup$ The fudge of moving away from 0 and 100 is difficult to defend here. At a minimum you would need to do some sensitivity analysis to see the effects of the constants you used. Also, tell us more about 0 and 100. It seems likely that there are spikes in your data if 0 and 100 occur at all, which rather undermines the idea of a beta distribution. Some people have worked with zero-inflated betas. $\endgroup$ – Nick Cox May 28 '13 at 0:07
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    $\begingroup$ @Nick Cox. Unfortunately, I don't know how to add a plot here. The distribution contains six 0s and zero 1s (out of 10K+ observations). There is a spike at about 3%, and about 2/3 observations fall between 0% to 7%. The max is about 18%. Why would this undermine the idea of a beta distribution? I thought the beta dist. were ideal for exactly this situation (providing there's no 0 or 1 inflation)? $\endgroup$ – Chris May 28 '13 at 0:40
  • $\begingroup$ Agreed that the spikes sound minor, but now you need to address your fudging. Using a generalised linear model with logit link shouldn't require fudging. I don't think you are going to get an approach intuitive to a non-statistical audience either way. $\endgroup$ – Nick Cox May 28 '13 at 0:43
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    $\begingroup$ As I said, my suggestion was a GLM with logit link, not a beta distribution fit. That does not depend on numerator and denominator being known separately, nor on Bernoulli trials. Nor are observed 0s and 1s a problem. See stata-journal.com/sjpdf.html?articlenum=st0147 for a review with details of how to do it in Stata. (Excellent if your audience is happy with odds ratios.) $\endgroup$ – Nick Cox May 28 '13 at 1:09
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    $\begingroup$ No zero inflation, no one inflation; just that observed zeros and ones are not fatal. Fractional logit would be one name. The reference to binomial in software calls is just a trick but the point of the literature is that the trick is a fair one. The model goes back to Wedderburn at least. $\endgroup$ – Nick Cox May 28 '13 at 6:40

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