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I have the following data structure:

Percent-"yes"    Average-score    Region
70%              0.03             A
66%              0.07             B
57%              0.09             C
85%              0.06             D
.... etc

I have aggregated data by regions. The outcome variable is Percent-"yes" (indicating the percent of people answering "yes" for a survey question) and explanatory variable is Average-score (indicating the average of a score by all the people in that region).

The statistical model used is beta regression using logit link function. The beta-coefficient for Average-score is 0.06.

I interpret it as "For 1 unit increase in Average-score, there is a 0.06 units increase in log-odds of Percent-"yes"". A colleague told me the 2 bolded elements in the statement are wrong, I have a tough time figuring out why that is the case despite exhausting all my reference material. Any insights or material I can check out to figure it out?

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I think your interpretation is correct - not sure why your colleague indicated that this is wrong. Unless I'm overlooking something, the only caveat in the interpretation is that this does not necessarily correspond to individual probabilities/odds due to the averaging within the region.

Another useful approach to interpreting the output of betareg is to set up a new data frame with values of the regressor(s) that are "of interest" and then predict() the desired quantities, e.g., the expectation, variance, quantiles etc. And then you can graph these or present them in a table.

For a worked example of this approach see Figure 2 in vignette("betareg", package = "betareg") that shows the fitted mean of the response for varying the main regressor and keeping the other regressor fixed at a "typical" level. The constructed data frame with the values "of interest" is simply: data.frame(temp = 150:500, batch = "6"). See code chunk number 5 in edit(vignette(...)) for the exact replication code.

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  • $\begingroup$ I was hinted that my "0.06 units increase" being wrong has something to do with the unit of the regressor. The individual level Score is from 0-100%. When I aggregate it, I think it should still range from 0-100%. I still can't see how this plays a role in interpreting the change in log odds. $\endgroup$
    – KubiK888
    Commented Aug 19, 2016 at 16:20
  • $\begingroup$ When the coefficient is to be interpreted as "1 unit change in regressor", does it mean it changes from 0 to 1? So in my case it changes from 0% to 100%? And if I want to define how much log odds it changes the outcome by "1% change in the regressor", does it mean I need to divide the beta-coefficient by 100? $\endgroup$
    – KubiK888
    Commented Aug 19, 2016 at 16:25
  • $\begingroup$ The regression equation for the expectation of your response mu = E(percent_yes) is logit(mu) = a + b * average_score then a 1-unit increase in average_score leads to an increase of b units in logit(mu). So far this is hopefully obvious. The question is whether logit(mu) are the log-odds of percent_yes. I think it is ok to say this but one can argue that it is a bit sloppy. Because mu is not the individual probability to choose "yes" but an average frequency over a population. But I guess it depends on your application whether it is ok/useful to say so or not. $\endgroup$
    – Achim Zeileis
    Commented Aug 19, 2016 at 19:40

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