I would like to model a percentage response. This percentage is not quite a probability or ratio of 2 quantities. It is reported by customers and expresses they pleasure of shopping. They report it using 10% intervals, I mean: 0%, 10%, 20%, 30%, .... 100%.
I want to analyse the relationship between this and a few predictors: percentage = x1 + x2
The response is not an ordinal variable, but rather discretized continuous. Fractional predictions, like 22% or 67.25% would make perfect sense to me.But it cannot go lower than 0 and more than 100%.
I think I have three options:
linear regression, where the interpretation would be very easy. But I was told my response is a truncated one, and I don't want to play with -10% or 120%. Also, I was told that percentages and proportions may expose problems with variance, which may depend on the mean, so the standards errors will be incorrect. I am not sure, if my response is a proportion? Just a number from range 0-1, but well, yes, it's a % of the range.
fractional logistic regression - but I don't understand the outcomes, so let's skip this.
beta regression. I will handle the 0 and 100% by adding/subtracting 0.001 from it. I was told to use the logit link. But now I don't understand the outcome.
But how to read the print out? What does it mean, say, exp(x1) = 1.2? I know, that it usually means "change in log odds", but what does the "odds" correspond to? I don't have any "categories", to which my customers belong, just percentages.
So, how can I read the output of my beta regression, where exp(x1) is 1.2? That "unit change in x1" multiplies my percentages by 1.2?
So, if x1 changes by 1, and the percentage was 10%, will it be 12% now?
I will be happy if you can propose me another methods of analysis (I heard about truncated linear regression), but first of all, kindly please, refer to the beta regression.