For my analysis I have a continuous quantitative variable (whose values are between 0 and 1) that I consider to be a dependent variable and qualitative and quantitative explanatory variables.
What is the appropriate model to use given that for the dependent variable there are observations 0 and 1 ( i.e. in the interval [0 , 1] )?
In my opinion, beta regression can only be used when the response variable takes values between 0 and 1 except for the exception of the two extreme values ( i. e. in interval ]0 , 1[ ).
Indeed, with the logit transformation used for beta models, we will have values -Inf and +Inf that are not real numbers.
If the only two values that you have for your data are 0 and 1, then you need to use logistic regression.
Dear @David L Morgan,
Thank you for your comment.
The depedent variable is continuous with values ranging from 0 to 1 (minimum= 0 ans maximum=1).
Hello Mugumaarhahama,
You could recode values of 0 to some small, nearby value (such as .001), and do similar for values of 1 (say, to .999). How much impact that has on your data set is likely a function of how many extreme values you have in your data set.
You're correct about beta regression excluding 0, 1 as legitimate values (for the reason you mention). But, the function certainly still works as values "approach" 0 or 1, respectively.
OLS regression probably not a good choice, since values aren't constrained to fall within the interval [0,1].
Good luck with your work.
I came across the same problem two weeks ago. If your dependent variable is continuous on the unit interval and the boundaries 0 and 1 are included, you can use the following transformation (Smithson and Verkuilen, 2006) to ''push" your extreme boundary values into the unit range:
[ y * (n-1)+0.5 ]/n, where n is your sample size and y are the original values of your dependent variable
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