I have a dependent variable that is a ratio, i.e. it takes the values between 0 and 1. Some 30% of values are 1s. The dependent variable measures the distribution of funds, i.e. it is calculated just like so: amount of distributed money / the total amount of proposed money. It so happens that often times all of the proposed money is disbursed.

I am building a model to see what factors influence the disbursement rate.

I was told that a fractional regression could be appropriate for such a dependent variable.

However, I was also told in this post that I could use a logistic regression with the original values that have made up this ratio variable. Indeed, I have the original values available. However, I cannot understand how could I use a logistic regression for this? How many dependent variables would I have then (2?), and how would all of this work?

Do you think this latter advice is sound? If so, do you have any sources that would explain how to do that?

Any justified arguments are much appreciated.


1 Answer 1


Don't use a logistic regression with the original values because your data are not counts (in the two categories: amount distributed and amount not distributed) and the total sample size (amount proposed = amount distributed + amount not distributed) would be huge.

The page in the link you provided suggested to use the fractions directly in a binomial or quasibinomial GLM with so-called "robust" standard errors. Maybe that will work but how does one evaluate the quality of the results?

Another hack for for percentage data is to apply an arcsine transform to the response variable and then perform an Ordinary Least Squares regression (Crawley 2008. The R Book. p. 570). Be sure to check the OLS diagnostics (the residuals should be normally distributed and have a constant variance).

I get the impression that you are not highly proficient in statistical modelling (like me) and am looking to pass judgement on someone else's published work. You need to take care that your re-analysis is reliable.

  • $\begingroup$ Thanks, arcsine transformation does help somewhat with the normality of residuals, though it is still quite far from perfect. However, heteroscedasticity remains. $\endgroup$
    – Ken Lee
    Jun 1, 2021 at 12:09
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    $\begingroup$ The frm R package (which was on Michael Clark's page) has some useful fractional regression functions for econometrics including goodness of fit tests. It could help and could be acceptable to your peers. This question explains how it works: stackoverflow.com/questions/37584715/… $\endgroup$
    – stweb
    Jun 7, 2021 at 11:58
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    $\begingroup$ This question (and the paper it references) also seems relevant: stackoverflow.com/questions/19893133/… $\endgroup$
    – stweb
    Jun 8, 2021 at 11:59
  • $\begingroup$ A beta regression could be an alternative, search this site. $\endgroup$ Mar 9, 2022 at 11:48

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