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I have a ratio as a response variable (typically in (0,1) ) which is the result of repeated measurement of a population satisfying a criteria over the total population for the time period. The thing is that those populations might fail to be numerous enough to be confident in the value of the response for some periods.

I am constrained to use a linear regression to model the response with independent gaussian noises and I was wondering (I am quite sure this must have been studied, it might even be a classical set up) if there is a referenced estimation procedure that would match the following : covariance matrix for the noise process is such that the variances are deterministically depending on the sampling uncertainty of the response variable (the idea would be to base dependency on the measurable uncertainty (typically the variance) of a binomial random variable sampling uncertainty) with null correlations. Does this rings a bell to someone ? My investigations so far on the web gave me either some too specific frameworks that do not seem too match with mine or solutions for measurement errors where I am not able to specialize the results with my objective.

TheBridge
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  • Do you know the numerator and denominator og the ratio? – kjetil b halvorsen Dec 17 '16 at 10:58
  • @ kjetil b halvorsen : Yes absolutely, for every period I know the number of events measured ( numerator) and number of the population (denominator). Regards – TheBridge Dec 17 '16 at 11:50
  • Why are you "constrained" in this way? Other types of model like logistic regression would be more usual in this setting. – mdewey Dec 17 '16 at 12:02
  • then definitely don't model the ratio - see [this very good answer](http://stats.stackexchange.com/q/243335/58675). Note that the answer starts by considering the case where only the ratio is available, because that was the case for my question, but it explains **why** it's much better to model numerator and denominator separately, and **how** to do that. – DeltaIV Dec 17 '16 at 12:09
  • I know this might seem odd to everyone but when I say this is a constraint this is because it is ... and I am not allowed to bypass this. See that as if it was an homework assignment (it is not for notice) or a theoretical problem where changing the approach would simply mean that you are off the subject. But please be aware that I do think that it is appropriate to model proportions with a direct linear regression. Best regards. – TheBridge Dec 18 '16 at 13:39
  • https://stats.stackexchange.com/questions/58664/ratios-in-regression-aka-questions-on-kronmal/410465#410465 – kjetil b halvorsen Feb 02 '20 at 03:30

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