Difference between regression methods for proportions I have a set of data where the response is a proportion.  For each event in the experiment, a system will correctly tag X of Y items.  In the end, I will have something like 100 different results.  I have been trying to determine what is the most correct method of fitting the response variable.  So far I have uncovered 4 number of options.


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*R's built-in glm using one line for each of the Y items in each experimental event

*R's built-in glm using a proportion (X/Y) with the weight set to Y for each experimental event

*The betareg fit method from the R betareg package

*Quasi-likliehood method proposed by Papke and Wooldridge (pdf)



I am unsure how to rank these different methods to know which is the most appropriate.  Here are some specific questions:


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*How does the likelihood change for these different options (especially between options 1 and 2)?

*What are the pros and cons of the different methods?

*Do these methods have limitations on the types of factors that can be built into the model?

*For the betareg function, are the weights specified the same way as the glm function?

*Most people would tell me to use option 2 listed above, but I have seen a lot of pull for option 3.  Why should I choose option 3 over option 2?

*What do you do if you do not know the denominator of the proportion (i.e., you cannot properly weight the data for option 2)?


As you can see these questions are quite general and could be the elements of a full academic text.  I was just not sure where to go to get the answers to these questions.  
 A: You're making it too complicated.  Don't model the proportion, model the success/failures.  Your data come from a Binomial distribution (X successes, Y trials).  Therefore use a logistic regression model.
glm(formula = cbind(X, Y) ~ ..., family = binomial)

A: The model's reported degrees of freedom in the output will differ between 1 & 2, but this won't have any effect on anything else. For comparisons between models, so long as both were fit grouped or both ungrouped, there will be no difference. If you know the number of trials & the number of successes, your data are binomial, so you use logistic regression as @Glen_b notes (you can flip a coin between 1 & 2). 
If you know the number of successes, but not the number of trials, you can fit a count regression, (probably a negative binomial or other over-dispersed Poison). 
If you have a proportion, but don't know either the total number of trials or the number of successes, you will have to fit a beta regression.  Beta regression is for continuous proportions, so it wouldn't be ideal, but if the proportions were based on a large number of trials, it probably wouldn't be too biased.  
