Wouldn't it be better to use poisson regression for count data? Also in logistic regression what is the advantage of using the log link versus the logit link? I know you can get the log relative risk with the log link. But why use relative risks as opposed to odds ratios?
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2$\begingroup$ Can you give some context? It seems you came across someone/some article that claimed to use logistic regression for count data, and to use the log link for binary data. Can you link to that? That way we are sure we are talking about the same arguments. $\endgroup$– Maarten BuisMay 22, 2014 at 15:25
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Your question starts with a premise, namely that people actually use logistic regression for count data. I have not seen so, except when employing a hurdle model. Logistic (and probabilistic) models are designed for binary dependent variables. Because of this, the coefficients (which are odds ratios) can be transformed to marginal effects on probability of having a 1 in the dependent variable. I don't see how this can be meaningful for count data. I also think that you run into errors when you regress a logistic model with count data that actually has no 0 values - which is possible.
Also, Poisson regression is not the only possibility to deal with count data. There is negative binomial as well. The difference between these two: Poisson restricts the first two moments (mean and variance) to be equal, while negative binomial doesn't.
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3$\begingroup$ Logit models can easily be used for predicting proportions, even continuous proportions. Historically, this usage long preceded logit models for binary responses, as logistic curves were used for modelling population change long before logit models in something like the current form were introduced. So, although now logit models are often first met (and by some researchers only met) as ways of handling binary responses, it's incorrect to imply that to be their only use. $\endgroup$– Nick CoxMay 29, 2015 at 13:59
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1$\begingroup$ Logit is used a lot in default modeling. The defaults are counts, but can be converted into frequencies by dividing by the outstanding accounts each period. This way they become hazards. You could also model them as default probabilities, i.e.continuous values from 0 to 1. So Logit is used for proportions, as @NickCox mentioned. $\endgroup$– AksakalMay 29, 2015 at 14:06
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$\begingroup$ @Aksakal "frequencies" without qualification I think normally means what "counts" does. So it seems that "converted into frequencies" should be "converted into fractions/probabilities/proportions". Otherwise we are saying similar things. $\endgroup$– Nick CoxMay 29, 2015 at 14:16
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$\begingroup$ @NickCox, the term "default frequencies" usually means probabilities in finance, but I agree that in stats it's counts. $\endgroup$– AksakalMay 29, 2015 at 14:25
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$\begingroup$ That's totally new for me - I learned that count data should best be used with Poisson or NegBin. And frankly: I came across a lot of count data regression, but none of them used logit (if any, people used OLS by simply assuming that there's enough data to make the distribution look like normal). Maybe you write an answer of yourself, @NickCox? $\endgroup$– MERoseMay 29, 2015 at 14:32