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I have a simple website with a home page that has 5 different images on it. All images have a fixed set of 'features' associated with them (size, color, position etc.,). When a visitor comes to the page, he can either click on one of the images or simply leave.

For a given time interval, since both the number of views for the page as well as the number of clicks on an image are 'counts', they can be modeled as Poisson RVs. I want to build a regression model for the click-through-rate (CTR) ie., # clicks / # views (where # views is common to all 5 images and # clicks is obviously different).

I'm using the generalized linear model (glm) in R for this:

model <- glm(log(numClicks) ~ (features) + offset(log(numViews)), family=poisson, data=mydata)

Is this the right approach? I don't know if it's correct to take the ratio of two Poissons in combination with the canonical log link function and glm.

Is there a better way to model CTR?

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    $\begingroup$ It seems reasonable; however, you might want to at least contemplate the possibility that the coefficient may be other-than-one (perhaps it may be that the response is not-proportional to numViews). One way to investigate that if you considered it a serious possibility would be to also have it as a predictor (as well as an offset); if the coefficient was close to zero the offset should be sufficient. $\endgroup$
    – Glen_b
    Commented Jan 21, 2015 at 2:42
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    $\begingroup$ Thanks, I didn't know that you could have it in both the predictor and the offset. I will give that a try. $\endgroup$
    – user2602740
    Commented Jan 21, 2015 at 16:10

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Partially answered in comments:

It seems reasonable; however, you might want to at least contemplate the possibility that the coefficient may be other-than-one (perhaps it may be that the response is not-proportional to numViews). One way to investigate that if you considered it a serious possibility would be to also have it as a predictor (as well as an offset); if the coefficient was close to zero the offset should be sufficient.

– Glen_b

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