Hi, I've wondered about logistic analysis.
In glm(generalized linear model), link function value of mean = linear predictot. So, classical model's responses is described as g(E(Y))=Xb where X:design matrix, b:coefficient vactor, and g is link function since Y~normal distribution.
But, in the case of logistic model, responses are binomial distribution(n_i,p_i).
So I think that g(n_i*p_i )=Xb where g is a link function.
However, My text book says g(p_i)=Xb, i.e., the parameter n_i is not considered.
Why is this occured?
Whether you're modeling binomial or bernoulli the idea is still the same. We consider the n_is to be fixed quantities so it doesn't matter if we model n_i*p_i or p_i. But it makes more sense to just model the p_i since for each observation n_i could be different. If you wanted to when you have binomial data you could always pretend like you have bernoulli data just by creating a dataset of success/failure from each binomial trial.
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