Group v.s. individual data:

Suppose we have a dataset presented at an individual-level: {Zij, xij}, where Xij is a p-dimensional vector of predictors. The binary responses are coded as: Zij E {0, 1} and are assumed to be independent with E( Zij) = mi - i.e. Zij ~ Bernoulli(Ti) with Xij = Xi for j = 1, . .., ni; i = 1, . .., n. Another representation is using grouped-level form: {Yi, ni, xi}, where Yi = En Zij for i = 1, ..., n. The model for such data can be written as Y; ~ Binomial (ni, mi) with mi = g (x; 3) (using the notations in the class notes) Show that the score function of 3 is the same under the two representations of the same data