(a) (10 points) Group vs. Individual level 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 {0, 1} and are assumed to be independent with E(Zij ) = i - i.e. Zij Bernoulli(i) with xij = xi for j = 1, . . . , ni ; i = 1, . . . , n. Another representation is using grouped-level form: {Yi , ni , xi}, where Yi = P ni j=1 Zij for i = 1, . . . , n. The model for such data can be written as Yi Binomial(ni , i) with i = g 1 (x T i ) (using the notations in the class notes)