Question: Consider the loglinear random effects model log[E(Y it | u i )] = x? it ? + z? it u i , where {? i

Consider the loglinear random effects model

log[E(Y_it | u_i)] = x?_it ? + z?_it u_i,

where {?_i} are independent N(0, ?). Show that this implies the marginal loglinear model

with the same fixed effects but with offset term. For the random-intercept case, indicate the role of ? on the size of the offset. Explain what happens when ? = 0.

log[ E(Y;4)] ,"2 z, = x;,, X',B, 2

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