For a binary response, consider the random effects model logit[P(Y it = 1|u i )] = + t + u i , t

For a binary response, consider the random effects model

logit[P(Y_it = 1|u_i)] = α + β_t + u_i, t = 1,..., T,

where {u_i} are independent N(0, σ²), and the marginal model

logit[P(Y_t = 1)] = α + β_t^*, t = 1,..., T.

For identifiability, β_T = β_T^* = 0. Explain why all β_t = 0 implies that all β_t^* = 0. Is the converse true?