6. (a) For a random effects model Yij = a + Btij + ui + Eij. Assume iid ui~ N(0, 0,3) iid Eija N(0, 3) Ui and Eij are independent. Find the covariance Cov(Yij, Yik) for all j + k. (b) For a model y = X B+E, with E(8) = 0 and Var(8) = o-V. i. Show that w = = (xTwx)-'xTwy is unbiased, whatever the choice of W. ii. For an estimator = (x+x)-?xTy, show that Var(B) = 02(xx)-'xTvx(x+x)-?. iii. What do the above (6(b)i and 6(b)ii) imply in practice by using a classical general linear model to fit longitudinal data that ignores the dependency between repeated measurements. (c) When estimating the unknown parameters of a general linear mixed model, why does one prefer the Restricted Maximum Likelihood (REML) method over the Maximum Likeli- hood (ML) method? Explain. (d) To analyse longitudinal data, one might include fixed or random subject effects. Give a situation that a random subject effect model is better than a fixed subject effect model. Explain. 6. (a) For a random effects model Yij = a + Btij + ui + Eij. Assume iid ui~ N(0, 0,3) iid Eija N(0, 3) Ui and Eij are independent. Find the covariance Cov(Yij, Yik) for all j + k. (b) For a model y = X B+E, with E(8) = 0 and Var(8) = o-V. i. Show that w = = (xTwx)-'xTwy is unbiased, whatever the choice of W. ii. For an estimator = (x+x)-?xTy, show that Var(B) = 02(xx)-'xTvx(x+x)-?. iii. What do the above (6(b)i and 6(b)ii) imply in practice by using a classical general linear model to fit longitudinal data that ignores the dependency between repeated measurements. (c) When estimating the unknown parameters of a general linear mixed model, why does one prefer the Restricted Maximum Likelihood (REML) method over the Maximum Likeli- hood (ML) method? Explain. (d) To analyse longitudinal data, one might include fixed or random subject effects. Give a situation that a random subject effect model is better than a fixed subject effect model. Explain