Materials to ‘ A Finite Mixture Model for Working Correlation Matrices in GEE ’

1. A multivariate continuous model In this section, we provide the following concrete example that satisfies all the assumptions of Theorems 3 and 5 in our manuscript. Let yik be the response at time k for the i th subject from N(μik = β0 + xikβ1, 1), k = 1, . . . , T = 3, i = 1, . . . , n = 50. Let yi = (yi1, · · · , yiT ) . The true value of (β0, β1) is (1, -1). Covariates xik’s are iid randomly sampled from N(k, 1). We consider the case in which the true correlation of yi is given by a two component mixture of AR(1) and CS. Let R (α1) = RAR(1)(α1) and R (α2) = RCS(α2). The true values of the correlation parameters (α1, α2) and the relative component proportions (π1, π2) are (0.6,0.6) and (0.3,0.7). 1.1 Conditions of Theorem 3. In the following, we will present detailed verification of the conditions of Theorem 3. It is quite obvious that assumptions (i) and (ii) of Theorem 3 and the condition E{ ∂ψ } = ∂E{`(ψ)} ∂ψ are satisfied. For assumption(iii), we first have