Then As shown in Web Appendix B, differentiation of (12) gives and where ( Σ − $^{1}$)$_{·}$$_{k}$ and ( Ω − $^{1}$)$_{·}$$_{k}$ denote the k th columns of Σ − 1 and Ω − $^{1}$, respectively. Then, if we define ̂ η ⊗ 2 i = E ( η$_{i}$ ⊗ η$_{i}$ | y$_{i}$$_{·}$ ) and ̂ ξ ⊗ 2 ij = E ( ξ$_{ij}$ ⊗ ξ$_{ij}$ | y$_{i}$$_{·}$ ) , after some algebra we obtain: G$_{kl}$ = − 1 4 ( Σ − 1 ) kk ( Σ − 1 ) ll + 1 4 { ( Σ − 1 ) T · k ⊗ ( Σ − 1 ) T · k } E ( ̂ η ⊗ 2 i ̂ η ⊗ 2 i T ) {( Σ − 1 ) · l ⊗ ( Σ − 1 ) · l } , G$_{k,r}$ + l = − J 4 ( Σ − 1 ) kk ( Ω − 1 ) ll + 1 4 { ( Σ − 1 ) T · k ⊗ ( Σ − 1 ) T · k } E ( ̂ η ⊗ 2 i J ∑ j =1 ̂ ξ ⊗ 2 ij T ) {( Ω − 1 ) · l ⊗ ( Ω − 1 ) · l } , 14 avar( ˆ h$_{w}$ ) = { tr( Ω ) } 2 { tr( Σ ) + tr( Ω ) } 4 · r ∑ k =1 r ∑ l =1 ( G − 1 ) kl − 2tr( Σ )tr( Ω ) { tr( Σ ) + tr( Ω ) } 4 · r ∑ k =1 r ∑ l =1 ( G − 1 ) k,r + l + { tr( Σ ) } 2 { tr( Σ ) + tr( Ω ) } 4 · r ∑ k =1 r ∑ l =1 ( G − 1 ) r + k,r + l . ∂ ∂ Σ$_{kk}$ log f ( y$_{i}$$_{·}$ ) = − 1 2 ( Σ − 1 ) kk + 1 2 ( Σ − 1 ) T · $_{k}$E ( η$_{i}$η T i | y$_{i}$$_{·}$ ) ( Σ − 1 ) · k ∂ ∂ Ω$_{kk}$ log f ( y$_{i}$$_{·}$ ) = − J 2 ( Ω − 1 ) kk + 1 2 ( Ω − 1 ) T · k J ∑ j =1 E ( ξ$_{ij}$ ξ T ij | y$_{i}$$_{·}$ ) ( Ω − 1 ) · k ,