lab:mediation_model_maple_codes

Iden := Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1}) A := Matrix(3, 3, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (2, 1) = a, (2, 2) = 0, (2, 3) = 0, (3, 1) = c, (3, 2) = b, (3, 3) = 0}) S := Matrix(3, 3, {(1, 1) = sigma[1]^2, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = sigma[2]^2, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = sigma[3]^2}) with(linalg): omega := multiply(multiply(inverse(Iden-A), S), transpose(inverse(Iden-A))) Matrix(3, 3, {(1, 1) = sigma[1]^2, (1, 2) = a*sigma[1]^2, (1, 3) = (a*b+c)*sigma[1]^2, (2, 1) = a*sigma[1]^2, (2, 2) = a^2*sigma[1]^2+sigma[2]^2, (2, 3) = a*sigma[1]^2*(a*b+c)+b*sigma[2]^2, (3, 1) = (a*b+c)*sigma[1]^2, (3, 2) = a*sigma[1]^2*(a*b+c)+b*sigma[2]^2, (3, 3) = (a*b+c)^2*sigma[1]^2+b^2*sigma[2]^2+sigma[3]^2})