 The expected response matrix (E) is created, using Boolean inclusion, by comparing each row of the attribute pattern matrix (which is the transpose of the Qr matrix) to the columns of the Qr matrix.The expected response matrix is of order ("j,i"), where "j" is the number of examinees and i is the reduced number of items resulting from the constraints imposed by the hierarchy.The E matrix for the Ratio and Algebra hierarchy is shown below.