8.9 Item-level Relative Fit measures (Cont’d)

If this item is a ACDM item, we have $$P(11)-P(00)=[P(10)-P(00)]+[P(01)-P(00)]$$ or $$P(11)+P(00)-P(10)-P(01)=0$$ This is equivalent to say $$\begin{bmatrix} 1 & -1 & -1 & 1\\ \end{bmatrix} \begin{bmatrix} P(00)\\ P(10)\\ P(01)\\ P(11)\\ \end{bmatrix}=0$$ Or, $$\mathbf{R}\mathbf{P}=\mathbf{0}$$