model.

I generated data from a $3\times 3$ CTUM-MTMM model with equal loadings, and correlations that differed by a distance $\delta$: $$\begin{aligned}
\Lambda = \kbordermatrix{
 &   \eta_1 &\eta_2 & \eta_3 & \xi_1& \xi_2& \xi_3\\
 y_{11} &    1 & 0 & 0  & 1 & 0 & 0  \\
 y_{12} &    1 & 0 & 0  & 0 & 1 & 0  \\
 y_{13} &     1 & 0 & 0  & 0 & 0 & 1  \\
 y_{21} &    0 & 1 & 0  & 1 & 0 & 0  \\
 y_{22} &     0 & 1 & 0  & 0 & 1 & 0  \\
 y_{23} &     0 & 1 & 0  & 0 & 0 & 1  \\
 y_{31} &     0 & 0 & 1  & 1 & 0 & 0  \\
 y_{32} &     0 & 0 & 1  & 0 & 1 & 0  \\
 y_{33} &     0 & 0 & 1  & 0 & 0 & 1}, & \; &
    \Phi =  \kbordermatrix{
     &   \eta_1 &\eta_2 & \eta_3 & \xi_1& \xi_2& \xi_3\\
 \eta_1  &  1 & 0.5 - \delta & 0.5  & 0& 0& 0\\
 \eta_2 &  0.5 - \delta & 1 & 0.5 + \delta & 0& 