following conditions:

1.  All loadings are equal, $\lambda_{tm} = \lambda$ *and*;

2.  All correlations are equal, $\rho_{t t^\prime} = \rho$.

In this case, a basis for the nullspace is $$\label{eq:nullspace}
\text{Null}(\boldsymbol{\Delta}_{\text{\sc{sbmtmm}}}) = \kbordermatrix{
       & \lambda_{11} & \ldots & \lambda_{12} & \ldots & \psi_{1} & \psi_{2} & \ldots &\rho_{12} & \rho_{13} & \rho_{23} & \phi_{4} & \phi_{5} & \phi_{6} \\
& \frac{1}{2 \lambda \rho} & \ldots & -\frac{1}{2 \lambda \rho} & \ldots & +\frac{\rho-1}{\rho} & -\frac{\rho-1}{\rho} & \ldots & 0 & 0 & 0 & -1 & 1 & 1 \\
}$$ Crucially, $\text{Null}(\boldsymbol{\Delta}_{\text{\sc{sbmtmm}}})$ has zeroes in the three places that correspond to the three correlation parameters $\rho_{12}$, $\rho_{13}$, and $\rho_{23}$. The nullspace is orthogonal to these parameters, which are not involved in the dependency. We will see in the experiments that this means that models that appear to lack convergence, will actually converge for these three parameters, and estimates of these parameters will be stable in spite of high-variance (often inadmissible) estimates for the others.

The result that the Jacobian is deficient *only* under the above two conditions may seem somewhat surprising given the literature on MTMM.

First, @wald1950note and @kenny_analysis_1992 suggested that rank-deficiency of $\Lambda$ would generate an “underidentified” 