is commonly used in MTMM. It also explains how nonconvergence and “inadmissible” estimates can occur, even when the model is correctly specified. The relationship of rank deficiency with identification is explained, and some intuition regarding rank deficiencies of zero probability measure are given. The subsequent section defines the reduced-group correlated trait-uncorrelated method SB-MTMM model used by @saris_design_2014 [@revilla_split-ballot_2013], and @saris_comparing_2019, and derives the rank deficiency that occurs in this model using a computer algebra system. We then perform two Monte Carlo experiments that demonstrate the consequence of such rank deficiencies in simple factor models, as well as the CTUM RG-SB-MTMM model. Finally, the conclusion reflects on the role different types of parameters play in the estimation, the paradoxical role of sample size, the need to report nonconverged results in simulation studies, and, finally, the connection to modern unsupervised machine learning versions of LVM’s and regularization. It is hoped the methods presented in this paper can form the basis for routine evaluation of latent variable models, and can provide insight in the potential solutions to their woes.

Background
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Let $\textbf{y} \in \mathbb{R}^q$ be an $q$-vector of observable variables. For simplicity, we will assume all variables are centered. The basic confirmatory 