solving the problem of “inadmissible” estimates by excluding them from the optimization space. The same idea appears the norm in the literature on Bayesian SEM [@lee_structural_2007; @muthen_bayesian_2012; @merkle_blavaan:_2018]. However, others have pointed out that constrained estimation to prevent “inadmissible” estimates creates bias in the parameter estimates [e.g. @chen_improper_2001]. The estimates that would otherwise have been “inadmissible” will “pile up” along the constraint boundary, neglecting to cancel out sample estimates further to the opposite side of the true parameter value. In other words, the underlying problem is not a computational one, and “solving” it with a computational trick such as constrained estimation will simply transfer the problem to a different part of the overall procedure, like pushing on an air mattress to deflate it while forgetting to open the valve. Due to this “air matress” principle, we will refer mostly to the problem of “inadmissible” estimates, with the understanding that the reader who prefers constrained estimation may mentally substitute this for the problem of bias.

In discussions of rank-deficiencies of parametric models, the information matrix inverted in Equation \[eq:variance\] is taken as a point of departure [e.g. @wald1950note; @bekker_identification_2001]. In the case of linear and homoskedastic (SEM) models with full-rank estimation 