the sample estimates, causing inadmissibility and instability, and nearly singular gradients, generating nonconvergence. Therefore, although the probability of solutions to the objective being at the p.o.d. *exactly* is zero, the p.o.d. creates a zone of near-deficiency that will cause serious estimation problems in practice. Others have noted this issue as well; because of the dependency of practical problems on data, @aldrich_how_2002 suggested to abandon the idea of “identification” and suggested replacing it with a concept of the informativeness of data. @goodfellow_deep_2016 [ch. 8] discuss how the neural network community shifted its focus from the investigation of rank deficiencies to evaluating whether solutions that result are acceptable in terms of the cost function. In short, the econometric concept of “almost sure” stability may not be as comforting as it sounds. At the same time, the existence of rank deficiencies need not always generate serious problems with the estimation.

Finding rank-deficient points in the Jacobian is a challenging task. For factor analysis, and specifically multitrait-multimethod models, existing literature has developed several analytical results [see @shapiro_identifiability_1985; @kenny_analysis_1992; @grayson_identification_1994 and references therein]. An alternative approach is to employ computer algebra systems to investigate rank deficiency [@bekker_identification_2015]. This is what the following section will do 