What is model identifiability and how important an issue is it?
Model identifiability is a simple concept. Once understood, it should pose no problem for the researcher. An identified model is one there there exists one best solution. With a nonidentified model, more than one “best” solutions (in fact, an infinite number) exist; the situation is related to the problem of having more equations than unknowns. One may distinguish two types of nonidentifiability: intrinsic and empirical nonidentifiability. With intrinsic nonidentifiability, it is the model design–that is, the number of manifest variables, number of response levels for each manifest variable, and number of latent classes–that results in nonidentification; all instances of the same such design are unidentified (with, the possible exception of certain degenerate data structures). With empirical nonidentifiability, a model may or may not be identified, depending on the particular values of the observed data. We consider intrinsic nonidentifiability first.
Model identifiability is a simple concept. Once understood, it should pose no problem for the researcher. An identified model is one there there exists one best solution. With a nonidentified model, more than one “best” solutions (in fact, an infinite number) exist; the situation is related to the problem of having more equations than unknowns. One may distinguish two types of nonidentifiability: intrinsic and empirical nonidentifiability. With intrinsic nonidentifiability, it is the model design–that is, the number of manifest variables, number of response levels for each manifest variable, and number of latent classes–that results in nonidentification; all instances of the same such design are unidentified (with, the possible exception of certain degenerate data structures). With empirical nonidentifiability, a model may or may not be identified, depending on the particular values of the observed data. We consider intrinsic nonidentifiability first. The most common cause of intrins
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