DOI link for Equivalent Models
Equivalent Models book
When a researcher formulates a model with estimated parameters, he or she must consider the possibility that there are equivalent but distinct models that could be formulated that would reproduce the same covariance matrix when estimated against a given sample covariance matrix. The existence of equivalent models when supported by empirical evidence other than simple fit to the same covariance matrix creates a problem for the researcher, who must then seek to eliminate these alternatives in some way in favor of his or her model. In this section we will discuss the meaning of equivalent models mathematically and will also consider techniques for generating them for consideration.