Nested Sequence of Models

In the Structural Equation Modeling method of analysis, a set of models M(1), M(2), ... M(k) form a nested sequence if model M(i) is a special case of M(i+1) for i=1 to k-1. Thus, each model in the sequence becomes increasingly more general, but includes all previous models as special cases. As an example, consider one factor, two factor, and three factor models for 10 variables. The two factor model includes the one factor model as a special case (simply let all the loadings on the second factor be 0). Similarly, the three factor model contains the two and one factor models as special cases.