ABSTRACT
Structural equation modeling (SEM) is an important method for assessing multivariate data. Under certain mild regularity conditions, the basic asymptotic results for statistical inference of the method developed. Confidence regions of limits in SEM models can constructed based on the asymptotic normality of the generalized least squares (GLS) or the most likelihood (ML) estimator. However, this kind of confidence region is only a linear approximation of the general one. This chapter introduces a geometric approach for constructing more general and exact confidence regions that improves the linear approximation in the context of GLS estimation. The chapter using a geometric approach in GLS estimation, some better methods for constructing confidence regions derived. It shows that the improvement over the linear approximation is significant for nonlinear models and nonlinear constraints. Analogous theory in the context of ML analysis with the normal assumption or the asymptotically distribution-free analysis with arbitrary distribution can derived using the proposed geometric approach.
