| Abstract: | When a covariance structure model is misspecified, parameter estimates will be affected. It is important to know which estimates are systematically affected and which are not. The approach of analyzing the path is both intuitive and informative for such a purpose. Different from path analysis, analyzing the path uses path tracing and elementary numerical analysis to identify affected parameters when a 1-way or 2-way arrow in a path diagram is omitted. It not only characterizes how a misspecification affects model parameters but also facilitates a good understanding of the relation among different parts of the model. This article introduces and studies this technique and, for commonly used models, provides detailed analysis to identify the directions of change for various model parameters. Examples based on real data show that the technique of analyzing the path can reliably predict the direction of change in parameter estimates even when the true model is unknown. Conditions that interfere with the results are also discussed and advice is provided for its proper application. |
