Local influence in structural equation models

Local-influence diagnostics based on maximum likelihood (ML), generalized least squares (GLS), and unweighted least squares (ULS) fit functions are developed for structural equation models (SEMs). The influence of observations, components of observations, and variables is considered. The diagnostics are illustrated with an example data set, and comparisons are made with equivalent global measures of influence. The local influence of the data set on ML and GLS estimates is very similar, but it is much different from that of ULS. The local and global influence of observations is also very different. Although it is not possible to define a uniformly best measure of influence, the local-influence diagnostics developed here are more versatile than global-influence diagnostics in assessing an analysis with SEMs.