Parameter Influence in Structural Equation Modeling

In applications of structural equation modeling (SEM), investigators obtain and interpret parameter estimates that are computed so as to produce optimal model fit. The obtained parameter estimates are optimal in the sense that model fit would deteriorate to some degree if any of those estimates were changed. If a small change of a parameter estimate has large influence on model fit, such a parameter can be called highly influential, whereas if a substantial perturbation of a parameter estimate has negligible influence on model fit, that parameter can be called uninfluential. This is the idea of parameter influence. This article covers 2 approaches to quantifying parameter influence. One existing approach determines the direction vector of parameter perturbation causing maximum deterioration in model fit. In this article, we propose a new approach for quantifying the influence of individual parameters on model fit. In this new approach, the influence of individual parameters is quantified as the degree of perturbation required to produce a prespecified value of change in model fit. Using empirical examples, we illustrate how these 2 methods can be effectively employed, complementing each other and as a complement to conventional approaches to interpretation of parameter estimates obtained in empirical data analyses.