How to evaluate local fit (residuals) in large structural equation models

Abstract

Consistent with reporting standards for structural equation modelling (SEM), model fit should be evaluated at two different levels, global and local. Global fit concerns the overall or average correspondence between the entire data matrix and the model, given the parameter estimates for the model. Local fit is evaluated at the level of the residuals, or differences between observed and predicted associations for every pair of measured variables in the model. It can happen that models with apparently satisfactory global fit can nevertheless have problematic local fit. This may be especially true for relatively large models with many variables, where serious misspecification is indicated by some larger residuals, but their contribution to global fit is diluted when averaged together with all the other smaller residuals. It can be challenging to evaluate local fit in large models with dozens or even hundreds of variables and corresponding residuals. Thus, the main goal of this tutorial is to offer suggestions about how to efficiently evaluate and describe local fit for large structural equation models. An empirical example is described where all data, syntax and output files are freely available to readers.