The Effects of Model Parsimony and Sampling Error on the Fit of Structural Equation Models

The fit between a structural equation model and a data set is operationalized as the value of goodness-of-fit indices. The discrepancy between the estimated value and the value indicating perfect fit has three sources: misspecification, error arising from theoretical parsimony in the description of the model (parsimony error), and sampling error. Misspecification, which represents a disparity between “realworld” relationships and relationships in the model, is the most important source of error for researchers. It cannot be accurately assessed, however, unless parsimony error and sampling error are taken into account. Parsimony error occurs in measurement models when secondary relationships are excluded. Secondary relationships are defined here as secondary factor loadings and error term correlations that have small values, no theoretical bases, and no substantive meaning. A simulation was conducted to examine the effects of parsimony error on perfect measurement models and to establish appropriate criteria for model fit when parsimony error is present.