A multiple imputation score test for model modification in structural equation models

Structural equation modeling (SEM) applications routinely employ a trilogy of significance tests that includes the likelihood ratio test, Wald test, and score test or modification index. Researchers use these tests to assess global model fit, evaluate whether individual estimates differ from zero, and identify potential sources of local misfit, respectively. This full cadre of significance testing options is not yet available for multiply imputed data sets, as methodologists have yet to develop a general score test for this context. Thus, the goal of this article is to outline a new score test for multiply imputed data. Consistent with its complete-data counterpart, this imputation-based score test provides an estimate of the familiar expected parameter change statistic. The new procedure is available in the R package semTools and naturally suited for identifying local misfit in SEM applications (i.e., a model modification index). The article uses a simulation study to assess the performance (Type I error rate, power) of the proposed score test relative to the score test produced by full information maximum likelihood (FIML) estimation. Due to the two-stage nature of multiple imputation, the score test exhibited slightly lower power than the corresponding FIML statistic in some situations but was generally well calibrated. (PsycInfo Database Record (c) 2020 APA, all rights reserved).