Assessing the fit of structural equation models with multiply imputed data.

Abstract

Multiple imputation has enjoyed widespread use in social science applications, yet the application of imputation-based inference to structural equation modeling has received virtually no attention in the literature. Thus, this study has 2 overarching goals: evaluate the application of Meng and Rubin's (1992) pooling procedure for likelihood ratio statistic to the SEM test of model fit, and explore the possibility of using this test statistic to define imputation-based versions of common fit indices such as the TLI, CFI, and RMSEA. Computer simulation results suggested that, when applied to a correctly specified model, the pooled likelihood ratio statistic performed well as a global test of model fit and was closely calibrated to the corresponding full information maximum likelihood (FIML) test statistic. However, when applied to misspecified models with high rates of missingness (30%-40%), the imputation-based test statistic generally exhibited lower power than that of FIML. Using the pooled test statistic to construct imputation-based versions of the TLI, CFI, and RMSEA worked well and produced indices that were well-calibrated with those of full information maximum likelihood estimation. This article gives Mplus and R code to implement the pooled test statistic, and it offers a number of recommendations for future research. (PsycINFO Database Record

The relationship between moral injury appraisals, trauma exposure, and mental health in refugees

“…For each variable, missing data were less than 10% of overall responses, except for the trauma variable (11.3% missing). Consistent with contemporary guidelines, we generated 20 data sets (Bodner, 2008;Graham, Olchowski, & Gilreath, 2007), a number that has also been found to be reliable in estimating model fit in structural equation modeling with even high rates (30-40%) of missing data (Enders & Mansolf, 2018). Consistent with contemporary guidelines, we generated 20 data sets (Bodner, 2008;Graham, Olchowski, & Gilreath, 2007), a number that has also been found to be reliable in estimating model fit in structural equation modeling with even high rates (30-40%) of missing data (Enders & Mansolf, 2018).…”

“…Therefore, multiple imputations (Rubin, 1996) of the trauma variable were used to ensure that power to detect study effects was not reduced due to missing data. Consistent with contemporary guidelines, we generated 20 data sets (Bodner, 2008;Graham, Olchowski, & Gilreath, 2007), a number that has also been found to be reliable in estimating model fit in structural equation modeling with even high rates (30-40%) of missing data (Enders & Mansolf, 2018). Therefore, a robust maximum likelihood estimator of covariance matrices was used during subsequent analyses, resulting in robust standard errors and chi-squared test statistics.…”

Evaluating methods for handling missing ordinal data in structural equation modeling

“…For example, the Type I error rates might be inflated when the threshold values, missing data mechanisms, or missing data proportions are substantially different across items (Savalei & Falk, 2014). It is important to note that valid model fit test statistics cannot be obtained from the multiple imputation methods investigated in this study, because there is no good way so far to pool the rescaled test statistics across imputations for cat-DWLS or RML (Enders & Mansolf, 2018). For this reason, we did not report fit indices in the Results section.…”

Alternative Multiple Imputation Inference for Categorical Structural Equation Modeling

“…Three methods of dealing with missing data in SEM are featured prominently in the literature: full-information maximum likelihood (FIML; Anderson, 1957;Arbuckle, 1996), multiple imputation (Schafer, 1997), and a two-stage procedure based on the Expectation-Maximization algorithm (EM2S; Allison, 2001;Cai & Lee, 2009;Enders & Peugh, 2004;Yuan & Bentler, 2000). While multiple imputation (Rubin, 1987) is one of the most widely used techniques for handling missing data, research on its use in the SEM context is surprisingly limited (e.g., Enders & Mansolf, 2018;Lee & Cai, 2012).…”

“…Second, the commonly used fit statistics such as root mean square error of approximation (RMSEA; Browne & Cudeck, 1993) or Tucker-Lewis index (TLI; Tucker & Lewis, 1973) are not readily available in the standard multiple imputation approach. In a recent effort to resolve this issue, Enders and Mansolf (2018) defined commonly used SEM fit indices from Meng and Rubin (1992)'s pooling procedure for likelihood ratio statistics. We believe an even simpler procedure exists in our approach.…”