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Examining how missing data affect approximate fit indices in structural equation modelling under different estimation methods Zhang, Xijuan


The full-information maximum likelihood (FIML) is a popular estimation method for missing data in structural equation modeling (SEM). However, it is not commonly known that approximate fit indices (AFIs) can be distorted, relative to their complete data counterparts, when FIML is used to handle missing data. In the first part of the dissertation work, we show that two most popular AFIs, the root mean square error of approximation (RMSEA) and the comparative fit index (CFI), often approach different population values under FIML estimation when missing data are present. By deriving the FIML fit function for incomplete data and showing that it is different from the usual maximum likelihood (ML) fit function for complete data, we provide a mathematical explanation for this phenomenon. We also present several analytic examples as well as the results of two large sample simulation studies to illustrate how AFIs change with missing data under FIML. In the second part of the dissertation work, we propose and examine an alternative approach for computing AFIs following the FIML estimation, which we refer to as the FIML-Corrected or FIML-C approach. We also examine another existing estimation method, the two-stage (TS) approach, for computing AFIs in the presence of missing data. For both FIML-C and TS approaches, we also propose a series of small sample corrections to improve the estimates of AFIs. In two simulation studies, we find that the FIML-C and TS approaches, when implemented with small sample corrections, can estimate the complete data population AFIs with little bias across a variety of conditions, although the FIML-C approach can fail in a small number of conditions with a high percentage of missing data and a high degree of model misspecification. In contrast, the FIML AFIs as currently computed often performed poorly. We recommend FIML-C and TS approaches for computing AFIs in SEM. Supplementary materials available at: http://hdl.handle.net/2429/77300

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