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Revisiting the Current Issues IN Multilevel Structural Equation Modeling (MSEM): The Application of Sampling Weights and the Test of Measurement Invariance in MSEM
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Multilevel structural equation modeling (MSEM) has been widely used throughout the applied social and behavioral sciences. This dissertation revisited current issues in MSEM, including: the application of sampling weights and the test of measurement invariance. The impact of using sampling weights on testing multilevel mediation effects in large-scale, complex survey data was evaluated in Study 1. This study compared design-based, weighted design-based, model-based, and weighted model-based approaches in a noninformative sampling design. First, results showed that the model-based approaches produced unbiased indirect effect estimates and smaller standard errors. Second, ignoring sampling weights led to substantial bias in the design-based approaches. Finally, in the model-based approaches, weighted parameter estimates and standard errors differed moderately from unweighted results. The model-based approaches were thereby suggested for testing multilevel mediation effects in large-scale, complex survey data. In addition, researchers were always encouraged to apply sampling weights in analysis. The advantages of applying sampling weights in model-based approach were less obvious when cluster sizes were large, and particularly when ICC was small. The pursuit of evaluating various goodness-of-fit indices for testing measurement invariance has been a focus over the past decade. Study 2 expanded the investigation in MSEM. ICC and between-group difference accounted for a large proportion of variance in the model fit change. Among five model fit indices investigated in this study (i.e., X^2, CFI, RMSEA, SRMR, and TLI), ΔCFI and ΔSRMR in the level-specific approach had identical results to that of the standard approach. ΔSRMRB appeared to be the most sensitive to noninvariant factor loadings among all criteria. ΔSRMRB performed equally well in examining lack of intercept invariance when between-group difference was large. ΔRMSEA was less sensitive. Fractional changes in ΔCFI and ΔTLI indicated that neither was sensitive regardless of the level-specific approach or the standard approach. ΔX^2 was able to detect noninvariant intercepts when between-group difference was large, whereas only detected noninvariant factor loadings when both ICC and between-group difference were large. In conclusion, level-specific ΔSRMRB was suggested as a major index for examining between-level factor loading and intercept invariance in MSEM. ΔX^2 can be a supplementary index.
large-scale, complex survey data
multilevel mediation effects
test of measurement invariance
level-specific model fit indices
Zhu, Leina (2015). Revisiting the Current Issues IN Multilevel Structural Equation Modeling (MSEM): The Application of Sampling Weights and the Test of Measurement Invariance in MSEM. Doctoral dissertation, Texas A & M University. Available electronically from