Using Level-Specific Fit Evaluation of Model Fit to Assess Multilevel Structural Equation Model

While a level-specific approach has been proposed for the valid evaluation of multilevel structural equation modeling (MSEM), the traditional simultaneous approach remains predominant among researchers. In fact, research on level-specific approaches is limited, and some studies have focused on multilevel confirmatory factor analysis models. This study conducted a Monte Carlo study to explore the performance of a LS approach for MSEM with a direct path between variables under five design factors: intraclass correlation (ICC), the number of groups (NG), group size (GS), the size of path coefficient (PCS), and misspecification type (MT). The results showed that the LS approach performed better than the SI approach even in MSEM at between-group level. This study identified three key findings. First, the performance of RMSEA was found to improve with an increase of ICC or GS. Second, the performance of LS fit indices (RMSEA, CFI, and TLI) was more promising for detecting the misspecified between-level model with a decrease of PCS. Third, the effect of PCS on CFI or TLI was strong when ICC was small. The study concludes with a summary and implications of the results.