Abstract
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.
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