The Impact of Intraclass Correlation on the Effectiveness of Level-Specific Fit Indices in Multilevel Structural Equation Modeling : A Monte Carlo Study

Abstract

Several researchers have recommended that level-specific fit indices should be applied to detect the lack of model fit at any level in multilevel structural equation models. Although we concur with their view, we note that these studies did not sufficiently consider the impact of intraclass correlation (ICC) on the performance of level-specific fit indices. Our study proposed to fill this gap in the methodological literature. A Monte Carlo study was conducted to investigate the performance of (a) level-specific fit indices derived by a partially saturated model method (e.g., $\mathrm{CF}{I}_{\mathrm{PS}\_B}$ and $\mathrm{CF}{I}_{\mathrm{PS}\_W}$ ) and (b) $\mathrm{SRM}{R}_W$ and $\mathrm{SRM}{R}_B$ in terms of their performance in multilevel structural equation models across varying ICCs. The design factors included intraclass correlation (ICC: ICC1 = 0.091 to ICC6 = 0.500), numbers of groups in between-level models (NG: 50, 100, 200, and 1,000), group size (GS: 30, 50, and 100), and type of misspecification (no misspecification, between-level misspecification, and within-level misspecification). Our simulation findings raise a concern regarding the performance of between-level-specific partial saturated fit indices in low ICC conditions: the performances of both $\mathrm{TL}{I}_{\mathrm{PS}\_B}$ and $\mathrm{RMSE}{A}_{\mathrm{PS}\_B}$ were more influenced by ICC compared with $\mathrm{CF}{I}_{\mathrm{PS}\_B}$ and SRMR _B . However, when traditional cutoff values ( RMSEA≤ 0.06; CFI, TLI≥ 0.95; SRMR≤ 0.08) were applied, $\mathrm{CF}{I}_{\mathrm{PS}\_B}$ and $\mathrm{TL}{I}_{\mathrm{PS}\_B}$ were still able to detect misspecified between-level models even when ICC was as low as 0.091 (ICC1). On the other hand, both $\mathrm{RMSE}{A}_{\mathrm{PS}\_B}$ and $\mathrm{SRM}{R}_B$ were not recommended under low ICC conditions.