Detecting Misspecified Multilevel Structural Equation Models with Common Fit Indices: A Monte Carlo Study.

This study investigated the sensitivity of common fit indices (i.e., RMSEA, CFI, TLI, SRMR-W, and SRMR-B) for detecting misspecified multilevel SEMs. The design factors for the Monte Carlo study were numbers of groups in between-group models (100, 150, and 300), group size (10, 20, 30, and 60), intra-class correlation (low, medium, and high), and the types of model misspecification (Simple and Complex). The simulation results showed that CFI, TLI, and RMSEA could only identify the misspecification in the within-group model. Additionally, CFI, TLI, and RMSEA were more sensitive to misspecification in pattern coefficients while SRMR-W was more sensitive to misspecification in factor covariance. Moreover, TLI outperformed both CFI and RMSEA in terms of the hit rates of detecting the within-group misspecification in factor covariance. On the other hand, SRMR-B was the only fit index sensitive to misspecification in the between-group model and more sensitive to misspecification in factor covariance than misspecification in pattern coefficients. Finally, we found that the influence of ICC on the performance of targeted fit indices was trivial.

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

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., [Formula: see text] and [Formula: see text]) and (b) [Formula: see text] and [Formula: see text] 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 [Formula: see text] and [Formula: see text] were more influenced by ICC compared with [Formula: see text] and SRMRB . However, when traditional cutoff values (RMSEA≤ 0.06; CFI, TLI≥ 0.95; SRMR≤ 0.08) were applied, [Formula: see text] and [Formula: see text] were still able to detect misspecified between-level models even when ICC was as low as 0.091 (ICC1). On the other hand, both [Formula: see text] and [Formula: see text] were not recommended under low ICC conditions.

An analytical, variable resolution, complete description of static molecules and their intermolecular binding properties.

A fully analytical description of molecular shape, as defined by the shrink-wrap isodensity or solvent-excluded surfaces and local properties related to Coulomb, donor/acceptor, and polarizability (dispersion) interactions is described. The molecular surface and four local properties adequate for describing intermolecular interactions (the molecular electrostatic potential and the local ionization energy, electron affinity, and polarizability) are fitted to spherical-harmonic expansions, which provide a compact and information-rich description of the properties of the static molecule. The resolution of the description can be varied from isotropic to near atomistic detail by adjusting the order of the individual spherical-harmonic expansions. Examples are given to illustrate the effect of truncating the different spherical-harmonic approximations.