Finally, the relative fit of the non-nested SEM models (M2, M3, and M4) was compared using the AIC and BIC model-fit indices.
In addition, relative fit measures (CFI, TLI > .95) and absolute fit measures (RMSEA < .08, SRMR < .10) suggest that most estimated models reproduce the data well.
Meanwhile, CFI, RMSEA, and SRMR are useful in detecting model misspecification, and relative fit indices (e.g., AIC and BIC) are mainly used for model selection (Curran et al. 1996; Fan and Sivo 2005; Ryu 2011).
According to Cheung & Rensvold (2002), other important indexes to compare the target model with the null model are relative fit index (RFI), comparative fit index (CFI), normal fit index (NFI), and incremental fit index (IFI).
The Weibull model provided the best relative fit (ln L = − 49.954), whereas the gamma had an intermediate fit (ln L = − 49.957) and the lognormal had relatively poor fit (ln L = − 50.384) to the Kachchh catalog.
However, when considering the relative fit (i.e., change in a fit index from configural to metric or metric to scalar) via changes in CFI and RMSEA, the authors found that the change in RMSEA associated with the metric invariance hypothesis to be increased or larger than a typically accepted difference of.010.
The relative fit of regression models was estimated with Nagelkerke's adjusted R2.
Additionally, a likelihood ratio test was used to compare the relative fit of the Poisson model to the negative binomial model.
Statistical significance of the effect of each variable was calculated through Wald's test, and the relative fit of regression models (variance explained) was estimated with Nagelkerke's adjusted R2.
Independent risk factors were identified in the multivariate analysis using a forward selection procedure, using univariate p<0.12 as inclusion criteria and the likelihood ratio test to assess the relative fit of the different models.
The relative fit of codon substitution models was evaluated with likelihood ratio tests (LRT), which were assumed to be χ2 distributed with degrees of freedom equal to the difference in number of parameters between models.
