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Additional file 1: Tables SA, SB demonstrate measurement invariance (MI) for almost all constructs, as indicated by the non-significant reduction of the model fit index CFI (<.020) when testing a more restricted model (strong MI) against the less restricted one (weak MI) (Chen 2007; Cheung and Rensvold 2002).
The χ value is obtained by subtracting the −2 log likelihood (−2LL) of the more restricted model from the −2LL of the less restricted model.
The difference in the χ2 values between models two and three was statistically significant: the more restricted model three achieved a statistically significant worse fit.
Interestingly, using this more restricted model, five factors showed an interaction with the SNCA promoter as well as with the ncECRs.
Hence the failure of the more restricted model may, or may not, be signaling the improperness of even a fitting Figure 1 style model.
The more restricted model gained degrees of freedom for stricter model testing and provided a more comprehensible view on the relative usefulness of the constructs.
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Further security hardships in more restricted models (i.e. in which stronger corruptions are allowed) are also discussed.
For modeling interactions, the MFG parameterization of Sinsheimer et al. [2003] or the more restricted models used by Palmer et al. [2006], Parimi et al. [2008] and Li et al. [2009] would seem most biologically intuitive, although we note that all of these models are essentially captured via our default (statistically based) EMIM parameterization.
In order to test whether the estimated ω is significantly greater than 1, model M8 was compared with a more restricted null model (M8a).
To take account for the elevated type I error rates, the original model M8 was compared with a more restricted null model (M8a), where the extra site class was constrained to have ω = 1.
If the model also showed an acceptable fit, the more restricted invariance model was accepted.
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