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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.
Here we also present the results of comparisons with several, more restricted models, and with randomized networks.
The saturated model is fully parameterized (i.e. it has no constraints) and is used to evaluate the fit of nested, more restricted models.
Fitting nested (increasingly more restricted) models allows testing for significance of the GRPS, the environmental factor of interest, and their interaction effect.
A series of nested (increasingly more restricted) models was fitted to the raw data, in which parameters were fixed to zero to test for their significance.
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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 more restricted model gained degrees of freedom for stricter model testing and provided a more comprehensible view on the relative usefulness of the constructs.
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.
Hence the failure of the more restricted model may, or may not, be signaling the improperness of even a fitting Figure 1 style model.
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