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If more than one mixed-effect model showed significant improvement over the standard fixed-effect model, the optimal mixed-effect model was chosen by the likelihood ratio test if models were nested or by the corrected Akaike's information criterion (AICc), otherwise.

All these models were nested.

The likelihood ratio test (LRT) was used to determine model fit when the models were nested in parameters.

If two models were nested models, the more parsimonious model was selected if the χ difference was not significant based on AIC.

Because the two models were nested, we used -2 log likelihood, known as the "change in the deviance", which has a chi-square distribution to test whether the difference between the two models was statistically significant (Table 4).

Models were nested and an improvement in the objective function was referred to the Chi-squared distribution to assess significance e.g. an objective function change (OBJ) of 3.84 is significant at α = 0.05.

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Sequential modelling ensures that the models are nested and can be compared using standard statistical test.> -wrap-foot> NotEstimatedated standard errors in parenthesis.

The subcells' constitutive models are nested through a numerical stress-update algorithm.

The independence (null) models are nested inside the undirected joint and conditional models and contain one less parameter.

This likelihood ratio test requires that the models are nested, i.e., that one model can be defined in terms of the second.

These models are nested, and the differences between the models provides a test of the hypotheses.

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