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For men, the transformed model significantly improved model fit relative to the untransformed model (Deviance Difference = 231.79, p-value < 0.001), the linear-quadratic model (Deviance Difference = 105.62, p-value < 0.001) and the categorical model (Deviance Difference = 81.63, p-value < 0.001).
The proportion of explained deviance (Deviance difference) in each model is shown.
The significance of associations was measured using the deviance difference as an approximate chi-square statistic.
After finding the best fit for the main model, the age-smoking history (Deviance Difference = 15.88, p-value < 0.001) and BMI-age interactions (Deviance Difference = 35.31, p-value < 0.001) were both identified as statistically significant in the female sample.
After including the age-BMI interactions, the age-smoking history interaction remained significant (Deviance Difference = 15.44, p-value < 0.001).
A deviance difference test showed a statistically significant improvement in model fit compared to other BMI functions.
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We will use deviance differences to quantify the additional lack-of-fit when a model is fitted on one data set and predictions are made on another data set [ 53].
Nested models are compared through deviance statistics (difference in −2 log likelihood) over the difference in degrees of freedom using an ordinary chi-square distribution [ 8].
Differences in deviance determined whether the different specifications of the time course were significant or not.
To test for the significance of effects between nested models, we compared the difference in deviance between these different models using the F test.
To test for significance of effects between the full three-factor model and nested models (i.e. two-factor age-period and age-cohort models), we compared the difference in deviance between these different models using the F test (Mccullagh and Nelder, 1983).
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