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Significance among factor levels (e.g. among the 4 different group sizes) was determined by model simplification, where we evaluated whether combining >1 factor level into a single level led to a significant increase in deviance of the model, using F-tests [42].
The difference in deviance of two nested models has a χ2 distribution with degrees of freedom equal to the number of additional parameters in the larger model.
Significant differences in rates of injuries due to groups, levels, positions and injury type was assessed by comparing the fit (via changes in deviance) of a series of models.
The difference in deviance of two models can be used as a test statistic with a χ distribution, with the number of different parameters as the degrees of freedom (Hayes 2006).
Similar to analysis of variance in ordinary linear regression, we examined the overall significance of location using the difference in deviance of the complete model (equation 1) and the reduced model omitting the smoothing term.
The assumption of proportional odds between treatments and centers was tested using the ML method by comparing the change in deviance of the various models (Table 4) to the chi-squared χ1- α 2 (2 df) which equals 5.99.
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All nested models were compared with a simpler random-effects model using the change in deviance on removal of a term from the model, as well as the Akaike Information Criterion [ 43], to test for each model's ability to describe the data.
The difference in deviances of the two models was compared with a χ-distribution with five degrees of freedom.
Models were compared using difference in deviances of the nested models (likelihood ratio tests which approximately follows a Chi-square distribution) with the appropriate degrees of freedom [ 9, 12, 13].
Table 1 shows the change in deviance, a measure of goodness-of-fit, in the sequential building of the maximum likelihood APC models.
Table 3-wrap> shows the change in deviance, or goodness-of-fit, in the sequential building of the models.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com