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Akaike's Information Criterion is equal to the deviance of the maximum likelihood model, offset by a penalty for complexity equal to twice the number of parameters in the model.
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For the Dewey's total deviance score, the maximum is 57.
Consequently, model selection can proceed by minimizing the deviance,, where is the maximum likelihood estimate (MLE) of θ.
Table 1 shows the change in deviance, a measure of goodness-of-fit, in the sequential building of the maximum likelihood APC models.
The maximum likelihood estimates of b and tm were obtained by minimizing the binomial deviance of the model from the observed data.
The overdispersion parameter (c-hat) was calculated as the ratio between the mean deviance of simulated models and the deviance of the observed model [18].
Null deviance of the model was 93.19 (df = 68) and residual deviance was 76.34 (df = 64).
We then computed the deviance of the fitted model and summed the deviances for that given threshold over all cities.
The deviance of the natural spline model fitted to the cohort studies was smaller than the deviance of the corresponding linear model [deviance = 8.43 and 11.97 respectively; chi square test (1 df), p = 0.06].
Table 2 shows the deviances of the different models used.
As shown in Figure 2A, the typical profile of the R-squared deviance presents a maximum that allows selecting the best period.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com