Model construction
In general, since there is no clear criterion for configuring the optimal DLNM model8, various approaches can be taken to construct this. Many studies use Akaike’s information criterion to select the model with the best performance.9Therefore, we also considered a quasi Akaike information criterion (QAIC) and a partial autocorrelation function (PACF) to choose the optimal construction for the DLNM model. The quasi Akaike information criterion (QAIC)10, the quasi-likelihood adjustments of Akaike’s information criterion (AIC)11, provides important information on the explanatory power of quasi Poisson models that is used for overdispersed count data. The partial autocorrelation function (PACF) evaluates the level of partial autocorrelation in model residuals. We compared the mean of the absolute values of PACF (mPACF) for the first 100 days of the models.
Table 1 shows the values of QAIC and mPACF for various models we compared. Each model was selected by forward selection using a greedy approach. The M5 model was selected because its QAIC was the lowest (3289.498) while its PACF value was the second lowest (0.02849), which was greater than the lowest by only 0.00002.