Thus, we take preparation time and travel time as effective factors to be examined for later intervals. Table 2 shows the candidate variables used in this study. 4.2. Distribution Choice and Model Development To choose a spline function, the number and position of the knots, that is, the number of degrees of freedom (d.f.), must be decided. The optimal (optimized) Carfilzomib PR-171 knot position does not appear to be critical for a good fit and may even be undesirable, in that the fitted curve may follow the small-scale features of the data too closely [37]. A previous study [36] suggested

that knot positions are based on the empirical centiles of the distribution of log time. In terms of the number of knots, one study suggested [37] that a two- or three-d.f. spline model would be a reasonable initial or default choice for smaller datasets, whereas five or six d.f. would be necessary with

larger datasets. As mentioned above, previous studies have found that several distributions can be used for the hazard-based model to analyze or predict traffic incident duration time. Thus, in the present study, except for the flexible parametric model based on restricted cubic splines, four other commonly used distributions are also used as candidates in parametric hazard-based models, namely, Weibull, log-normal, log-logistic, and generalized gamma. Informally, the AIC, Bayesian Information Criterions (BIC), or others [35] can be used as criteria for choosing the “best-fit” model. This study used BIC, which is expressed as follows: BIC=−2l+log⁡nd, (9) where l is the maximized value of the log-likelihood for a given model, n is the number of the observations, and d is the number of free parameters to be estimated. 4.3. Selected Model In this study, 17 candidate different models with different distributions were used to fit the data. The best-fit model was chosen according to the BIC value. For

each incident phase, these 17 models include AFT model with Weibull, log-logistic, generalized gamma with or without frailty, and flexible parametric model with 1 to 10 degrees of freedom. Table 3 lists the BIC value of each model. The best-fit model is used to analyze the effective factors of each incident and predict Batimastat the time of each incident phase. Table 3 Different BIC values for each model. As shown in Table 3, the AFT hazard-based model with generalized gamma distribution is the best-fit model for preparation time and total time, the flexible parameter model with six knots (five degrees of freedom) is the best-fit model for travel time, and the log-logistic model is the best-fit model for clearance time. 4.4. Effective Factor Analysis The best-fit model can be used to analyze the effect of effective factors for each incident phase. Table 4 shows the regression coefficients of different factors and the percentage change for each incident phase. Table 4 Regression coefficients of different factors and the percent change for each incident. 4.4.1.