Selection of Computer Software for Modelling

Several software packages can be used to estimate traffic accident duration in HBDMs, such as R, SPSS, STATA, SAS, LIMDEP, SUDAAN, MLwiN, and S-Plus (Box- Steffensmeier and Jones, 2004). In this research, the software package Stata 10 was used to estimate HBDMs because of the availability of this software in the school. This section intends to illustrate some of the main commands used in Stata for the purpose of data declaration, data preparation, data examination, and the application of a fully parametric AFT approach.

In Stata, the data declaration is conducted using ‘stset’ command. When all accidents faced the event of interest by the end of the interval time, the command that will be used is ‘stset variable’. Here the ‘variable’ refers to the dependent variable of the model for each interval time, such as reporting time, response time and clearance time.

After running ‘stset’ command, four variables will appear in the dataset, including _t0,

_t, _d, and _st. The variables _t0 and _t record the start time and end time for each

accident in minutes. Each accident interval time starts at _t0 and concludes at _t. The variable _d denotes the outcome at the end of each interval time, where 1 represents the interval time that ends in failure (meet the event of interest), while 0 represents when it does not end. The variable _st reports whether an accident is relevant to the analysis. For each accident, the variable contains 1 if the accident is to be used and 0 if it is to be

69 ignored. Finally, all variables _t0, _t, _d, and _st were used to run the analysis while ignoring initial variables such as time and event (Acock, 2006).

In the data preparation step, it is necessary to apply several commands prior to commencing data analysis. The first command is ‘stsum’. The purpose of this command is to give a summary of the survival time. In the output, several types of information could be extracted, including time at risk, incident rate, number of subjects, and the 25th, 50th, and 75th percentiles of survival time (see Table 4-3).

Table 4-3 Summary of the survival time Time at risk Incident Rate Number of Subjects […………Survival Time……….] 25% 50% 75% Total 1596 0.2274436 363 3 4 6

The second command is ‘stdes’. This command describes the survival time that has been set and detects whether any gap exists (Table 4-4). Thus, the most important result of the outcome is if subjects with gap are shown.

Table 4-4 Description of the survival time

Category total mean min median Max

no. of subjects 363

no. of records 363 1 1 1 1

(first) entry time 0 0 0 0

(final) exit time 4.396694 2 4 7

subjects with gap 0 time on gap, if gap 0

time at risk 1596 4.396694 2 4 7

Failures 363 1 1 1 1

It can be seen from the output that no subjects with gap were found. This indicates that the survival time of each accident was recorded from the beginning of each interval time until facing the event of interest. So, the same result should appear in the outcome, because all accidents were followed from the start point and end point of each interval time. However, if the results show that there are some subjects with gap, then this indicates an error in data entry, and this should be corrected before conducting the analysis.

The last command of data examination is ‘stvary’. This command reports whether the explanatory variables are changing over time and displays whether there are any missing values of any independent variable (Table 4-5).

70 Table 4-5 Variation of the explanatory variables

Variable Constant Varying Never

Missing Always Missing Sometimes Missing Road condition 363 0 363 0 0 Severity 363 0 363 0 0 Visibility 363 0 363 0 0

Out of the three independent variables used in this example, it is clear that no accident has a variable that changes over time, and no accident in the dataset has missing values for these variables. These results indicate that complete data of these variables were collected and entered for each accident. Since the collected independent variables in this study are constant over time, the varying column should be 0 in all independent variables. Also, because all values of independent variables were collected completely from the accident report, none of the output should show ‘always missing’. However, if any variable is found to be missing, it is necessary to check for the missing value of the dataset and edit it before carrying out the analysis (Acock, 2006).

Using a fully parametric AFT approach means that there are many alternative distributions available to assume the shape of the distribution of the times about the mean, such as Exponential, Weibull, Log-logistic, and Log-normal. In Stata, the selection of these distributions can be done by means of the ‘streg’ command followed by any distribution. For example, if the distribution assumed is to be Weibull, the command is ‘streg var1, dist(Weibull) nohr’, where ‘var1’ denotes the explanatory variable, and ‘nohr’ denotes the use of coefficients instead of hazard ratios. Furthermore, since most of these distributions have a scale parameter and shape parameter, the ‘streg’ command is used to calculate these parameters’ values. All of these values are computed using maximum likelihood estimation, which is the main role of the ‘streg’ command. Finally , the command “ predict t_mean, time mean” is used to predict the mean duration with consideration of the significant variables at each interval time (StataCorp, 2007). The results will be used to develop a decision tree.

4.8 Summary

This chapter begins by describing the initial and revised study areas. Subsequently, it presents the methodology of modelling each interval time of the total traffic accident duration, starting by collecting the required data from FTSS and ASCIS databases. In

71 addition, the approaches to selecting the best-fit distribution and result interpretation are illustrated. Finally, the methodological approach in developing an accident duration prediction tool using the decision tree is presented. Further details of data description and the study area are discussed in Chapter 5.

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