There is a strong evidence of over-dispersion for all models, which is indicated by the significant estimated
dispersion value in the Negative Binomial regression as shown in Table 1: 0.811, 0.667 for vehicle disabilities
and crashes in environmental effect analysis, and 0.673, 0.770 for two types of incidents in traffic effect analysis
respectively.
Since the number of observations for each day is 12 and for each segment is also 12, the correlation structure is
a symmetric matrix and its dimension is 12 with one in each diagonal position. The autoregression structure
assumes that the correlations between the multiple observations for a certain day will decrease as the time-gap
increase and the correlation is multiplied by the parameter for one more hour gap. In this case, the correlation
estimated is 0.223 in environmental analysis models for vehicle disabilities. That is to say, the autoregression
structure has correlation of 0.223 for each successive two hours and correlation 0.050 for time periods with onehour
gap. This conclusion in turn has proved the rationality of choosing weather condition in previous two hours
in Pre. Snow and Pre. Rain variables, since the correlation could be ignored for hours with two-hour gap or
more. The correlation parameter is 0.240 for crashes, and a similar conclusion could be drawn. In traffic effect
analysis models, the correlation parameter values are 0.705, 0.770 for vehicle disabilities and crashes, much
higher than those in environmental analysis. This may be because the correlation of traffic condition among
different hours is more closely. As a result, the effect of traffic condition on incident occurrence could last 4
hours or more (the correlation of time periods with three-hour gap is about 0.25).
Moreover, it is found that, both in environmental and traffic effects assessment, the estimated correlation
parameters of vehicle disabilities are lower than those of crashes. This indicates the occurrence of crashes is more
correlated in a temporal scale.