Regression technique and goodness of fit

The GLM approach assuming a negative binomial error stracture was used, and modeling was done in the R statistical software [RCO 13], Several statistical measures were used to assess the goodness of fit of the models. 

The Pearson of the model must be less than a critical value of the distribution value, that is based on the model s degrees of freedom (DF) and a level of significance of a. 

The Scaled Deviance (SD) is defined as the likelihood ratio test statistic measuring twice the difference between the log likelihoods of the studied model and the full or saturated model. The full model has as maity parameters as there are observations so that the model fits the data perfectly. Therefore, the full model, which possesses the maximum log likelihood achievable under the given data, provides a baseline for assessing the goodness-of-fit of an intermediate model with p parameters [MCC 89], 

The Akaike s Information Criterion (AIC) can be used for model selection and is applicable to compare models. The AIC value is calculated according to equation [6.2]  

Cumulative residual analysis was also used to evaluate the model form. The residual is equal to the difference between the observed and estimated values of the dependent variable. Cumulative residuals (CURE) were plotted versus AADT for each homogeneous section. The closer the curve stays to the x-axis, the more appropriate the model form is, and a ciuve that stays within two standard deviations is considered to be satisfactory [HAU 97]. 

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