5 4 Significance of Condition Attributes In rough sets models, t

5.4. Significance of Condition Attributes In rough sets models, the significance of condition attributes is measured by their presence of the derived rules [29]. When a condition attribute shows more frequently among rules, it is more frequently used to describe travel modes and hence more significant to distinguish mode choices. selleck Presence of a condition attribute is represented with presence percentage which is calculated by summing its presence in each rule weighted with cases of the associated rule divided by total cases. Moreover, since condition attributes with more categories tend to distinguish

between travel mode choices more effectively, comparisons are made on those with the same number of categories, shown in Figure 2. Figure 2 Presence percentage of condition attributes. There are total 12 condition attributes in this study selected to model mode choices. Figure 2 indicates that all variables make contributions to model estimation. Gender, distance, household annual income, and occupation are those with higher presence percentage among all condition attributes with two, three, six, and seven categories. 6. Comparisons with a Multinomial Logit (MNL) Model The MNL model gives the choice probabilities of each alternative as a function of the systematic portion of the utility of all the alternatives. The general expression of the probability of choosing an alternative “i” from a set of J alternatives is as follows:

Pr⁡⁡i=exp⁡⁡Vi∑j=1Jexp⁡⁡Vj, (6) where Pr (i) is the probability of the decision maker choosing alternative i and Vj is the systematic component of the utility of alternative j. We use the same training set to estimate the MNL model. The car mode is arbitrarily used as the base alternative. From the estimation results, the most significant variables to influence a traveler’s mode choice decision include car ownership, license ownership,

gender, distance, and occupation. These variables approximately match the important variables induced by the rough sets models. The confusion matrix induced by the MNL model using the same testing set is shown in Table 7. Table 7 Confusion matrix generated by MNL model. An overall performance comparison was conducted based on the prediction results of the two models using the testing set. Figure 3 shows the prediction accuracy and coverage of the models by each mode, in which the actual numbers of observations for each mode are also labeled. Figure 3 Prediction performance comparisons between rough sets model and MNL model. The two models show Cilengitide similar prediction performances. Neither of them gives a perfect prediction rate for each mode on accuracy and coverage, especially for the insufficient observations in the dataset. On the accuracy of prediction, the rough sets model shows a better performance over the MNL model in the prediction of the bicycle, SOV, and transit modes. And the overall performance of the rough sets model (77.3%) is also better than the MNL model (75.2%).

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