We surveyed 450 respondents in central business districts, outlets, transportation hubs, office buildings, and large enterprises in Tangshan. Out of the total of 424 questionnaires received, 419 are qualified. The calculation is executed by SPSS Estrogen Receptor Pathway software. 4.2. Utility Function The MNL model is used to model the individual travel mode choice. It is assumed that all the factors are independent from each other and obey the Gumbel distribution with zero mean. Equation (4) is the utility function: Vin=θiXin=θi0+∑k=1KθikXink, i∈An.
(4) In (5), Pin is the probability of traveler n selecting travel mode i: Pin=expVin∑j∈AnexpVjn=expθiXin∑j∈AnexpθXjn, i∈An, (5) where Vin is the utility function when traveler n chooses travel mode i; Xin = [Xin0, Xin1,…, Xink,…, XinK] is an eigenvector of traveler n choosing travel mode i; the component Xink is the value of variable k when traveler n chooses mode i, Xin0 = 1; θi = [θi0, θi1,…, θik,…, θiK] is the vector
of utility coefficients; and θik is the impact coefficient of variable k on travel mode i. 4.3. Results and Model Validation SPSS17.0 is used to process the data. The results of the MNL model are shown in Table 2. Table 2 The calculated parameters of the MNL model. The calculated parameters in Table 2 and the variable values in Table 1 are put into (4) and (5) to calculate the utility value and choice probability. Therefore, it is possible to forecast the sample individuals’ choice. The observed and forecasted choices are presented in Table 3. Table 3 Comparison of predicted and observed selection. There are different tests for model validation, the main ones of which are the goodness-of-fit test, F-test, and t-test. These three methods are fitted to test the linear model. Because the MNL model is a nonlinear
exponential model and the unbiased estimate of the error variance cannot be obtained from the estimated residuals, the t-test or F-test cannot be used here to test the significance either for the individual or for the population . Furthermore, the model residuals do not necessarily sum to zero and ESS and RSS do not necessarily add up to TSS; therefore, R2 = ESS/TSS may not be a meaningful descriptive statistic for this model. Consequently, an alternative to pseudo R-square is proposed to estimate the goodness GSK-3 of fit. It can be seen as a rough approximation of model prediction accuracy . Three pseudo R-squares calculated by SPSS are shown in Table 4. Generally, the pseudo R-squared value falls in [0, 1]. When the independent variable is completely unrelated to the dependent variable, the pseudo R-squared value will be close to zero; otherwise, it will be close to 1, which indicates that the model perfectly predicts the objective. The results listed in Table 4 show that the model is acceptable. Table 4 Pseudo R-square. 5. Analysis and Implication 5.1.