Applications

In this section, the proposed models are applied to modeling the decision-making of pedestrians in shopping streets. The satisficing model is applied to the decision of terminating the shopping trip, or the Go-Home decision; the comparative model is applied to the decision of walking direction choice. Both models are compared with the conventional MNL models. The data were collected in East Nanjing Road (ENR), a popular shopping street in Shanghai, China.

The Go-Home Decision

Model specification

Two kinds of real time are used in the models as explanatory factors: relative time () and absolute time (tA), both in minutes. Relative time refers to the time elapsed since a pedestrian starts the shopping trip. It correlates with the progress of purchasing the planned items during the shopping trip, visiting schedules and how tired the pedestrian has become. Absolute time refers to the time difference between the current clock time and the 0:00 base. It correlates with available time budgets reflecting when the pedestrian must turn to other business.

Under the framework of HHM, a pedestrian decides to go home, if

Here is an N-element (more accurately, N is specific to each X) row vector of factor state values, is a column vector of factor threshold values and Ψ(ψ) is an element-wise identity function being 1 for the true relationships, being 0 for the false relationships. That means if the overall value of going-home is larger than the overall threshold, then the pedestrian will go home. Otherwise, he/she will keep shopping.

To estimate the distribution of A as depicted inEq. (5.16), the value of each decision heuristic is calculated. The estimations of and provide the preference structure, from which the stopping conditions for each heuristic can be inferred. To complete the calculation of mental effort, the effort for processing each factor can be estimated as separate effort parameters. However, the results showed that estimating factor-specific effort parameters does not bring significant improvement to the model compared to only one effort parameter for all factors. Furthermore, this effort parameter cannot be separated from the weight parameter in Eq. (5.23). Thus, is assumed to be negative to represent some kind of cost.

The last element required for calculating mental effort is the probability beliefs of factors being in certain states. Although people may have different belief distributions, which can be estimated for each factor state, the results showed that they add more complexity than goodness-of-fit to the model compared with uniform probability beliefs. The uniform probability means that the belief that a factor being in a

(5.31)

particular state is equally probable. With the probability beliefs, the risk perception of each heuristic can be calculated.

Given the estimated distribution of preference structures, the expected probability of a pedestrian deciding to go home is estimated using the latent-class structure described in Eq. (5.14). In total, the parameters that are simultaneously estimated include, factor state weights, WX, and factor thresholds, ΔX. The number of their elements are not set a priori, but estimated through model selection. The parameter for mental effort, β6, as discussed before, is assumed to be negative; the parameter for risk perception, βr, is assumed to be positive because pedestrians, ceteris paribus, are assumed to prefer diverse decision outcomes to betting on very few highly probable outcomes; the sign of the parameter for expected outcome, β°, is not assumed, but determined empirically.