How Many Customers Would Be Brought Back from Suburban Shopping Malls to the City Center by Redeveloping the City Center Station Building, JR Oita City, Japan? A Multivariate Poisson Model with Competitive Destinations

Oita City is located in the north east part of the Kyushu island, the southmost island among four islands composing Japan. The Oita city is the capitol city for the Oita prefecture with population 475,614 as of 2020 according to census 2020. The Oita city is the largest populated city in the Oita prefecture whose population is 1,123,852 persons accoring to census 2020.

JR Oita station is a railroad station on the NippoHonsen, a railroad line JR operates that stretches from Kokura station to Kagoshima station or extends from the northmost part to the south end of Kyushu island along the east coastline of Kyushu island with a total length of 462.6 km. The location of JR Oita station is 132.9 km from Kokura station.

We use here the term, “competitive destinations,” which might be confusing with the term, “competing destinations” Fotheringham [1] originated. If deeply read, the concept of Fotheringham’s competing destinations contains various notions such as hub effects, intervening opportunities, and competitive effects. Thus the concept of the competing destinations broadly implies the interactions between the destinations. Hence we use the term, the competitive destinations in its original meaning. We see a similar use in [2].

We call this framework as “consumer behavior approach.” For further details on the approach, see Yamashiro [3] and Saito [4]. For concrete research instances applying the framework, refer to the volume by Saito and Yamashiro [5] and several chapters contained there [6‐10], their original papers in Japanese [11‐15], and related papers and chapters in this volume [16‐18].

The seventh Citizen Hearing Opinion Exchange discussed crossing National Route 10 between the Oita station and Tokiwa, the east side of the central shopping district, and indicated alternative methods (Cf. [24]).

Here we follow the same procedure as described in our previous forecasting study on the effects of the JR Hakata City’s opening, except that we omit the estimation of the entrance choice probability model. For more details, refer to Chap. 10 in this volume by Saito et al. [18], particularly the procedure diagram depicted in Fig. 10.2.

As stated before, we did not formulate and estimate the entrance choice model to forecast the entrance choice probability after JR Oita City’s opening since it is natural to assume that the increased visitors choose JR Oita City as their entrance to the city center. To say further, if the increased visitors are supposed to be the customers who return from the suburban shopping malls, the above assumption becomes much more persuasive.

We set the location reference point for the city center of Oita City as the location of Oita Forus, which stands in the Centporta ChuoMachi shopping street.

The derivation of the formula is as follows. To approximate \( {e}^{\log \left({\lambda}_{i1}^a\right)} \) by the first-order Taylor expansion at \( \log \left({\lambda}_{i1}^b\right) \), we have \( {e}^{\log \left({\lambda}_{i1}^a\right)}={e}^{\log \left({\lambda}_{i1}^b\right)}+{e}^{\log \left({\lambda}_{i1}^b\right)}\left(\log \left({\lambda}_{i1}^a\right)-\log \left({\lambda}_{i1}^b\right)\right) \). The second term of the right hand side of this equation is equivalent to the left-hand side of the formula. The exponential function of the right-hand side of the first equation of Eq. (2) with referring to Eq. (3) becomes as follows.

\( {\lambda}_{i1}\left({S}_1,z,w\right)={t}_{i1}^{\alpha }{c}_{i1}^{\beta }{S}_1^{\gamma }{\left(\left({S}_2/{t}_{i2}\right)/\left({S}_1/{t}_{i1}\right)\right)}^{\delta_{21}}{\left(\left({S}_3/{t}_{i3}\right)/\left({S}_1/{t}_{i1}\right)\right)}^{\delta_{31}}={t}_{i1}^{\alpha }{c}_{i1}^{\beta }{S}_1^{\gamma }{z}^{\delta_{21}}{w}^{\delta_{31}} \).

Here we can ignore t_ij, j = 1, 2, 3, and c_i1, which do not change. To save space, we use the notation z and w for the corresponding competitive terms. We approximate \( {\lambda}_{i1}^a={\lambda}_{i1}\left({S}_1^a,{z}^a,{w}^a\right) \) by the first-order Taylor expansion evaluated at \( {\lambda}_{i1}^b={\lambda}_{i1}\left({S}_1^b,{z}^b,{w}^b\right) \).

Then, we have

\( {\lambda}_{i1}^a={\lambda}_{i1}^b+\frac{\partial }{\partial {S}_1}{\lambda}_{i1}\left({S}_1^b,{z}^b,{w}^b\right)\left({S}_1^a-{S}_1^b\right)+\frac{\partial }{\partial z}{\lambda}_{i1}\left({S}_1^b,{z}^b,{w}^b\right)\left({z}^a-{z}^b\right)+\frac{\partial }{\partial w}{\lambda}_{i1}\left({S}_1^b,{z}^b,{w}^b\right)\left({w}^a-{w}^b\right) \).

Note that

\( \frac{\partial }{\partial {S}_1}{\lambda}_{i1}\left({S}_1^b,{z}^b,{w}^b\right)={\gamma \lambda}_{i1}^b/{S}_1^b \), \( \frac{\partial }{\partial z}{\lambda}_{i1}\left({S}_1^b,{z}^b,{w}^b\right)={\delta}_{21}{\lambda}_{i1}^b/{z}^b \), and \( \frac{\partial }{\partial w}{\lambda}_{i1}\left({S}_1^b,{z}^b,{w}^b\right)={\delta}_{31}{\lambda}_{i1}^b/{w}^b \). Hence,

\( {\lambda}_{i1}^a-{\lambda}_{i1}^b={\gamma \lambda}_{i1}^b\left({S}_1^a/{S}_1^b-1\right)+{\delta}_{21}{\lambda}_{i1}^b\left({z}^a/{z}^b-1\right)+{\delta}_{31}{\lambda}_{i1}^b\left({w}^a/{w}^b-1\right) \).

Returning to the original notation, we have Eq. (7) since \( \left({z}^a/{z}^b-1\right)=\left({w}^a/{w}^b-1\right)=\left({S}_1^b/{S}_1^a-1\right) \).

By dividing the shop floor area’s or the policy change’s interval into eight equal-length intervals, we performed the successive approximations by averaging the approximations evaluated at the lower and the upper ends of each small interval and obtained the following approximate decomposition; The log-linearize approximation of the total increase of 10,272 persons per day is 10,273. The decomposition into the three contributions turns out that the contribution due to the increase in the shop floor area of the city center is 2357, that of bringing back the customers from Tokiwa-Wasada Town 7180, and that from Park Place Oita is 739 persons per day, which does not differ much from the above result.

The Tokiwa department store kindly provided us with the number of daily incoming customers on the four survey days. Using these numbers, the total number of net incoming visitors to the city center of Oita City varies from 33,000 to 48,000 persons per day.

For simplicity, as shown in Eq. (10), we have explained that the probability P_ii of quitting Kaiyu is proportional to the shop floor area S_i of the node or the division district from which a visitor leaves the city center. In the estimation below, we employ the expression that P_ii is proportional to S_i/T_ii, considering the differences in searching time according to the dispersion of attractive facilities in the node or the division district.

We can call this method the consistent aggregate estimation of the Kaiyu choice model. We can also refer to this model as a simplified aggregate estimation method compared with the consistent disaggregate estimation method. Note that the consistent estimation method gives each sample the weight to remove the choice-based sampling biases. By using these weights, we can perform this disaggregate consistent estimation as the maximum likelihood estimation of a logit model for the weighted samples, where we form the samples by decomposing all samples’ Kaiyu paths into all consecutive Kaiyu OD pairs or all included Kaiyu choices with quitting and give them the weights obtained from the consistent estimation.

For details of the Kaiyu Markov model, refer to Saito et al. [31] “Basics of Kaiyu Markov models,” Chap. 4 in this volume. Also see [16, 17].

While we define the nodes and area segmentation in the city center as the 22 division districts, we delete the division “outside the city center” for the analysis here.

Concretely, before JR Oita City’s opening, we refer to the sixth row and column of Table 10 and perform the row and the column sums except for the diagonal. The sum over the sixth row except for the diagonal corresponds to the outflow Kaiyu from the station district to other districts and equals 7010 = 167 + 1466 + 2485 + 621 + 2271. The sum over the sixth column corresponds to the inflow Kaiyu from other districts to the station district and equals 7220 = 97 + 2360 + 2514 + 525 + 1725. Thus, before the opening, the Kaiyu flows between the station and other districts in both directions amount to 14,230. Similarly, after JR Oita City’s opening with setting a pedestrian crossing, we refer to Table 12. The sum over the sixth row except for the diagonal corresponds to the outflow from the station district and equals 13,855 = 278 + 2531 + 4528 + 1322 + 5195. The sum over the sixth column except for the diagonal corresponds to the inflow from other districts to the station district and equals 12,410 = 149 + 3573 + 4122 + 1001 + 3566. Thus, after the opening, the Kaiyu flows between the station and other districts in both directions amount to 26,265.

For more details, refer to Saito et al. [31] in this volume.

We organized and held the symposium under the support of the Oita City Government at Compal Hall on September 28th, 2014. Several newspaper articles reported the symposium and our forecast. (For example, see [34]).

The original abridged versions of some parts of this chapter first appeared in Yamashiro et al. [37] and Iwami et al. [38].