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01.07.2014

Travel demand forecasts improved by using cross-sectional data from multiple time points

verfasst von: Nobuhiro Sanko

Erschienen in: Transportation | Ausgabe 4/2014

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Abstract

Forecasts of travel demand are often based on data from the most recent time point, even when cross-sectional data is available from multiple time points. This is because forecasting models with similar contexts have higher transferability, and the context of the most recent time point is believed to be the most similar to the context of a future time point. In this paper, the author proposes a method for improving the forecasting performance of disaggregate travel demand models by utilising not only the most recent dataset but also an older dataset. The author assumes that the parameters are functions of time, which means that future parameter values can be forecast. These forecast parameters are then used for travel demand forecasting. This paper describes a case study of journeys to work mode choice analysis in Nagoya, Japan, using data collected in 1971, 1981, 1991, and 2001. Behaviours in 2001 are forecast using a model with only the most recent 1991 dataset and models that combine the 1971, 1981, and 1991 datasets. The models proposed by the author using data from three time points can provide better forecasts. This paper also discusses the functional forms for expressing parameter changes and questions the temporal transferability of not only alternative-specific constants but also level-of-service and socio-economic parameters.

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Badoe and Miller (1995b) compared the forecasts of models using 1964 data updated with a small number of observations from 1986 with the forecasts of models using only a small number of observations from 1986. They examined the effect on forecast performance of the number of observations from 1986. In their dataset, the updated 1964 models provided little or no improvement over the 1986 models with 400–500 samples. This suggests that the most recent data provides better results when an adequate number of observations are available. On the other hand, Karasmaa and Pursula (1997) argued that more than 400–500 samples were required for some updating methods.

If the constraint is relaxed for all parameters, the estimates are identical to those estimated by using each dataset separately.

They calculated an MAE by segmenting the study area into seven arbitrary areas, calculating differences between actual and predicted users by each mode in each segment, summing up the differences over entire modes and segments, and dividing the summed value by total number of the users. The segmentation does not have any statistical meaning, and different segmentations result in different MAE.

Badoe and Miller (1998) made a similar analysis as Badoe and Wadhawan (2002). One of the differences between these studies is the selection of explanatory variables. Badoe and Wadhawan compared models with both level-of-service and socio-economic variables and with only level-of-service variables, the latter of which is believed to be similar to Badoe and Miller’s work. Actually, they found that the former specification had a better forecasting performance, indicating the superiority of models with both level-of-service and socio-economic variables. (Note that models with more variables do not always result in better forecasts.) Hence, the implications of Badoe and Miller’s work are limited. Badoe and Miller provided evidences that were a bit in favour of their methodology. They concluded that one of the joint models outperforms the model with only 1986 data based on a disaggregate measure and that some of the joint models are better than the model with only 1986 data based on an aggregate measure.

Actually, the idea behind combining two data sources is to complement the weakness of one source with the strength of the other. However, it is not clear in their work which weakness in the most recent data is complemented by which strength in the older data.

Habib et al. (2012) took a similar approach, but their consideration of functional form was limited to the alternative-specific constants and the scale parameters of GEV (Generalised Extreme Value) models.

Further assumptions of functional forms for scale parameters are avoided, since the model is difficult to interpret. The following example explains this. Assume \( \mu_{\text{LOS}}^{t} = \mu_{\text{LOS}} + \mu_{\text{dLOS}} f\left( t \right) \), where \( \mu_{\text{LOS}} \) and \( \mu_{\text{dLOS}} \) denote the base scale parameter and a historically changing scale parameter, respectively. However, the estimated parameters take the form of the scale parameter multiplied by the level-of-service parameter: \( \begin{aligned} \mu_{\text{LOS}}^{t} \beta_{{{\text{LOS}},ik}}^{t} & = \left( {\mu_{\text{LOS}} + \mu_{\text{dLOS}} f\left( t \right)} \right)\left( {\beta_{{{\text{LOS}},ik}} + \beta_{{{\text{dLOS}},ik}} f\left( t \right)} \right) \\ & = \left( {\beta_{{{\text{LOS}},ik}} + {{\mu_{\text{dLOS}} \beta_{{{\text{LOS}},ik}} f\left( t \right)} \mathord{\left/ {\vphantom {{\mu_{\text{dLOS}} \beta_{{{\text{LOS}},ik}} f\left( t \right)} \mu }} \right. \kern-0pt} \mu }_{\text{LOS}} } \right)\left( {\mu_{\text{LOS}} + {{\mu_{\text{LOS}} \beta_{{{\text{dLOS}},ik}} f\left( t \right)} \mathord{\left/ {\vphantom {{\mu_{\text{LOS}} \beta_{{{\text{dLOS}},ik}} f\left( t \right)} {\beta_{{{\text{LOS}},ik}} }}} \right. \kern-0pt} {\beta_{{{\text{LOS}},ik}} }}} \right). \\ \end{aligned} \) The estimates do not distinguish between \( \mu_{{{\text{d}}{\text{LOS}}}} \) in the former expression and \( {{\mu_{\text{LOS}} \beta_{{{\text{dLOS}},ik}} } \mathord{\left/ {\vphantom {{\mu_{\text{LOS}} \beta_{{{\text{dLOS}},ik}} } {\beta_{{{\text{LOS}},ik}} }}} \right. \kern-0pt} {\beta_{{{\text{LOS}},ik}} }} \) in the latter expression. The same is true for \( \beta_{{{\text{dLOS}},ik}} \) and \( {{\mu_{\text{dLOS}} \beta_{{{\text{LOS}},ik}} } \mathord{\left/ {\vphantom {{\mu_{\text{dLOS}} \beta_{{{\text{LOS}},ik}} } \mu }} \right. \kern-0pt} \mu }_{\text{LOS}} \). This problem is not solved even when \( \mu_{\text{LOS}} = 1 \) is assumed.

Scale parameters related to alternative-specific constants are assumed to be unities, so the alternative-specific constants in this specification include the effects of the scale parameters. The same applies to the level-of-service and socio-economic parameters, when \( \mu_{\text{LOS}}^{t} = \mu_{\text{SE}}^{t} = 1 \) \( \forall t \) is assumed.

Magota (1972) reported 81.7 % in 1969 (quoted in Sasajima 2009).

Although it is sometimes difficult to obtain data for travel costs in the past, the author can avoid this problem when analysing commuting behaviours in Japan, since travel cost has a smaller effect on commuting trips. The following experience of the author explains this. Sanko et al. (2012) estimated commuting mode choice models between car and public transportation and found that the estimate for the car cost parameter was not significant. Moreover, the public transportation cost parameter was not included because it had the wrong sign.

These findings can benefit from Sanko and Morikawa (2010), who analysed factors affecting the temporal transferability of alternative-specific constants updated to improve spatial transferability. They utilised data collected in 1971 and 1991 in the same Nagoya metropolitan area used in this study, but estimated mode choice models for trips of all purposes. They suggest that temporal change in the alternative-specific constants can be related to the non-transferability of the parameters of other explanatory variables, especially the Nagoya dummy and, perhaps, travel time and travel cost. The results from the present study also imply that the Nagoya dummy and the travel time are not transferable. Sanko and Morikawa also imply that transferability of other socio-economic variables has fewer problems, which is somewhat consistent with the present study.

Alternative-specific constants are analysed in the same manner using α and α _d instead of β and β _d.

Setting aside the J-FNcFNpFs models, Table 6 suggests a huge gap between J-DcFp2Ds and I-81, indicating that models with a 1991-specific component, such as I-91 and J-DcFp2Ds, provide better forecasts than the models without it, such as I-81, J-FcFpFs, and I-71.

The forecasting performance of the J-FNcFNpFs model is based on the results shown in Table 5. However, the estimates include insignificant historically changing parameters. The author imposed a restriction on the linear form: the male dummy for car alternative, the 20 years old or older dummy, and the 65 years old or older dummy must be the same during the two decades and applied the estimates to the 2001 data. This model’s forecast for 2001 produced a log-likelihood of −4,796.24 and an MAE of 0.041, so the discussion in the “Forecasting performance” Section is not changed.

The test statistic for the best model, J-FNcFNpFs (log), is 49.12 [= −2 × (−4,740.84 + 4,716.28)] and is rejected even at a significance level of 10⁻⁷. The simple linear model, J-FNcFNpFs (linear), has a test statistic of 146.66 [= −2 × (−4,789.61 + 4,716.28)] and is rejected even at a significance level of 10⁻²⁷. However, these are much better than the test statistic for the I-91 model, which is 171.02 [= −2 × (−4,801.79 + 4,716.28)] and is rejected even at a significance level of 10⁻³².

Combinations of estimates for (base parameter, historically changing parameter) when the base year is 1961 are expressed: (β − β _d , β _d) for the linear form, and (β, exp(−1) × β _d) for the exponential form, where β and β _d denote the base and the historically changing parameters, respectively, when the base year is 1971. Note that α and α _d apply to alternative-specific constants.

Using the same notations shown in footnote 16, when 20 years is selected as the interval, the combinations are (β, 2β _d) for the linear form, (β, 4β _d) for the square form, and (β, \( \sqrt 2 \) × β _d) for the square root form.

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Titel: Travel demand forecasts improved by using cross-sectional data from multiple time points
verfasst von: Nobuhiro Sanko
Publikationsdatum: 01.07.2014
Verlag: Springer US
Erschienen in: Transportation / Ausgabe 4/2014
Print ISSN: 0049-4488
Elektronische ISSN: 1572-9435
DOI: https://doi.org/10.1007/s11116-013-9464-7

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