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A comparison of Euclidean Distance, Travel Times, and Network Distances in Location Choice Mixture Models

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Abstract

This article investigates the selection of a distance measure in location modeling. While in the empirical literature the choice usually boils down to picking one single measure, this research proposes a flexible approach in which several measures may be used in parallel to capture the surrounding economic landscape. This is intended to acknowledge that interactions between agents may take several forms, occurring through different channels and as such being based on different measures. The methodology is applied to the location choice of establishments in the Paris region, using a mixture of ”mono-distance” hurdle-Poisson models. Seven distance measures are considered: Euclidean distance, the travel times by car (for the peak and off-peak periods) and by public transit, and the corresponding network distances. For all the economic sectors considered, the mixture of hurdle-Poisson models performs significantly better than the “pure” mono-distance models. This corroborates that local spatial spillovers are indeed channeled by different means, hence best represented using several measures. The combination of peak and off-peak road travel times (slightly) outperforms other combinations including the Euclidean distance, supporting the choice of meaningful over more abstract measures in spatial econometric models. The distance measure most likely to capture local spatial spillovers varies depending on the economic sector examined, reflecting differences between sectors in operations and location choice criteria.

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Notes

  1. As noticed by Miller and Wentz (2003), many researchers adopt the Euclidean distance without realizing its underlying assumptions or its alternatives. This representation has been originally proposed due to scarce data and low computational power at the time, rather than because of its alleged universality. Yet, it remains largely applied to this day.

  2. In the case of continuous data, spatial cross-regressive models have already been used to combine several measures (e.g., Kang and Dall’erba (2016)).

  3. Nguyen et al. (2012) develops a relocation choice model using an average travel distance as a proxy for the distance among zones and firms.

  4. In this paper, local spatial spillovers refer to the direct effect of the characteristics of other zones onto the profitability of a given zone. Following the terminology used in Márquez et al. (2010) or LeSage (2014), formally they are represented using spatially lagged explanatory variables as visible in Eq. 2. Endogenous spatial lags (such as in spatial auto-regressive models) are not considered.

  5. One might set this parameter at a value smaller or larger than 1 to obtain stronger or weaker local spillover effects. Similarly, one may also allow μm,k to vary with the variables k and/or the measure m. These possibilities are left aside for further research.

  6. More specifically, the basic specification (i.e. before the mixture) used in this paper might be regarded as a nonlinear counterpart of the spatial lag of X model (SLX) in the discrete case, with two specificities relatively to the standard SLX formulation (see, e.g., LeSage (2014)): the vector of spatially lagged explanatory variables WX is transformed with a logarithm, and a hurdle model is included.

  7. The Paris region, also called Île-de-France, is a vibrant and innovative region with over 5.6 million jobs, 37 percent of national executives, and 40 percent of the national workforce in research and development. It is the 1st R&D hub in Europe and the third worldwide. 11.7 million people representing over 19 percent of the country population live in an area which covers only 2.2 percent of national grounds. The GDP of the region amounts to 31 percent of total French GDP (http://www.grand-paris.jll.fr/fr/paris/chiffres-cles/) that is 612 billion euros (2012). The Paris region is the 1st European region considering the number of firms classified in Fortune 500 (July 2014). The Paris region consists of 1300 municipalities encompassing the inner city of Paris and its suburbs. Yet, very large differences in population and employment densities are to be found between the Paris city and its outer periphery.

  8. Distance matrices based on a transport network being relatively stable over time at a regional scale, especially in the Paris region where the transport networks are already well developed, this one year difference should have a very limited impact on our results.

  9. These three sectors were chosen as best representative of the usefulness of the methodology as well as of the diversity of situations regarding which distance measure best captures spatial effects. For the other sectors, similar results were obtained, though the model improvement (in terms of BIC) was slightly less important. For a very few sectors, the mixture was also found not bring significant improvement. Detailed results for all sectors are available upon request from the authors.

  10. By comparison, Combes and Lafourcade (2005) find a correlation coefficient of 0.990 between the great circle distance and the road network distance and Rietveld et al. (1999) a value of 0.966 between the Euclidean distance and the road network distance.

  11. This issue is closely related to the type of trip undertaken: short distances typically correspond to intra-urban trips, and longer distances to inter-urban trips.

  12. While the detour factor well illustrates the proximity difference between two points when using either the Euclidean distance or a given network distance, it does not well reflect the level of spatial correspondence between the two corresponding paths, so that more suitable indicators should be used instead for these ends (see Matisziw and Demir (2016), on this issue). Here, the analysis focuses on the notion of proximity and does not intend to exploit differences at the path-level, so that the mean detour factor is informative enough.

  13. All three combinations are based on sets of two measures (i.e., \(\vert \mathcal {M}\vert = 2\)). To keep the exposition of the results simple, larger sets (\(\vert \mathcal {M}\vert >2\)) or sets containing mixtures of the described measures were not considered. For instance, including linear combinations of the three measures considered would allow considering establishments that are not purely oriented toward peak/off-peak travel time or toward the crow-fly distance when approximating the profit level of a zone. While this represents a limitation of the present study, search for the optimal number of clusters and their exact definitions will be the object of future works.

  14. Readers interested in this issue may refer to Buczkowska and de Lapparent (2017).

  15. See, e.g., http://www.mgm.fr/PUB/Mappemonde/M198/LangloisDenain.pdf.

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Acknowledgements

The authors would like to thank Professor Josep-Maria Arauzo-Carod and Professor James LeSage, all the anonymous reviewers, and the editor for their constructive suggestions and very helpful comments on the paper. We also thank the DRIEA-IF and Caliper for providing access to the MODUS model and the TransCAD software, respectively.

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Authors and Affiliations

  1. Lokad, 83 - 85 Boulevard Vincent Auriol, 75013, Paris, France

    Sabina Buczkowska

  2. LVMT, UMR-T 9403, Ecole des Ponts, IFSTTAR, UPEM, Champs-sur-Marne, 77455, France

    Nicolas Coulombel

  3. School of Business and Engineering Vaud (HEIG-VD), HES-SO University of Applied Sciences and Arts Western Switzerland, Avenue des sports 20 - CP 521 -1401, Yverdon-les-Bains, Switzerland

    Matthieu de Lapparent

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  1. Sabina Buczkowska
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Correspondence to Sabina Buczkowska.

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An earlier version of this paper was presented at the 55th European Regional Science Association Congress (Lisbon, Portugal, August 25-29, 2015), 14th International Workshop on Spatial Econometrics and Statistics (Paris, France, May 27-28, 2015), and published as a Ecole Polytechnique Fédérale de Lausanne Technical Report. The usual disclaimers apply.

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Appendix

Fig. 3
figure 3

Google map image: Possible barriers which require to make detours: a river, lakes, an attraction island theme park, parks, a highway, departmental roads, train routes, electric and thermic centers, cemetery. Euclidean (2.66 km) versus real distance (8.2 km and 13 min) from point A to B in the area of Champs-sur-Marne, the Paris region. Source: Google My Maps

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Table 6 Probabilistic mixture of hurdle-Poisson models for special, scientific and technical and real estate activities using two latent classes for case #1: ED (class #1) with TtVhMph (class #2). Hurdle and truncated-at-zero Poisson parts reported. The dependent variables are the counts of newly-created establishments from the special, scientific and technical and real estate activities sectors in the different zones
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Buczkowska, S., Coulombel, N. & de Lapparent, M. A comparison of Euclidean Distance, Travel Times, and Network Distances in Location Choice Mixture Models. Netw Spat Econ 19, 1215–1248 (2019). https://doi.org/10.1007/s11067-018-9439-5

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