A systematic review and meta-analysis of interaction models between transportation networks and territories
AA systematic review and meta-analysis of interaction models betweentransportation networks and territories
Juste Raimbault , , , ∗ Center for Advanced Spatial Analysis, University College London UPS CNRS 3611 ISC-PIF UMR CNRS 8504 G´eographie-cit´es ∗ [email protected] Abstract
Modeling and simulation in urban and regional studies has always given a significant place to models relatingthe dynamics of territories with transportation networks. These include for example Land-use Transport Inter-action models, but this question has been investigated from different viewpoints and disciplines. We proposein this paper a systematic review to construct a corpus of such models, followed by a meta-analysis of modelcharacteristics. A statistical analysis provides links between temporal and spatial scale of models, their level ofinterdisciplinarity, and the paper year, with disciplines, type of model and methodology. We unveil in particularstrong disciplinary discrepancies in the type of approach taken. This study provides a basis for novel and inter-disciplinary approaches to modeling interactions between transportation networks and territories.
Keywords:
Systematic review; Meta-analysis; Modeling; Transport-territories interactions
Within urban and territorial systems, infrastructure networks constitute a backbone for the dynamics of agents andcomponents. Transportation networks have thus a strongly shaping role in urban dynamics, at small time scales bysustaining daily mobility [1]. At longer time scales, transport networks determine accessibility patterns which inturn influence residential and employment relocations [2]. Computational models have been introduced for a longtime in the literature to understand, anticipate and manage such interactions between transportation networks andterritories.Such models stem from diverse disciplines and answer different research questions, focusing on various processesand dimensions of interactions. In economics for example, the impact of network on urban form is studied byaccounting for the location of economic sectors [3]. The role of networks in urban growth is also investigated fromthe economic viewpoint [4]. In transportation or urban planning, the focus is made on changes in accessibilitylandscapes [5]. Operational urban models such as Land-use Transport Interaction models [2] are also closely relatedto the discipline of planning. At other scales, geography focuses on the dynamics of urban systems and the roleof networks within [6], but also on the relation between road network topology and urban form [7]. The field oftransportation science, including transportation geography, ranges from accessibility studies [8] to transportationand traffic models [9].Altogether, this wide variety of approaches to the same conceptual object makes it difficult to overview them syn-thetically, to relate them and the respective disciplines, and to potentially investigate for new and interdisciplinarymodeling approaches. [10] provides a literature mapping in terms of citation network and semantic network, givingalready a first insight into this issue. However, the characteristics of models themselves and the research questionsanswered are not studied in details. We propose in this paper to dig deeper into model properties, in relation withthe disciplinary context, in a systematic way. Our contribution is thus twofold: (i) through a systematic review, webuild an interdisciplinary corpus of 145 papers studying interaction models between transportation networks andterritories; (ii) after extracting models properties, we proceed to a meta-analysis by estimating statistical modelssearching for significant covariates of these properties.The rest of this paper is organised as follows: we first describe the methods used both for the systematic reviewand the meta-analysis; we then give descriptive results, both qualitative observations and quantitative measures,1 a r X i v : . [ c s . D L ] D ec temming from the systematic review; we proceed to the meta-analysis with statistical models; we finally discussthe implications of our results in terms of building new interaction models. Systematic literature reviews mostly take place in fields where a very targeted request, even by article title, willyield a significant number of studies studying quite the same question: typically in therapeutic evaluation, wherestandardised studies of a same molecule differ only by the size of samples and statistical modalities (control group,placebo, level of blinding). The PRISMA reporting guidelines for systematic reviews enter this frame [11]. Inthis case corpus construction is straightforward first thanks to the existence of specialised bibliographic databasesallowing very precise requests, and furthermore thanks to the possibility to proceed to additional statistical analysesto confront the different studies (for example network meta-analysis, see [12]). In our case, the exercise is less directfor the reasons exposed above and others: objects are hybrid, problematics are diverse, and disciplines are numerous.The different points we will raise in the following will often have as much thematic value as methodological value,suggesting crucial points for the realisation of such an hybrid systematic review.We propose an hybrid methodology coupling the two methodologies developed in [13] and [14], with a moreclassical procedure of systematic review. We aim both at a representativity of all the disciplines we discovered, butalso a limited noise in the references taken into account for the meta-analysis of model characteristics. Therefore,we combine the corpus obtained in the literature mapping through citation network analysis by [10] and a corpusconstructed through keywords requests, in a way similar to [15]. The protocol is thus the following:1. Starting from the citation corpus constructed by [10], we isolate a number of relevant keywords, by selectingthe 5% of links having the strongest weight (arbitrary threshold), and among the corresponding nodes theones having a degree larger than the quantile at 0.8 of their respective semantic class. The first filtrationallows to focus on the “core” of observed disciplines, and the second to not introduce size bias without loosingthe global structure, classes being relatively balanced. A manual screening allows to remove keywords thatare obviously not relevant (remote sensing, tourism, social networks, . . . ), what leads to a corpus of K = 115keywords ( K is endogenous here).2. For each keyword, we automatically do a catalog request (google scholar) while adding model* to it, of a fixednumber n = 20 of references. The supplementary term is necessary to obtain relevant references, after testingon samples.3. The potential corpus composed of obtained references, with references composing the citation network, ismanually screened (review of titles) to ensure a relevance regarding the state of the art reviewed extensivelyby [10], yielding the preliminary corpus of size N p = 297.4. This corpus is then inspected for abstracts and full texts if necessary. We select articles elaborating a modelingapproach, ruling out conceptual models. References are classified and characterised according to criteriadescribed below. We finally obtain a final corpus of size N f = 145, on which quantitative analyses arepossible.The method is summarised in Fig. 1, with parameter values and the size of the successive corpuses.For the choice of initial keywords for the indirect construction (through semantic request), a possible alternativecould be to extract the relevant keywords for each sub-community of the citation network, and then select the mostrelevant for each domain. We make the choice of extracting them on the complete corpus, and then to collect themby sub-community thereafter. For a small corpus, the second option is more suitable, since the notion of relevanceis less importance than for very large corpuses, in which some relevant words may be drowned and less relevantto emerge in a spurious way. In other words, the keyword selection method appears to be more robust on smallercorpuses, as suggest the comparison of this application with the one done on the Cybergeo journal by [14] and theone done on the patent corpus by [16].The methods used do not allow to avoid some “noise”, i.e. retrieving articles that are not relevant to the subject,even with a very low tolerance threshold. We obtained for example articles from unrelated disciplines such as genderstudies, biology, criminology, urban geology. This confirms that the manual filtering stage is essential.This noise can for example be due to: 2igure 1: Methodology of the systematic review.
Rectangles correspond to corpuses of references, ellipses tocorpuses of keywords, and dashed lines to initial corpuses. At each stage the size of the corpus is given.3 effective citations for diverse reasons, but having only a low relevance in the citing article; • noise intrinsic to the keyword search; • catalog classification errors. The second part of our study is devoted to a mixed analysis based on the corpus constructed through the systematicreview. It aims at extracting and to precisely decompose ontologies, scales and processes, and then to study possiblelinks between these characteristics of the models and the context in which they have been introduced. It is thus in away the meta-analysis, that we can also designate as “modelography” following [17]. It is indeed not a meta-analysisstrictly speaking since we do not combine similar analysis to extrapolate potential results from larger samples. Ourapproach is close to the one of [18] which gathers references having quantitatively studied Zipf’s law for cities, andthen links the characteristics of studies to the methods used and the assumptions formulated.The first part consists in the extraction of the characteristics of models. An automation this work would consistin a research project in itself, as we develop in discussion below, but we are convinced of the relevance to refinesuch techniques in the context of developing integrated disciplines. We focus here on a manual extraction that willaim at being more precise that an approximatively convincing data mining attempt.We extract from models the following characteristics: • what is the strength of coupling between territorial ontologies and the ones of the network, in other words isit a co-evolution model in the sense of [10] or a weak coupling. To the best of our knowledge there does notexist generic approaches to model coupling that would be not linked to a particular formalism. We will takethe approach given in introduction of [10], by distinguishing here a weak coupling as a sequential coupling(outputs of the first model become inputs of the second) from a dynamical strong coupling where the evolutionis interdependent at each time step (either by a reciprocal determination of by a common ontology). We willtherefore classify into categories following the representation of figure 2: { territory ; network ; weak ;coevolution } , which results from the analysis of literature in [10]; • maximal time scale; • maximal spatial scale; • domain “a priori”, determined by the origin of authors and the domain of the journal; • methodology used (statistical models, system of equations, multi-agent, cellular automaton, operational re-search, simulation, etc.); • case study (city, metropolitan area, region or country) when relevant.We also collect in an indicative way, but without objective for objectivity nor exhaustivity, the “subject” ofthe study (i.e. the main thematic question) ans also the “processes” included in the model. An exact extractionof processes remains hypothetical, on the one hand because it is conditioned to a rigorous definition and takinginto account different levels of abstraction, of complexity, or scale, on the other hand as it depends on technicalmeans out of reach of this modest study. We will comment these in an indicative way without including them insystematic studies.We also gather scale, range and in a sense resolution to not make the extraction more complicated. Even if itwould be relevant to differentiate when an element does not exist for a model (NA) to when it is badly defined bythe author, this task seem to be sensitive to subjectivity and we merge the two modalities.Based on the citation network mapping done in [10], we add to the previous characteristics the following variables: • citation domain (when available, i.e. for references initially present in the citation network, what correspondsto 55% of references); • semantic domain, defined by the domain for which the document has the highest probability; • index of interdisciplinarity. 4igure 2: Schematic representation of the distinction between different types of models couplingnetworks and territories.
This typology is based on the one of [10], by distinguishing approaches in whichterritory or network are given as a context (Luti and network growth) from a sequential coupling between a modelfor each. Ontologies are represented as ellipses, submodels by full boxes, models by dashed boxes, couplings byarrows. We highlight in red the co-evolution approach which remains rare in the literature and has significantdevelopment potential. 5emantic domains and the interdisciplinarity measure have been recomputed for this corpus through the collec-tion of keywords, and then keyword extraction following the method described in [14], with K W = 1000, θ w = 15and k max = 500. We obtain more targeted communities which are relatively representative of thematics and meth-ods: Transit-oriented development ( tod ), Hedonic models ( hedonic ), Infrastructure planning ( infra planning ),High-speed rail ( hsr ), Networks ( networks ), Complex networks ( complex networks ), Bus rapid transit ( brt ).An “appropriate choice” of characteristics to classify models is similar to the issue of choosing features in machinelearning: in the case of supervised learning, i.e. when we aim at obtaining a good prediction of classes fixed a priori(or a good modularity of the obtained classification relatively to the fixed classification), we can select featuresoptimising this prediction. We will therein discriminate models that are known and judged different. If we wantto extract an endogenous structure without any a priori (unsupervised classification), the issue is different. Wewill therefore test in a second time a regression technique which allows to avoid overfitting and to select features(random forests). To construct the corpus, we used the open source tools developed by [14] and available at https://github.com/JusteRaimbault/BiblioData . Corpus data and processing code for the meta-analysis are openly available at https://github.com/JusteRaimbault/CityNetwork/tree/master/Models/QuantEpistemo/HyperNetwork . TheR software was used for preparing the data, network analysis and statistical models.
During the manual classification achieved when screening abstracts, the following points are of interest in terms ofqualitative methodological results: (i) the “a priori” disciplines are judged based on the journal in which the articlewas published - in particular, we operate the following particular choices (for other journals such as physics journalsthere is no ambiguity): Journal of Transport Geography, Environment and Planning B: Geography; Journal ofTransport and Land-use, Transportation Research: Transportation; (ii) geography in our sense includes urbanismand urban studies is these are not too close from planning (urban sustainability for example).The systematic review procedure first of all allows revealing several methodological points, which knowledge canbe an asset to proceed to similar hybrid systematic reviews: • Catalog bias seem to be inevitable. We rely on the assumption that the use of google scholar allows a uniformsampling regarding catalog errors or bias. The future development of open tools for cataloging and mapping,allowing contributed efforts for a more precise knowledge of extended fields and of their interfaces, is a crucialissue for the reliability of such methods as illustrated by [19]. • The availability of full texts is an issue, in particular for such a broad review, given the multiplicity of editors.The existence of tools to emancipate science such as Sci-hub ( http://sci-hub.cc/ ) allows effectively accessingfull texts. Echoing the recent debate on the negotiations with publishers regarding the exclusivity of full textsmining, it appears to be more and more salient that a reflexive open science is totally orthogonal to the currentmodel of publishing. We also hope for a rapid evolution of practices on this point. • Journals, and indeed publishers, seem to differently influence the referencing, potentially increasing the biasduring requests. Grey literature and preprints are taken into account in different ways depending on thedomains. • Manual screening of large corpora allows to not miss “crucial papers” that could have been omitted before [20].The issue of the extent to which we can expect to be informed in the most exhaustive way possible of recentdiscoveries linked to the subject studied is very likely to evolve given the increase of the total amount ofliterature produced and the separation of fields, among which some are always more refined [21]. Followingthe previous points, we can propose that tools helping systematic analysis will allow to keep this objective asreasonable. • Results of the automatised review are significantly different from the domains highlighted in a classical lit-erature review: some conceptual associations, in particular the inclusion of network growth models, are notnatural and do not exist much in the scientific landscape as we previously showed.Furthermore, the operation of constructing the corpus already allows to draw thematic observations that areinteresting in themselves: 6
The articles selected imply a clarification of what is meant by “model”. In the sense of [22], a very broaddefinition of model which applies to any scientific perspectives can be given. Our selection here does notretain conceptual models for example, our choice criteria being that the model must include a numerical orsimulation aspect. • A certain number of references consist in reviews, what is equivalent to a group of model with similar char-acteristics. We could make the method more complicated by transcribing each review or meta-analysis, orby weighting the records of corresponding characteristics by the corresponding number of articles. We makethe choice to ignore these reviews, what remains consistent in a thematic way still with the assumption ofuniform sampling. • A first clarification of the thematic frame is achieved, since we do not select studies uniquely linked to trafficand mobility (this choice being also linked to the results obtained by [23]), to pure urban design, to pedestrianflows models, to logistics, to ecology, to technical aspects of transportation, to give a few examples, even ifthese subjects can from a specific viewpoint be considered as linked to interactions between networks andterritories. • Similarly, neighbour fields such as tourism, social aspects of the access to transportation, anthropology, werenot taken into account. • We observe a high frequency of studies linked to High Speed Rail (HSR), recalling the necessary associationof political aspects of planning and of research directions in transportation.
Regarding the existence of a case study and its localisation, 26% of studies do nothave any, corresponding to an abstract model or toy model (close to all studies in physics fall within this category).Then, they are spread across the world, with however an overrepresentation of Netherlands with 6.9%. Processesincluded are too much varied (in fact as much as ontologies of concerned disciplines) to be the object of a typology,but we will observe the dominance of the notion of accessibility (65% of studies), and then very different processesranging from real estate market processes for hedonic studies, to relocations of actives and employments in thecase of Luti, or to network infrastructure investments. We observe abstract geometric processes of network growth,corresponding to works in physics. Network maintenance appears in one study, as political history does. Abstractprocesses of agglomeration and dispersion are also at the core of several studies. Interactions between cities are aminority, the systems of cities approaches being drown in accessibility studies. Issues of governance and regulationalso emerge, more in the case of infrastructure planning and of TOD approaches evaluation models, but remain aminority. We will stay with the fact that each domain and then each study introduces its own processes with arequasi-specific to each case.
Corpus characteristics
The domains “a priori” (i.e. judged, or more precisely inferred from journal or institutionto which authors belong), are relatively balanced for the main disciplines already identified: 17.9% Transportation,20.0% Planning, 30.3% Economics, 19.3% Geography, 8.3% Physics , the rest in minority being shared between envi-ronmental science, computer science, engineering and biology. Regarding the share of significant semantic domains,TOD dominates with 27.6% of documents, followed by networks (20.7%), hedonic models (11.0%), infrastructureplanning (5.5%) and HSR (2.8%). Contingence tables show that Planning does almost only TOD, physics onlynetworks, geography is equally shared between networks and TOD (the second corresponding to articles of thetype “urban project management”, that have been classified in geography as published in geography journals) andalso a smaller part in HSR, and finally economics is the most diverse between hedonic models, planning, networksand TOD. This interdisciplinarity however appears only for classes extracted for the higher probability, since av-erage interdisciplinarity indices by discipline have comparable values (from 0.62 to 0.65), except physics which issignificantly lower at 0.56 what confirms its status of “newcomer” with a weaker thematic depth.
Models studied
It is interesting for our problematic to answer the question “who does what ?”, i.e. which typeof models are used by the different disciplines. We give in Table 1 the contingency table of the type of model asa function of a priori disciplines, of the citation class and of the semantic class. We observe that strongly coupledapproaches, the closest of what is considered as co-evolution models, are mainly contained in the vocabulary of7able 1:
Types of models studied according to the different classifications.
Contingence tables of thediscrete variable giving the type of model (network, territory or strong coupling), for the a priori classification, thesemantic classification and the citation classification.Discipline economics geography physics planning transportationnetwork 5 3 12 1 4strong 4 3 0 0 2territory 35 22 0 28 20Semantic hedonic hsr infra planning networks todnetwork 1 0 0 14 2strong 0 0 0 5 1territory 15 4 8 11 37Citation accessibility geography infra plan-ning LUTI networks TODnetwork 0 0 0 0 24 0strong 0 0 0 2 5 0territory 13 1 6 18 2 3networks, what is confirmed by their positioning in terms of citations, but that the disciplines concerned are varied.The majority of studies focus on the territory only, the strongest unbalance being for studies semantically linked toTOD and hedonic models. Physics is still limited as focusing exclusively on networks.
Studied scales
To then answer the question of the how, we can have a look at temporal and spatial typical scalesof models. Planning and transportation are concentrated at small spatial scales, metropolitan or local, economicsalso with a strong representation of the local through hedonic studies, and a spatial range a bit larger with theexistence of studies at the regional level and a few at the scale of the country (panel studies generally). Again,physics remains limited with all its contributions at a fixed scale, the metropolitan scale (which is not necessarilyclear nor well specified in articles in fact since these are toy models which thematic boundaries may be very fuzzy).Geography is relatively well balanced, from the metropolitan to the continental scale. The scheme for temporalscales is globally the same. The methods used are strongly correlated to the discipline: a χ test gives a statistic of169, highly significant with p = 0 .
04. Similarly, spatial scale also is but in a less strong manner ( χ = 50 , p = 0 . We now study the influence of diverse factors on characteristics of models through simple linear regressions. Ina multi-modeling approach, we propose to test all the possible models to explain each of the variables from theothers. The number of observations for which all the variables have a value is very low, we need to take into accountthe number of observations used to fit each model. Furthermore, model performances can be characterised bycomplementary objectives. Following [24], we apply a multi-objective optimization, to simultaneously maximise theexplained variance (adjusted R in our case) and the information captured (corrected Akaike information criterionAICc - AIC is a measure of the information gain between two models, and allows to avoid abusive overfitting througha too large number of parameters; AICc is a version taking into account the size of the sample, the measure varyingsignificantly for the small samples). It is realised conditionally to the fact of having the number of observations N >
50 (fixed threshold regarding the distribution of N on all models). The optimization procedure is detailed inSupplementary Material for each variable. Time scale and interdisciplinarity exhibit compromises difficult choosefrom, and we adjust the two candidates. Other variables exhibit dominating solutions and we adjust only a singlemodel.Complete regression results are given in Table 2. Temporal and spatial scales, together with year, are thevariables the best explained in the sense of the variance. Time scale is very significantly influenced by the type ofmodel: territory which decreases it, or strong coupling which increases it. The fact to be in physics also significantlyinfluences, and broadens the time range of models. On the contrary, engineering approaches (often optimal design8able 2: Explanation of models characteristics.
Results of the Ordinary Least Squares (OLS) estimation of se-lected linear models, for each variable to be explained: temporal scale (TEMPSCALE), spatial scale (SPATSCALE),interdisciplinarity index (INTERDISC), publication year (YEAR).
Explained variable:
TEMPSCALE SPATSCALE INTERDISC YEAR(1) (2) (3) (4) (5) (6)YEAR 0.674 − ∗ − ∗ TYPEstrong 100.271 ∗∗∗ − − ∗∗∗ − ∗∗∗ TEMPSCALE − − − − − ∗ − − − − ∗∗∗ ∗ ∗∗∗ − − − − − ∗ INTERDISC 2.357 − − − − ∗ − − − − − − − − − − − − ∗ ∗∗ ∗∗ ∗∗∗ Observations 64 94 94 64 98 64R Note: ∗ p < ∗∗ p < ∗∗∗ p < We conclude this study by regressions and classification with random forests, which are a very flexible methodallowing to unveil a structure from a dataset [25]. To complement the previous analysis, we propose to use it todetermine the relative importances of variables for different aspects. We use each time forests of size 100000, a nodesize of 1 and a number of sampled variables in √ p for the classification and p/ p is thetotal number of variables. To classify the type of models, we compare the effects of discipline, of the semantic class9nd of the citation class. The latest is the most important with a relative measure of 45%, whereas the disciplineaccounts for 31% and the semantic of 23%. This way, the disciplinary compartmentalization is found again, whereasthe semantic and this partly ontologies, is the most open. This encourages us in our aim at getting out of thiscompartmentalization. When we apply a forest regression on interdisciplinarity, still with these three variables,we obtain that they explain 7.6% of the total variance, what is relatively low, witnessing a semantic disparityon the whole corpus independently of the different classifications. In this case, the most important variable isthe discipline (39%) followed by the semantic (31%) and citation (29%), what confirms that the journal targetedstrongly conditions the behavior in the language used. This alerts on the risk of a decrease in semantic wealth whentargeting a particular public. This way, we have unveiled certain structures and regularities of models related tothe question of interactions between transportation networks and territories, which implications could prove usefulduring the construction of novel modeling approaches. A possible development could consist in the construction of an automatised approach to this meta-analysis, from thepoint of view of modular modeling, combined to a classification of the aim and the scale. Modular modeling consistsin the integration of heterogeneous processes and the implementation of these processes in the aim of extractingmechanisms giving the highest proximity to empirical stylised facts or to data [26]. The idea would be to be ableto automatically extract the modular structure of existing models, starting from full texts as proposed in [19], inorder to classify these bricks in an endogenous way and to identify potential couplings for new models.Altogether, meta-analysis protocols in the case of multiple disciplines and multiple models remain to be elab-orated. Similarly, being able to extrapolate synthetic results from heterogenous model results remains an openissue.
We can summarize the main points obtained from this meta-analysis that could influence choices made towards novelmodeling approaches. First of all, the interdisciplinary presence of approaches realising a strong coupling confirmsour need to build bridges and to couple approaches, and also retrospectively confirms the conclusions of [10] onthe consequence of discipline compartmentalization in terms of the models formulated. Secondly, the importanceof the vocabulary of networks in a large part of models will lead us to confirm this anchorage. The specificity ofTOD and accessibility approaches, relatively close to the LUTI models, will be of secondary importance for us. Therestricted span of works from physics, confirmed by the majority of criteria studied, suggests to remain cautious ofthese works and the absence of thematic meaning in the models. The wealth of temporal and spatial scales coveredby geographical and economical models confirms the importance of varying these in our models, ideally to reachmulti-scale models. Finally, the relative importance of classification variables on the type of model also suggest thedirection of interdisciplinary bridges to cross ontologies.
We finally propose to synthesise processes taken into account by models encountered during the meta-analysis, inorder to proceed to a similar effort than the one concluding the thematic approach of [10]. We can neither havean exhaustive view (as already mentioned in the methodology above) nor render with a high precision each modelin the details, since almost each is unique in its ontology. The exercise of the synthesis allows then to take a stepback from this limits and take a certain height, and have thus an overview on modeled processes (keeping in mindselection choices, which lead for example to not have mobility processes within this synthesis).The table 3 proposes this synthesis from the 145 articles obtained from the modelography and for which aclassification of the type was possible, i.e. that there existed a model entering the typology recalled above. Beingfully exhaustive would be similar to an interdisciplinary meta-modeling approach which is far out of the reach ofour work, and the list given here remain indicative.We find again the correspondences between disciplines, scales and types of models obtained in statistical resultsabove. We still observe the principal lessons, echoing the synthesis table obtained in [10]:1. The dichotomy of ontologies and processes taken into account between scales and between types is even moreexplicit here in models than in processes in themselves. Since this study was more detailed, it also appears10able 3:
Synthesis of modeled processes.
These are classed by scale, type of model and discipline.Networks → Territories Territories → Networks Networks ↔ TerritoriesMicro
Economics: real estate mar-ket, relocalization, employmentmarket NA
Computer Science : sponta-neous growth
Planning: regulations, devel-opment
Economics: real estate mar-ket, transportation costs, ameni-ties
Economics: network growth,offer and demand
Economics: investments, re-localizations, offer and demand,network planningMeso
Geography: land-use, central-ity, urban sprawl, network effects
Transportation: investments,level of governance
Geography: land-use, net-work growth, population diffu-sion
Planning/transportation: accessibility, land-use, relocal-ization, real estate market
Physics: topological correla-tions, hierarchy, congestion, lo-cal optimization, network main-tenance
Economics: economic growth,market, land-use, agglomeration,sprawl, competition
Economics: interactions be-tween cities, investments
Economics: offer and demandMacro
Geography: accessibility, in-teraction between cities, relocal-ization, political history
Geography: interactions be-tween cities, potential break-down
Transportation: network cov-erage
Transportation: accessibility,real estate market
Transportation: networkplaningstronger, since a greater precision allows exhibiting abstract categories. We postulate that there indeed existsdifferent processes at the different scales, and we suggest that multi-scale models or companion models atdifferent scales should be investigated [27].2. The compartmentalization of disciplines shown by [13] can be found in a qualitative way in this synthesis: itis clear that they originally diverge in their different founding epistemologies. New approaches should aimat integrating paradigms from different disciplines, while taking into account the limits imposed by modelingprinciples (for example, the parsimony of models necessarily limits the integration of heterogenous ontologies).3. An important gap between this synthesis and the one of thematic processes done by [10] is the quasi absencehere of models integrating governance processes. This may also be a direction to be explored as suggested by[28].4. On the contrary, a very good correspondance can be established between geographical models of urban systemsand the theoretical positioning of the evolutive urban theory introduced by [29]. This correspondance, moredifficult to exhibit for all the other approaches reviewed, also suggests that this may be a relevant directionto follow.
The processes linking transportation networks and territories are multi-scalar, hybrid and heterogenous. Therefore,the possible viewpoints and research questions are necessarily broad, complementary and rich. This could be afundamental characteristic of socio-technical systems, which Pumain advocates for in [30] as “a new measure ofcomplexity”, which would be linked to the number of viewpoints necessary to grasp a system at a given level ofexhaustivity.In order to better understand the neighbouring scientific landscape, and quantify the roles or relative weights ofeach, we have lead several bibliometrics and literature mapping analysis in [10]. A first preliminary analysis basedon an algorithmic systematic review by [13] suggests a certain compartmentalization of domains. This conclusion isconfirmed by the citation and semantic network analysis of [10], which also allowed drawing disciplinary boundariesmore precisely, both for the direct relations (citations) but also their scientific proximity for the terms and methods11sed. This paper completes these studies by using the constituted corpus and this knowledge of domains to achievea semi-automatic systematic review, providing a corpus of papers directly dealing with interaction models. We thenfully screened full texts, allowing to extract characteristics of models. A meta-analysis through statistical modelslinked these to the different domains. This provides a clear picture of what is done on this subject, why, how, andby which discipline. We finally discussed potential future directions for new interaction models, stemming from thisanalysis.
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Supplementary material
We give here the full numerical results of statistical analysis linking model characteristics and explicative variables.
Modalities of variables
We recall here the variables used in the meta-analysis and their modalities. These are: • Type of model (
TYPE ): strong, territory, network. • Publication year (
YEAR ), integer number. • Citation community (
CITCOM ), defined within the citation network: Accessibility, Geography, Infra Planning,LUTI, Networks, TOD. • A priori discipline (
DISCIPLINE ): biology, computer science, economics, engineering, environment, geography,physics, planning, transportation. • Semantic community (
SEMCOM ): brt, complex networks, hedonic, hsr, infra planning, networks, tod. • Methodology used: ca (Cellular Automaton), eq (analytical equations), map (cartography), mas (Multi-agentsimulation), ro (operations research), sem (Structural Equation Modeling), sim (simulation), stat (statistics). • Interdisciplinarity index (
INTERDISC ): real number in [0 , • Temporal scale (
TEMPSCALE ): given in years, is set to 0 for static analyses. • Spatial scale (
SPATSCALE ): continent (10000), country (1000), region (100), metro (10). These modalities arenumerically transformed in km by the values given in parenthesis (stylized scales).13able 4:
Linear models for interdisciplinarity
INTERDISC(1) (2)YEAR − − − ∗ − − ∗ TEMPSCALE − − − − − − − − − − − − − − − − − − − ∗ SEMCOMhsr − − − − − − − − − − − − − − − − ∗∗ ∗∗ Observations 64 98R ∗ (df = 13; 50) 1.789 ∗ (df = 9; 88) Note: ∗ p < ∗∗ p < ∗∗∗ p < Model selection
Regarding model selection, it is not achieved following a unique criteria, because of the low number of observationsfor some models, but by the optimization in the Pareto sense of contradictory objectives of adjustment (adjusted R ,to be maximized) and of the overfitting (corrected Akaike criterion AICc, to be minimized), while controlling thenumber of observation points. The Fig. 3 gives for each variable to be explained the localization of the set of potentialmodels within the objective space, and also the corresponding number of observations. For interdisciplinarity, twopoint clouds correspond to different compromises, and we select the two optimal models (one for each cloud). Forthe spatial scale, we postulate a positive R , and a single optimal model then emerges. For the temporal scale, wehave as for interdisciplinarity two compromise models. Finally for the year, the AICc gain between the two potentialoptima is negligible in comparison to the R loss, and we thus select the optimal model such that R > .
25 andAICc < Full results of statistical models
Interdisciplinarity
Interdisciplinarity is adjusted according to the linear models presented in Table 4.
Spatial scale
The spatial scale is adjusted following the linear model which adjustment is given in Table 5.
Time scale
The temporal scale is adjusted according to the linear models presented in Table 6.
Year
The publications year is adjusted following the linear model which adjustement is given in Table 7.14igure 3:
Multi-objective selection of linear models.
For each variable to be explained, we represent theposition of all linear models in the objective space (corrected Akaike criterion AICc and adjusted R ). The colorof points gives the number of observations. 15able 5: Linear model for the spatial scale.
SPATSCALETEMPSCALE − − − − − − ∗∗∗ DISCIPLINEphysics 292.559 ( − − − − − Note: ∗ p < ∗∗ p < ∗∗∗ p < Linear models for the temporal scale.
TEMPSCALE(1) (2)YEAR 0.674 ( − ∗∗∗ TYPEterritory − − − − − ∗∗∗ p = 0.194DISCIPLINEengineering − − − − ∗ p = 0.685DISCIPLINEenvironment 17.110 ( − − − − ∗ p = 0.003 ∗∗∗ DISCIPLINEplanning 1.304 ( − − − − − − − − − ∗ Observations 64 94R ∗∗∗ (df = 9; 54) 6.871 ∗∗∗ (df = 8; 85) Note: ∗ p < ∗∗ p < ∗∗∗ p < Linear model for the publication year.
YEARTYPEterritory 10.898 (3.045, 18.750), p = 0.010 ∗∗∗
TEMPSCALE 0.035 ( − − − − − − − − − − − − − − − − ∗ INTERDISC − − − − − − − − − − ∗∗∗ Observations 64R ∗∗ (df = 20; 43) Note: ∗ p < ∗∗ p < ∗∗∗ p <<