Space–Time Analysis: Concepts, Quantitative Methods, and Future Directions

Throughout most of human history, events and phenomena of interest have been characterized using space and time as their major characteristic dimensions, in either absolute or relative conceptualizations. Space–time analysis seeks to understand when and where (and sometimes why) things occur. In the context of several of the most recent and substantial advances in individual movement data analysis (time geography in particular) and spatial panel data analysis, we focus on quantitative space–time analytics. Based on more than 700 articles (from 1949 to 2013) we obtained through a key word search on the Web of Knowledge and through the authors' personal archives, this article provides a synthetic overview about the quantitative methodology for space–time analysis. Particularly, we highlight space–time pattern revelation (e.g., various clustering metrics, path comparison indexes, space–time tests), space–time statistical models (e.g., survival analysis, latent trajectory models), and simulation methods (e.g., cellular automaton, agent-based models) as well as their empirical applications in multiple disciplines. This article systematically presents the strengths and weaknesses of a set of prevalent methods used for space–time analysis and points to the major challenges, new opportunities, and future directions of space–time analysis.

[1]  May Yuan,et al.  Use of a Three‐Domain Repesentation to Enhance GIS Support for Complex Spatiotemporal Queries , 1999, Trans. GIS.

[2]  Rongrong Li,et al.  A geographically and temporally weighted autoregressive model with application to housing prices , 2014, Int. J. Geogr. Inf. Sci..

[3]  M. Kwan Beyond Space (As We Knew It): Toward Temporally Integrated Geographies of Segregation, Health, and Accessibility , 2013 .

[4]  David O'Sullivan Complexity science and human geography , 2004 .

[5]  Stephen J. Walsh,et al.  2.5D Morphogenesis: modeling landuse and landcover dynamics in the Ecuadorian Amazon , 2001, Plant Ecology.

[6]  J. K. Ord,et al.  Elements of spatial structure : a quantitative approach , 1976 .

[7]  Pip Forer,et al.  Movement beyond the snapshot - Dynamic analysis of geospatial lifelines , 2007, Comput. Environ. Urban Syst..

[8]  B. Pijanowski,et al.  Modeling the relationships between land use and land cover on private lands in the Upper Midwest, USA , 2000 .

[9]  M. Kulldorff,et al.  A Space–Time Permutation Scan Statistic for Disease Outbreak Detection , 2005, PLoS medicine.

[10]  M. Janssen,et al.  Multi-Agent Systems for the Simulation of Land-Use and Land-Cover Change: A Review , 2003 .

[11]  M. Kulldor,et al.  Prospective time-periodic geographical disease surveillance using a scan statistic , 2001 .

[12]  Yongwan Chun,et al.  Analyzing Space–Time Crime Incidents Using Eigenvector Spatial Filtering: An Application to Vehicle Burglary , 2014 .

[13]  P. Nijkamp,et al.  Continuous-Time Modeling with Spatial Dependence , 2010 .

[14]  Bent Natvig,et al.  Bayesian Hierarchical Space–time Modeling of Earthquake Data , 2007 .

[15]  Jonathan Raper,et al.  Development of a Geomorphological Spatial Model Using Object-Oriented Design , 1995, Int. J. Geogr. Inf. Sci..

[16]  Donna Peuquet,et al.  An Event-Based Spatiotemporal Data Model (ESTDM) for Temporal Analysis of Geographical Data , 1995, Int. J. Geogr. Inf. Sci..

[17]  J. Paul Elhorst,et al.  Dynamic spatial panels: models, methods, and inferences , 2012, J. Geogr. Syst..

[18]  Trisalyn A. Nelson,et al.  A review of quantitative methods for movement data , 2013, Int. J. Geogr. Inf. Sci..

[19]  Trisalyn A. Nelson,et al.  Toward a kinetic-based probabilistic time geography , 2014, Int. J. Geogr. Inf. Sci..

[20]  Donald G. Janelle,et al.  Geovisualization of Human Activity Patterns Using 3 D GIS : A Time-Geographic Approach , 2002 .

[21]  Shigeaki F. Hasegawa,et al.  Derivation of a yearly transition probability matrix for land-use dynamics and its applications , 2010, Landscape Ecology.

[22]  R. Assunção,et al.  Diffusion and prediction of Leishmaniasis in a large metropolitan area in Brazil with a Bayesian space–time model , 2001, Statistics in medicine.

[23]  Helen Couclelis,et al.  Ontologies of geographic information , 2010, Int. J. Geogr. Inf. Sci..

[24]  Li An,et al.  Annals of the Association of American Geographers Agent-based Modeling in Coupled Human and Natural Systems (chans): Lessons from a Comparative Analysis , 2022 .

[25]  Jiaqiu Wang,et al.  A Hybrid Framework for Space-Time Modeling of Environmental Data , 2011 .

[26]  Paul M. Torrens,et al.  High-resolution space–time processes for agents at the built–human interface of urban earthquakes , 2014, Int. J. Geogr. Inf. Sci..

[27]  M. Weisz Econometric Analysis Of Panel Data , 2016 .

[28]  Lung-fei Lee,et al.  Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large , 2008 .

[29]  Daniel G. Brown,et al.  Survival Analysis in Land Change Science: Integrating with GIScience to Address Temporal Complexities , 2008 .

[30]  David M Levinson,et al.  Markov Chain Model of Land Use Change in the Twin Cities , 2012 .

[31]  Risto Lehtonen,et al.  Multilevel Statistical Models , 2005 .

[32]  H R Huessy,et al.  Time and space. , 1978, The American journal of psychiatry.

[33]  Shahrokh Rouhani,et al.  Multivariate geostatistical approach to space‐time data analysis , 1990 .

[34]  John R. Hipp,et al.  Longitudinal Analysis for Continuous Outcomes: Random Effects Models and Latent Trajectory Models , 2004 .

[35]  V. Meentemeyer Geographical perspectives of space, time, and scale , 1989, Landscape Ecology.

[36]  E G Knox,et al.  The Detection of Space‐Time Interactions , 1964 .

[37]  Master Gardener,et al.  Mathematical games: the fantastic combinations of john conway's new solitaire game "life , 1970 .

[38]  Harry J. P. Timmermans,et al.  Incorporating activity-travel time uncertainty and stochastic space–time prisms in multistate supernetworks for activity-travel scheduling , 2014, Int. J. Geogr. Inf. Sci..

[39]  Atsushi Nara,et al.  Space–time representation and analytics , 2014, Ann. GIS.

[40]  Colin Robertson,et al.  STAMP: spatial–temporal analysis of moving polygons , 2007, J. Geogr. Syst..

[41]  Tomoki Nakaya,et al.  Analytical Data Transformations in Space–Time Region: Three Stories of Space–Time Cube , 2013 .

[42]  Bas C. van Fraassen,et al.  An Introduction To The Philosophy Of Time And Space , 1970 .

[43]  David A. Bennett,et al.  Agent‐based Modeling of Animal Movement: A Review , 2010 .

[44]  Robert Weibel,et al.  Movement similarity assessment using symbolic representation of trajectories , 2012, Int. J. Geogr. Inf. Sci..

[45]  Jarke J. van Wijk,et al.  Contour based visualization of vessel movement predictions , 2014, Int. J. Geogr. Inf. Sci..

[46]  Ulrich Frank,et al.  Multilevel Modeling , 2014, Business & Information Systems Engineering.

[47]  Alberto RibesAbstract,et al.  Multi agent systems , 2019, Proceedings of the 2005 International Conference on Active Media Technology, 2005. (AMT 2005)..

[48]  David Brosset,et al.  International Journal of Geographical Information Science Local and Global Spatio-temporal Entropy Indices Based on Distance- Ratios and Co-occurrences Distributions Local and Global Spatio-temporal Entropy Indices Based on Distance-ratios and Co-occurrences Distributions , 2022 .

[49]  L. Anselin Local Indicators of Spatial Association—LISA , 2010 .

[50]  I. Langner Survival Analysis: Techniques for Censored and Truncated Data , 2006 .

[51]  Ross Purves,et al.  How fast is a cow? Cross‐Scale Analysis of Movement Data , 2011, Trans. GIS.

[52]  M. Goodchild Prospects for a Space–Time GIS , 2013 .

[53]  M. Kwan Gender, the Home-Work Link, and Space-Time Patterns of Nonemployment Activities , 1999 .

[54]  Robert Gilmore Pontius,et al.  Comparison of Three Maps at Multiple Resolutions: A Case Study of Land Change Simulation in Cho Don District, Vietnam , 2011 .

[55]  Harvey J. Miller,et al.  Simulating visit probability distributions within planar space-time prisms , 2014, Int. J. Geogr. Inf. Sci..

[56]  Keith C. Clarke,et al.  A Self-Modifying Cellular Automaton Model of Historical Urbanization in the San Francisco Bay Area , 1997 .

[57]  L. An,et al.  Modeling human decisions in coupled human and natural systems : Review of agent-based models , 2012 .

[58]  Mark W. Horner,et al.  Probabilistic Potential Path Trees for Visualizing and Analyzing Vehicle Tracking Data , 2012 .

[59]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[60]  J. Paul Elhorst Spatial Panel Data Models , 2010 .

[61]  Luc Anselin,et al.  Spatial Externalities, Spatial Multipliers, And Spatial Econometrics , 2003 .

[62]  Monica Wachowicz,et al.  Exploring patterns of movement suspension in pedestrian mobility. , 2011, Geographical analysis.

[63]  Juan B. Valdés,et al.  Multivariate space - time analysis of PRE-STORM precipitation , 1994 .

[64]  I. Hinckfuss The existence of space and time , 1975 .

[65]  Joni A. Downs,et al.  Time-Geographic Density Estimation for Moving Point Objects , 2010, GIScience.

[66]  E. Spelke,et al.  Representations of space, time, and number in neonates , 2014, Proceedings of the National Academy of Sciences.

[67]  Atuq Eusebio Manga Quespi Pacha: un concepto andino de espacio y tiempo. , 1994 .

[68]  Orland Hoeber,et al.  Navigating spatio-temporal data with temporal zoom and pan in a multi-touch environment , 2014, Int. J. Geogr. Inf. Sci..

[69]  Julie Le Gallo,et al.  Space-Time Analysis of GDP Disparities among European Regions: A Markov Chains Approach: , 2004 .

[70]  Donna J. Peuquet,et al.  Representations of space and time , 2002 .

[71]  Stephan Winter,et al.  The elements of probabilistic time geography , 2011, GeoInformatica.

[72]  Shaowen Wang,et al.  HPABM: A Hierarchical Parallel Simulation Framework for Spatially‐explicit Agent‐based Models , 2009, Trans. GIS.

[73]  Dali Wang,et al.  A Space-Time Raster GIS Data Model for Spatiotemporal Analysis of Vegetation Responses to a Freeze Event , 2015, Trans. GIS.

[74]  Wenkai Li,et al.  Space-time analyses for forecasting future incident occurrence: a case study from Yosemite National Park using the presence and background learning algorithm , 2014, Int. J. Geogr. Inf. Sci..

[75]  M. Kwan Space-time and integral measures of individual accessibility: a comparative analysis using a point-based framework , 2010 .

[76]  Daniel G. Brown,et al.  Variations in development of exurban residential landscapes: timing, location, and driving forces , 2011 .

[77]  K. Seto,et al.  Advancing Land Change Modeling: Opportunities and Research Requirements , 2013 .

[78]  Mei-Po Kwan,et al.  Geovisualization of Human Hybrid Activity‐Travel Patterns , 2007, Trans. GIS.

[79]  B. Lenntorp Paths in space-time environments : a time-geographic study of movement possibilities of individuals , 1976 .

[80]  Martin Dijst,et al.  Space–Time Integration in a Dynamic Urbanizing World: Current Status and Future Prospects in Geography and GIScience , 2013 .

[81]  V. Marx Biology: The big challenges of big data , 2013, Nature.

[82]  D. Massey Space‐Time, ‘Science’ and the Relationship between Physical Geography and Human Geography , 1999 .

[83]  Shuang Yang,et al.  Comparative performance of logistic regression and survival analysis for detecting spatial predictors of land-use change , 2013, Int. J. Geogr. Inf. Sci..

[84]  Shih-Lung Shaw,et al.  Exploratory data analysis of activity diary data: a space-time GIS approach , 2011 .

[85]  David Butler,et al.  Space–Time Modeling of Grizzly Bears* , 2000 .

[86]  Aileen R. Buckley GEOGRAPHIC VISUALIZATION , 1998 .

[87]  Paul A. Longley,et al.  Handbook of applied spatial analysis: software tools, methods and applications, edited by M.M. Fischer and A. Getis , 2011 .

[88]  Kristopher J Preacher,et al.  Latent Growth Curve Modeling , 2008 .

[89]  D. Griffith Spatial Autocorrelation and Spatial Filtering , 2003 .

[90]  Tijs Neutens,et al.  Space-time research in GIScience , 2014, Int. J. Geogr. Inf. Sci..

[91]  Mei Po Kwan Beyond Space (As We Knew It): Toward Temporally Integrated Geographies of Segregation, Health, and Accessibility , 2013 .

[92]  K. Jones,et al.  Regional Variations in Voting at British General Elections, 1950–2001: Group-Based Latent Trajectory Analysis , 2009 .

[93]  Jin Chen,et al.  Developing land use scenario dynamics model by the integration of system dynamics model and cellular automata model , 2004, IGARSS 2004. 2004 IEEE International Geoscience and Remote Sensing Symposium.

[94]  Joseph Ying Jun Chow,et al.  Time-geographic relationships between vector fields of activity patterns and transport systems , 2015 .

[95]  Ningchuan Xiao,et al.  Assessing Activity Pattern Similarity with Multidimensional Sequence Alignment based on a Multiobjective Optimization Evolutionary Algorithm. , 2014, Geographical analysis.

[96]  D. Richardson Real-Time Space–Time Integration in GIScience and Geography , 2013, Annals of the Association of American Geographers. Association of American Geographers.

[97]  W. Tobler A Computer Movie Simulating Urban Growth in the Detroit Region , 1970 .

[98]  Kenneth A. Bollen,et al.  Latent curve models: A structural equation perspective , 2005 .

[99]  Kensy Cooperrider,et al.  The tangle of space and time in human cognition , 2013, Trends in Cognitive Sciences.

[100]  D. Peuquet It's About Time: A Conceptual Framework for the Representation of Temporal Dynamics in Geographic Information Systems , 1994 .

[101]  Yiannis Kamarianakis,et al.  Space-time modeling of traffic flow , 2002, Comput. Geosci..

[102]  NeXT Computer,et al.  Nextstep object‐oriented programming and the objective C language : 日本語版 , 1993 .

[103]  Harvey Goldstein,et al.  Multilevel Statistical Models: Goldstein/Multilevel Statistical Models , 2010 .

[104]  Jason Dykes,et al.  Facilitating Interaction for Geovisualization , 2005 .

[105]  Sergio J. Rey,et al.  STARS: Space-Time Analysis of Regional Systems , 2004 .

[106]  Torsten Hägerstraand WHAT ABOUT PEOPLE IN REGIONAL SCIENCE , 1970 .

[107]  Helle Rootzén,et al.  Space-time modeling of environmental monitoring data , 2004, Environmental and Ecological Statistics.

[108]  Space and Time: From Antiquity to Einstein and Beyond , 2006 .

[109]  Tijs Neutens,et al.  My space or your space? Towards a measure of joint accessibility , 2008, Comput. Environ. Urban Syst..

[110]  Danielle J. Marceau,et al.  Spatio‐Temporal Object‐Oriented Data Model for Disaggregate Travel Behavior , 2002, Trans. GIS.

[111]  Takanori Hirose,et al.  Preface to special issue , 2014, Brain Tumor Pathology.

[112]  Peter Nijkamp,et al.  Continuous-Time Modeling with Spatial Dependence , 2010 .

[113]  Eric M. Delmelle,et al.  Visualizing the impact of space-time uncertainties on dengue fever patterns , 2014, Int. J. Geogr. Inf. Sci..

[114]  Manfred M. Fischer,et al.  Handbook of Applied Spatial AnalysisSoftware Tools, Methods and Applications , 2010 .

[115]  Morton E. O'Kelly,et al.  A bootstrap based space–time surveillance model with an application to crime occurrences , 2008, J. Geogr. Syst..

[116]  Marc P. Armstrong,et al.  Temporality in Spatial Databases , 1988 .

[117]  M. N. Vrahatis,et al.  Preface Special issue , 2016 .

[118]  P. Guttorp,et al.  A space-time analysis of ground-level ozone data , 1994 .

[119]  N. Mantel The detection of disease clustering and a generalized regression approach. , 1967, Cancer research.

[120]  Ruojing W. Scholz,et al.  Detection of dynamic activity patterns at a collective level from large-volume trajectory data , 2014, Int. J. Geogr. Inf. Sci..

[121]  Gerhard Sorger,et al.  A Spatial-Temporal Model of Human Capital Accumulation , 2001, J. Econ. Theory.

[122]  D. Griffith,et al.  Modeling Network Autocorrelation in Space–Time Migration Flow Data: An Eigenvector Spatial Filtering Approach , 2011 .

[123]  Sergio J. Rey,et al.  Spatial Empirics for Economic Growth and Convergence , 2010 .

[124]  Charles Travis,et al.  Transcending the cube: translating GIScience time and space perspectives in a humanities GIS , 2014, Int. J. Geogr. Inf. Sci..

[125]  Manfred M. Fischer,et al.  Handbook of Applied Spatial Analysis , 2010 .

[126]  D. Nychka,et al.  Spatial patterns of probabilistic temperature change projections from a multivariate Bayesian analysis , 2007 .

[127]  Menno-Jan Kraak,et al.  A Visualization Environment for the Space-Time-Cube , 2004, SDH.

[128]  William Rand,et al.  Path dependence and the validation of agent‐based spatial models of land use , 2005, Int. J. Geogr. Inf. Sci..

[129]  E. Lambin,et al.  Land-Cover-Change Trajectories in Southern Cameroon , 2000 .

[130]  M. Kwan Gis methods in time‐geographic research: geocomputation and geovisualization of human activity patterns , 2004 .

[131]  Michael C. Carroll,et al.  Exploratory space-time analysis of local economic development , 2011 .

[132]  L. M. Berliner,et al.  Hierarchical Bayesian space-time models , 1998, Environmental and Ecological Statistics.

[133]  S. Simoens,et al.  Impact, regulation and health policy implications of physician migration in OECD countries. , 2004, Human resources for health.

[134]  J. Monahan,et al.  Quantifying Local Creation and Regional Transport Using a Hierarchical Space–Time Model of Ozone as a Function of Observed NOx, a Latent Space–Time VOC Process, Emissions, and Meteorology , 2011 .

[135]  Noam Shoval,et al.  Sequence Alignment as a Method for Human Activity Analysis in Space and Time , 2007 .

[136]  Shaowen Wang,et al.  A parallel agent-based model of land use opinions , 2011 .

[137]  Brian H. Spitzberg,et al.  Latent trajectory models for space‐time analysis: An application in deciphering spatial panel data , 2016 .

[138]  Harvey J. Miller,et al.  What about people in geographic information science? , 2003, Comput. Environ. Urban Syst..

[139]  T. Cresswell Geographic Thought: A Critical Introduction , 2013 .

[140]  Elinor Ostrom,et al.  Complexity of Coupled Human and Natural Systems , 2007, Science.

[141]  Manchun Li,et al.  Calibrating a cellular automata model for understanding rural–urban land conversion: a Pareto front-based multi-objective optimization approach , 2014, Int. J. Geogr. Inf. Sci..

[142]  Toby A Patterson,et al.  Classifying movement behaviour in relation to environmental conditions using hidden Markov models. , 2009, The Journal of animal ecology.

[143]  Daoqin Tong,et al.  Measuring Spatial Autocorrelation of Vectors , 2015 .

[144]  Alex Hagen,et al.  Fuzzy set approach to assessing similarity of categorical maps , 2003, Int. J. Geogr. Inf. Sci..

[145]  Di Wu,et al.  A representation framework for studying spatiotemporal changes and interactions of dynamic geographic phenomena , 2014, Int. J. Geogr. Inf. Sci..

[146]  Lung-fei Lee,et al.  Some recent developments in spatial panel data models , 2010 .

[147]  Hongbo Yu,et al.  A Space‐Time GIS Approach to Exploring Large Individual‐based Spatiotemporal Datasets , 2008, Trans. GIS.

[148]  Sang-Il Lee Correlation and Spatial Autocorrelation , 2016 .

[149]  B. Sansó,et al.  Venezuelan Rainfall Data Analysed by Using a Bayesian Space–time Model , 1999 .

[150]  Mark W. Horner,et al.  Voxel-based probabilistic space-time prisms for analysing animal movements and habitat use , 2014, Int. J. Geogr. Inf. Sci..

[151]  Ashton M. Shortridge,et al.  Exploring Complexity in a Human–Environment System: An Agent-Based Spatial Model for Multidisciplinary and Multiscale Integration , 2005 .

[152]  Samuel E. Bodily,et al.  A test of space-time arma modelling and forecasting of hotel data , 1990 .

[153]  William Rand,et al.  Exurbia from the bottom-up: Confronting empirical challenges to characterizing a complex system , 2008 .

[154]  May Yuan,et al.  Apply concepts of fluid kinematics to represent continuous space–time fields in temporal GIS , 2010, Ann. GIS.