Skip to main content

Categorical Data and Choice Analysis in a Spatial Context

  • Conference paper
Optimization and Discrete Choice in Urban Systems

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 247))

Abstract

This paper provides a comprehensive review of the techniques available for categorical data and discrete choice analysis in a spatial context. The first half of the paper reviews the class of models known as generalized linear models including log-linear models, linear logit regression models and latent class models. The second half of the paper focusses on techniques that may be used for categorical spatial choice analysis including utility-based models, multiattribute preference models and heuristic choice techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Aitkin, M., 1979, A Simultaneous Test Procedure for Contingency Table Models, Applied Statistics 28, 233–242.

    Article  Google Scholar 

  • Amemiyar v., 1976, Specification and Estimation of a Multinominal Logit Model, Technical Report 211, Institute of Mathematical Studies in the Social Sciences, Stanford University, Stanford, CA.

    Google Scholar 

  • Arminger, G., 1982, Klassische Anwendungen Verallgemeinenter Linearer Modelle in der Empirischen Sozialforchung, FB 6, Universität-Gesamthochschule Wuppertal (mimeographed).

    Google Scholar 

  • Arminger, G., 1983, Regressionsmodelle in der Exponentielle Familie, Arbeitspapiers des Fachbereichs Wirtschaftswissenschaft der Universität-Gesamthochschule Wuppertal, 18.

    Google Scholar 

  • Arminger, G., 1984, Analysis of Qualitative Individual Data of Latent Class Models with Generalised Linear Models, in Measuring the Unmeasurable, Nijkamp, P., Heitner, H. and Wrigley, N. (Eds.), Martinus Nijhoff, The Hague.

    Google Scholar 

  • Aufhauser, E., 1984, Log-lineare Modelle und Ihre Anwendung zur Analyse Räumlicher Interaktionsmatrizen, MA Thesis, Department of Geography, University of Vienna.

    Google Scholar 

  • Aufhauser, E. and Fischer, M.M., 1984, Log-linear Modelling and Spatial Analysis, paper presented at the 24th European Regional Science Conference, Milan.

    Google Scholar 

  • Bahrenberg, G., Fischer, M.M. and Nijkamp, P. (Eds.), 1984, Recent Developments In Spatial Data Analysist Methodology, Measurement, Models, Gower, Aldershot.

    Google Scholar 

  • Bartholomew, P.J., 1983, Latent Variable Models for Ordered Categorical Data, Journal of Econometrics 22, 229–243.

    Article  Google Scholar 

  • Ben-Akiva, M.E., 1974, Structure of Passenger Travel Demand Models, Transportation Research Record 526, 26–42.

    Google Scholar 

  • Ben-Akiva, M.E. and Lerman, S.R., 1979, Disaggregate Travel and Mobility Choice Models and Measures of Accessibility, in Behavioural Travel Modelling, Hensher, D.A. and Stopher, P.R. (Eds.), Croom Helm, London, 654–679.

    Google Scholar 

  • Bishop, Y.M.M., Fienberg, S.E. and Holland, P.W., 1976, Discrete Multivariate Analysis: Theory and Practice, 2nd Edition, MIT Press, Cambridge, MA.

    Google Scholar 

  • Brown, M.B., 1976, Screening Effects in Multidimensional Contingency Tables, Applied Statistics 25, 37–46.

    Article  Google Scholar 

  • Burnett, P. and Hanson, S., 1979, A Rationale for an Alternative Mathematical Paradigm for Movement as Complex Human Behaviour, Transportation Research Record 723, 11–24.

    Google Scholar 

  • Carpenter, S. and Jones, P. (Eds.), 1983, Recent Advances in Travel Demand Analysis, Gower, Aldershot.

    Google Scholar 

  • Chatfield, C. and Goodhartr G., 1975, Results Concerning Brand Choice, Journal of Marketing Research 12, 110–113.

    Article  Google Scholar 

  • Clark, W.A.V., 1983, Structures for Research on the Dynamics of Residential Search, in Evolving Geographical Structures, Griffith, D.A. and Lea, A.C. (Eds.), Martinus Nijhoff, The Hague, 372–397.

    Google Scholar 

  • Clark, W.A.V. and Cadwaller, M.T., 1973, Residential Preferences: An Alternative View of Intra-urban Space, Environment and Planning A, 5, 693–703.

    Article  Google Scholar 

  • Clark, W.A.V. and Smith, T.R., 1982, Housing Market Search Behaviour and Expected utility Theorv, Environment and Planning A, 14, 717–737.

    Article  Google Scholar 

  • Coleman, J.S., 1981, Longitudinal Data Analysis, Basic Books, New York.

    Google Scholar 

  • Daganzo, C. F. and Schoenfeld, L., 1978, CHOMP User’s Manual, Research Report UCB-ITS-RR-78-7, Institute of Transportation Studies, University of California at Berkelev, CA.

    Google Scholar 

  • Daganzo, C. F., 1979, Multinomial Probit. The Theory and Its Application to Demand Forecasting, Academic Press, New York.

    Google Scholar 

  • Damm, D., 1982, Parameters of Activity Behaviour for Use in Travel Analysis, Transportation Research A, 16, 135–138.

    Article  Google Scholar 

  • Dix, M.C., 1981, Structuring our Understanding of Travel Choices, in New Horizons in Travel Behaviour Research, Stopher, P.R., Meyburg, A.H. and Brög, W. (Eds.), Lexington Books, Lexington, MA, 89–109.

    Google Scholar 

  • Domencich, T.A. and McFadden, D., 1975, Urban Travel Demand: A Behavioural Analysis, North-Holland, Amsterdam.

    Google Scholar 

  • Fienberg, S.E., 1981, The Analysis of Cross-Classified Categorical Data, 2nd Edition, MIT Press, Cambridge, MA.

    Google Scholar 

  • Fienberg, S.E. and Meyer, M.M., 1983, Loglinear Models and Categorical Data Analysis with Psychometric and Econometric Applications, Journal of Econometrics, 22, 191–214.

    Article  Google Scholar 

  • Fingleton, B., 1981, Loglinear Modellinq of Geographical Contingency Tables, Environment and Planning A, 13, 1539–1551.

    Article  Google Scholar 

  • Fingleton, B., 1983, Log-Linear Models with Dependent Spatial Data, Environment and Planning A, 15, 801–813.

    Article  Google Scholar 

  • Finney, D.J., 1971, Probit Analysis, 3rd Edition, Cambridge University Press, London.

    Google Scholar 

  • Flowerdew, R. and Aitkin, M., 1982, A Method for Fitting the Gravity Model Based on the Poisson Distribution, Journal of Regional Science, 22, 191–202.

    Article  Google Scholar 

  • Fischer, M.M. and Maier, G., 1984, Discrete Choice and Labour Supply Modelling, paper presented at the Besancon Symposium of the IGU Working Group on Systems Analysis and Mathematical Models, August 21–23, 1984

    Google Scholar 

  • Fischer, M.M. and Nijkamp, P., 1984, Explanatory Discrete Spatial Data and Choice Analysis: A State-of-the-art Review, Research Memorandum, Department of Economics, Free University, Amsterdam.

    Google Scholar 

  • Gaudry, M.J.I, and Dagenais, M.G., 1979, The Dogit Model, Transportation Research B, 13, pp. 105–111.

    Article  Google Scholar 

  • Golob, Th. F., 1984, Analysing Activity Pattern Data Using Qualitative Multivariate Statistical Methods, in Measuring the Unmeasurable, Nijkamp, P., Heitner, H. and Wrigley, N. (Eds.), Martinus Nijhoff, The Hague.

    Google Scholar 

  • Goodman, L.A., 1973, The Analysis of Multidimensional Contingency Tables when some Variables are Posterior to Others: A Modified Path Analysis Approach, Biometrika 60, 179–192.

    Article  Google Scholar 

  • Goodman, L.A., 1978, Analysing Qualitative/Categorical Data. Log-Linear Models and Latent Structure Analysis, Addison-Wesley, London.

    Google Scholar 

  • Grizzle, J.E., Starmer, C.F. and Koch, G.G., 1969, Analysis of Categorical Data by Linear Models, Biometrics, 25, 489–504.

    Article  Google Scholar 

  • Haberman, S.J., 1978, Analysis of Qualitative Data. Vol. 1: Introductory Topics, Academic Press, New York.

    Google Scholar 

  • Haberman, S.J., 1979, Analysis of Qualitative Data, Vol. 2: New Developments, Academic Press, New York.

    Google Scholar 

  • Hägerstrand, T., 1970, What About People in Regional Science, Papers of the Regional Science Association, 24, 7–21.

    Google Scholar 

  • Halperin, W.C., 1984, The Analysis of Panel Data for Discreter Choices, in Measuring the Unmeasurable, Nijkamp, P., Leitner, H. and Wrigley, N. (Eds.), Martinus Nijhoff, The Hague.

    Google Scholar 

  • Hannan, M.T. and Tuma, N.B., 1984, Dynamic Analysis of Qualitative Variables: Applications to Organizational Demography, in Measuring the Unmeasurable, Nijkamp, P., Leitner, H. and Wrigley, N. (Eds.), Martinus Nijhoff, The Hague.

    Google Scholar 

  • Hartgen, D.T., 1974, Attitudinal and Situational Variables Influencing Urban Mode Choice, Transportation, 3, 377–392.

    Article  Google Scholar 

  • Hausman, J.A. and Wise, D.A., 1978, A Conditional Probit Model for Qualitative Choice, Econometrica, 46, 403–426.

    Article  Google Scholar 

  • Heckman, J.J., 1978, Dummy Endogenous Variables in a Simultaneous Equation System, Econometrica, 46, 931–959.

    Article  Google Scholar 

  • Heckman, J.J., 1978, Statistical Models for Discrete Panel Data, in Structural Analysis of Discrete Data with Econometric Applications, Manski, C.F. and McFadden, D. (Eds.), MIT Press, Cambridge, MA, 114–178.

    Google Scholar 

  • Hensher, D.A. and Johnson, L.w., 1981, Applied Discrete Choice Modelling, Croom Helm, London.

    Google Scholar 

  • Hensher, D.A. and Stopher, P.R. (Eds.), 1979, in Behavioural Travel Modelling, Croom Helm, London.

    Google Scholar 

  • Horowitz, J.L., 1984, Random Utility Models as Practical Tools of Travel Demand Analysis, in Transportation and Mobility in an Era of Transition, Jansen, G.R.M., Nijkamp, P. and Ruijgrok, C. (Eds.).

    Google Scholar 

  • Hutchinson, B.G., Contingency Table Analysis and Urban Travel Accounts, this volume

    Google Scholar 

  • Issaev, B., Nijkamp, P., Rietveld, P. and Snickars, F. (Eds.), 1982, in Multi-regional Economic Modelling: Practice and Prospect, North-Holland, Amsterdam.

    Google Scholar 

  • Johansson, B. and Nijkamp, P., 1984, Analysis of Episodes in Urban Event Histories, Working Paper, International Institute for Applied Systems Analysis, Laxenburg, Austria.

    Google Scholar 

  • Johnson, L. and Hensher, D., 1982, Application of Multinomial Probit to a Two-period Panel Data Set, Transportation Research A, 16, 457–464.

    Article  Google Scholar 

  • Koppelman, F.S. and Pas, E.I., 1984, Travel-activity Behaviour in Time and Space: Methods for Representation and Analysis, in Measuring the Unmeasurable, Nijkamp, P., Leitner, H. and Wrigley, N. (Eds.), Martinus Nijhoff, The Hague.

    Google Scholar 

  • Koppelman, F.S. and Rose, G., Geographic Transfer of Travel Choice Models: Evaluation and Procedures, this volume.

    Google Scholar 

  • Leonardi, G., 1983, An Optimal Control Representation of a Stochastic Multistage-multiactor Choice process, in Evolving Geographical Structures, Griffith, D.A. and Lea, A.C. (Eds.), Martinus Nijhoff, The Hague, 62–72.

    Google Scholar 

  • Lerman, S., 1979, The Use of Disaggregate Choice Models in Semi-Markov Process Models of Trip Chaining Behaviour, Transportation Science, 13, 273–291.

    Article  Google Scholar 

  • Lerman, S., Random Utility Models of Spatial Choice, this volume

    Google Scholar 

  • Lierop, W.J.F. van and Nijkamp, P., 1982, Disaggregate Models of Choice in a Spatial Context, Sistemi Urbani, 3, 331–368.

    Google Scholar 

  • Lierop, W.J.F. van and Rima, A., 1984, Trends and Prospects of Qualitative Disaggregate Spatial Choice Models, in Measuring the Unmeasurable, Nijkamp, P., Leitner, H. and Wrigley, N. (Eds.), Martinus Nijhoff, The Hague.

    Google Scholar 

  • Lierop, W.J.F. van and Nijkamp, P., 1984a, Perspectives of Dissagregate Choice Models on the Housing Market, in Discrete Spatial Choice Models, Pitfield, D.A. (Ed.), Pion, London, 141–162.

    Google Scholar 

  • Lierop, W.J.F. van and Nijkamp, P., 1984b, Disaggregate Residential Choice Models: Review and Case Study, Research Memorandum, Department of Economics, Free University, Amsterdam, (mimeoqraphed).

    Google Scholar 

  • Lierop, W.J.F. van, Residential Mobility With a Probit Model, this volume.

    Google Scholar 

  • Longley, P.A., 1984, Discrete Choice Modellinq and Complex Spatial Choice: An Overview, in Recent-Developments in Spatial Data Analysis: Methodology, Measurement, Models, Bahrenberg, G., Fischer, M.M. and Nijkamp, P. (Eds.), Gower, Aldershot, 375–392.

    Google Scholar 

  • Louviere, J.J. and Meyer, R.J., 1981, A Composite Attitude-Behaviour Model of Traveler Decision Making, Transportation Research B, 15, 411–420.

    Article  Google Scholar 

  • Manheim, M.L., 1979, Fundmentals of Transportation Systems Analysis, MIT Press, Cambridge, MA.

    Google Scholar 

  • Manski, CF., 1981, Structural Models for Discrete Data: The Analysis of Discrete Choice, in Sociological Methodology 1981, Leinhardt, S. (Ed.), Jossey-Bass, San Francisco, 58–109.

    Google Scholar 

  • Manski, C.F. and McFadden, D. (Eds.), 1981a, in Structural Analysis of Discrete Data with Econometric Applications, MIT Press, Cambridge, MA.

    Google Scholar 

  • Manski, C.F. and McFadden, D., 1981b, Alternative Estimators and Sample Designs for Discrete Choice Analysis, in Structural Analysis of Discrete Data with Econometric Applications, Manski, C.F. and McFadden, D. (Eds.), MIT Press, Cambridge, MA, 2–50.

    Google Scholar 

  • McCullaqh, P., 1980, Regression Models for Ordinal Data, Journal of the Royal Statistical Society B, 42.

    Google Scholar 

  • McCullaqh, P. and Neider, J.A., 1983, Generalized Linear Models, Chapman and Hall, London.

    Google Scholar 

  • McFadden, D., 1978, Modelling the Choice of Residential Location, in Spatial Interaction Theory and Planning Models, Karlqvist, A., Lundqvist, L., Snickars, F. and Weinbull, J.W. (Eds.), North-Holland, Amsterdam, 75–96.

    Google Scholar 

  • Miyao, T. and Shapiro, P., 1981, Discrete Choice and Variable Returns to Scale, International Economic Review, 22, 257–273.

    Article  Google Scholar 

  • Monkman, N. and Shortreed, J., Transport Impacts of Changing Household Structure, this volume

    Google Scholar 

  • Muthén, B., 1979, A Structural Probit Model with Latent Variables, Journal of the American Statistical Association 74, 807–811.

    Google Scholar 

  • Muthén, B., 1983, Latent Variable Structural Equation Modelling with Categorical Data, Journal of Econometrics, 22, 43–65.

    Article  Google Scholar 

  • Neider, J.A., 1974, Log-Linear Models for Contingency Tables: A Generalization of Classical Least Squares, Applied Statistics 23, 323–329.

    Article  Google Scholar 

  • Neider, J.A., 1984, Statistical Models for Qualitative Data, in Measuring the Unmeasurable, Niikamp, P., Leitner, H. and Wrigley, N. (Eds.), Martinus Nijhoff, The Haque.

    Google Scholar 

  • Neider, J.A. and Wedderburn, R.W.M., 1972, General Linear Models, Journal of the Royal Statistical Society A, 135, 370–384.

    Article  Google Scholar 

  • Nerlove, A. and Press, S.J., 1973, Univariate and Multivariate Log-linear and Logistic Models, Technical Report R-1306-EDA/NIH, Rand Corporation, Santa Monica, CA.

    Google Scholar 

  • Nijkamp, P., Leitner, H. and Wrigley, N. (Eds.), 1984, in Measuring the Unmeasurable, Martinus Nijhoff, The Hague.

    Google Scholar 

  • O’Brien, L.G. and Wrigley, N., 1984, A Generalized Linear Models Approach to Categorical Data Analysis, in Recent Developments in Spatial Data Analysis: Methodology, Measurement, Models, Bahrenberg, G., Fischer, M.M. and Nijkamp, P. (Eds.), Gower, Aldershot, 231–252.

    Google Scholar 

  • Odland, J. and Barff, R., 1982, A Statistical Model for the Development of Spatial Patterns: Applications to the Spread of Housing Deterioration, Geographical Analysis, 14, 327–339.

    Google Scholar 

  • Ortuzar, J.D. and Donoso, P.C.F., Modal Choice Modelling for Several Alternatives: Application of Disaqqregate Choice Models in Santiago, Chile, this volume.

    Google Scholar 

  • Richards, M.G. and Ben-Akiva, M., 1975, A Disaggregate Travel Demand Model, Saxon House, Farnborouqh.

    Google Scholar 

  • Roberts, F.S., 1979, Measurement Theory with Applications to Decisionmaking, Addison-Wesley, Reading, MA.

    Google Scholar 

  • Roqerson, P., 1983, The Effects of Job Search and Competition on unemployment and Vacancies in Reqional Labor Markets, in Evolving Geographical Structures, Griffin, D.A. and Lea, A.C. (Eds.), Martinus Nijhoff, The Hague, 349–371.

    Google Scholar 

  • Schmidt, P., 1981, Constraints on the Parameters in Simultaneous Tobit and Probit Models, in Structural Analysis of Discrete Data with Econometric Applications, Manski, CF. and McFadden, D. (Eds.), MIT Press, Cambridge, MA. and London.

    Google Scholar 

  • Sheffi, Y., Hall, R. and Daganzo, C.F., 1982, On the Estimation of the Multinomial Probit Model, Transportation Research A, 16, 447–456.

    Article  Google Scholar 

  • Sinha, H.K., Khanna, S.K. and Arora, M.G., Choice of Urban Transport Modes for Work Trips, this volume.

    Google Scholar 

  • Smith, T.R. and Lundberg, C.G., 1984, Psychological Foundations of Individual Choice Behaviour and a New Class of Decision Making Units, in Recent Developments in Spatial Data Analysis; Methodology, Measurement, Models, Bahrenberg, G., Fischer, M.M. and Nijkamp, P. (Eds.), Gower, Aldershot, 335–373.

    Google Scholar 

  • Sobel, K., 1980, Travel Demand Forecasting with the Nested Multinomial Logit Model, Transportation Research Record, 775, 48–55.

    Google Scholar 

  • Stopher, P.R. and Meyburg, A.H. (Eds.), 1976, in Behavioural Travel-Demand Models, Lexington Books, Lexington, MA.

    Google Scholar 

  • Thomson, R. and Baker, R.J., 1981, Composite Link Functions in Generalized Linear Models, Applied Statistics, 30, 125–131.

    Article  Google Scholar 

  • Timmermans, H.J.P., 1983, Decompositional Multiattribute Preference Models in Spatial Choice Analysis: A Review of Some Recent Developments, Progress in Human Geography.

    Google Scholar 

  • Timmermans, H.J.P., 1984, Decision Models for Predicting Preferences Among Multiattribute Choice Alternatives, in Recent Development in Spatial Analysis: Methodology, Measurement, Models, Bahrenberg, G., Fischer, M.M. and Nijkamp, P. (Eds.), Gower, Aldershot, 337–354.

    Google Scholar 

  • Tversky, A., 1972, Choice-by-Elimination, Journal of Mathematical Psychology, 9, 341–367.

    Article  Google Scholar 

  • Tversky, A. and Sattath, S., 1979, Preference Trees, Psychological Review, 86, 542–573.

    Article  Google Scholar 

  • Wedderburn, R.W.M., 1974, Ouasi-Likelihood Functions, Generalized Linear Models and the Gauss-Newton Method, Biometrika, 61, 439–447.

    Google Scholar 

  • Weibull, J.W., 1982, A Dynamic Model Framework for Analysis and Simulation of Housing Markets, paper IIASA Workshop on Spatial Choice Models in Housing, Transportation and Land Use Analysis, Laxenburg.

    Google Scholar 

  • Willekens, 1984, Log-linear Modelling of Spatial Interaction, Papers of the Regional Science Association, 52, 187–206.

    Article  Google Scholar 

  • Willenkens, F. and Guvenc, 1984, Hybrid Log-linear Models, in Measuring the Un-measureable, Nijkamp, P., Leitner, H. and Wrigley, N. (Eds.) Martinus Nijhoff, The Hague.

    Google Scholar 

  • Wrigley, N., 1976, An Introduction to the Use of Logit Models in Geography, Concepts and Techniques in Modern Geography 10, Geo Abstracts, Norwich.

    Google Scholar 

  • Wrigley, N., 1977, Probability Surface Mapping. An Introduction with Examples and Fortran Programmes, Concepts and Techniques in Modern Geography 16, Geo Abstracts, Norwich.

    Google Scholar 

  • Wriqlev, N., 1979, Developments in the Statistical Analysis of Categorical Data, Progress in Human Geography, 3, 315–355.

    Google Scholar 

  • Wrigley N., 1980, An Approach to the Modelling of Shop-Choice Patterns, in Geography and the Urban Environment, Herbert, D.T. and Johnston, R.J. (Eds.), John Wiley, Chichester, 45–85.

    Google Scholar 

  • Wrigley, N., 1981, Categorical Data Analysis, in Quantitative Geography: A British View, Wrigley, N. and Bennett, R.J. (Eds.), Routledge and Kegan Paul, 111-122.

    Google Scholar 

  • Wrigley, N., 1984a, Statistical Models for Discrete Choice Analysis, Proceedings of the 3rd European Conference on Theoretical and Quantitative Geography, Bahrenberg, G. and Fischer, M.M. (Eds.), Bremer Beiträge zur Geographie und Ramplanung 5, University of Bremen, Bremen.

    Google Scholar 

  • Wrigley, N., 1984b, Categorical Data Methods and Discrete Choice Modelling in Spatial Analysis: Some Directions for the 1980s, in Measuring the Unmeasurable, Nijkamp, P., Leitner, H. and Wrigley, N. (Eds.), Martinus Nijhoff, The Hague.

    Google Scholar 

  • Young, W., The Application of an Elimination-by-aspects Model in Urban Location Decisions, this volume

    Google Scholar 

  • Yu, W., 1979, A Prominence Theory of Choice, Working Paper 10, Regional Science Department, University of Pennsylvania, Philadelphia, PA.

    Google Scholar 

  • Zahavi, Y., The UMOT Project, Report DOT-RSPA-DPB-20-79-3, U.S. Department of Transportation, Office of Systems Engineering, Washington, D.C.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fischer, M.M., Nijkamp, P. (1985). Categorical Data and Choice Analysis in a Spatial Context. In: Hutchinson, B.G., Nijkamp, P., Batty, M. (eds) Optimization and Discrete Choice in Urban Systems. Lecture Notes in Economics and Mathematical Systems, vol 247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51020-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-51020-5_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15660-4

  • Online ISBN: 978-3-642-51020-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics