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Statistical Analysis of Spatial Data in the Presence of Missing Observations: A Methodological Guide and an Application to Urban Census Data


  • D A Griffith

    (Department of Geography, Syracuse University, Syracuse, NY 13244, USA)

  • R J Bennett

    (Department of Geography, London School of Economics, Houghton Street, London WC2A 2AE, England)

  • R P Haining

    (Department of Geography, University of Sheffield, Sheffield S10 2TN, England)


In this paper a simple introduction and guide to a widely applicable method for estimating missing data in fields of enquiry such as census maps or LANDSAT images are presented. The method given is a maximum likelihood procedure. This is argued to have the particularly favourable characteristics (1) that its distribution properties are known, (2) it is applicable both to regularly and to irregularly spaced observations, (3) it can handle different spatial configurations of missing cells, (4) it makes full use of the information contained in the known spatial data (particularly its spatial autocorrelation), (5) it has no systematic tendency to error, and (6) it provides ‘probability limits’. The algorithm is presented in the form of a simple tutorial guide. An example, of median income levels in Houston, is worked through in detail for missing cells in census data. The example is characterised by a variable mean and a general variance — covariance matrix.

Suggested Citation

  • D A Griffith & R J Bennett & R P Haining, 1989. "Statistical Analysis of Spatial Data in the Presence of Missing Observations: A Methodological Guide and an Application to Urban Census Data," Environment and Planning A, , vol. 21(11), pages 1511-1523, November.
  • Handle: RePEc:sae:envira:v:21:y:1989:i:11:p:1511-1523

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    Cited by:

    1. Giuseppe Arbia & Giuseppe Espa & Diego Giuliani, 2016. "Dirty spatial econometrics," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 56(1), pages 177-189, January.
    2. Thomas Keywood & Jörg Baten, 0. "Elite violence and elite numeracy in Europe from 500 to 1900 CE: roots of the divergence," Cliometrica, Springer;Cliometric Society (Association Francaise de Cliométrie), vol. 0, pages 1-71.
    3. Takahisa Yokoi, 2018. "Spatial lag dependence in the presence of missing observations," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 60(1), pages 25-40, January.
    4. J. Paul Elhorst & Katarina Zigova, 2011. "Evidence of Competition in Research Activity among Economic Department using Spatial Econometric Techniques," Working Paper Series of the Department of Economics, University of Konstanz 2011-04, Department of Economics, University of Konstanz.
    5. Takafumi Kato, 2020. "Likelihood-based strategies for estimating unknown parameters and predicting missing data in the simultaneous autoregressive model," Journal of Geographical Systems, Springer, vol. 22(1), pages 143-176, January.

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