IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0146865.html
   My bibliography  Save this article

Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression

Author

Listed:
  • Yanguang Chen

Abstract

In geo-statistics, the Durbin-Watson test is frequently employed to detect the presence of residual serial correlation from least squares regression analyses. However, the Durbin-Watson statistic is only suitable for ordered time or spatial series. If the variables comprise cross-sectional data coming from spatial random sampling, the test will be ineffectual because the value of Durbin-Watson’s statistic depends on the sequence of data points. This paper develops two new statistics for testing serial correlation of residuals from least squares regression based on spatial samples. By analogy with the new form of Moran’s index, an autocorrelation coefficient is defined with a standardized residual vector and a normalized spatial weight matrix. Then by analogy with the Durbin-Watson statistic, two types of new serial correlation indices are constructed. As a case study, the two newly presented statistics are applied to a spatial sample of 29 China’s regions. These results show that the new spatial autocorrelation models can be used to test the serial correlation of residuals from regression analysis. In practice, the new statistics can make up for the deficiencies of the Durbin-Watson test.

Suggested Citation

  • Yanguang Chen, 2016. "Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-19, January.
    • Handle: RePEc:plo:pone00:0146865
    DOI: 10.1371/journal.pone.0146865
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0146865
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0146865&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0146865?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Yanguang Chen, 2015. "A New Methodology of Spatial Cross-Correlation Analysis," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-20, May.
    2. Yanguang Chen, 2012. "On the four types of weight functions for spatial contiguity matrix," Letters in Spatial and Resource Sciences, Springer, vol. 5(2), pages 65-72, July.
    3. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-174, January.
    4. Yanguang Chen, 2013. "New Approaches for Calculating Moran’s Index of Spatial Autocorrelation," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-14, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yanguang Chen, 2020. "New framework of Getis-Ord’s indexes associating spatial autocorrelation with interaction," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-25, July.
    2. Alderete Peralta, Ali & Balta-Ozkan, Nazmiye & Longhurst, Philip, 2022. "Spatio-temporal modelling of solar photovoltaic adoption: An integrated neural networks and agent-based modelling approach," Applied Energy, Elsevier, vol. 305(C).
    3. Vinicius Francisco Rofatto & Marcelo Tomio Matsuoka & Ivandro Klein & Maurício Roberto Veronez & Luiz Gonzaga da Silveira Junior, 2020. "On the effects of hard and soft equality constraints in the iterative outlier elimination procedure," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-29, August.
    4. Alejandro Colomo Magaña & Ernesto Colomo Magaña & Francisco D. Guillén-Gámez & Andrea Cívico Ariza, 2022. "Analysis of Prospective Teachers’ Perceptions of the Flipped Classroom as a Classroom Methodology," Societies, MDPI, vol. 12(4), pages 1-15, June.
    5. Haosu Zhao & Bart Julien Dewancker & Feng Hua & Junping He & Weijun Gao, 2020. "Restrictions of Historical Tissues on Urban Growth, Self-Sustaining Agglomeration in Walled Cities of Chinese Origin," Sustainability, MDPI, vol. 12(14), pages 1-29, July.
    6. YoungSeok Hwang & Jung-Sup Um & Stephan Schlüter, 2020. "Evaluating the Mutual Relationship between IPAT/Kaya Identity Index and ODIAC-Based GOSAT Fossil-Fuel CO 2 Flux: Potential and Constraints in Utilizing Decomposed Variables," IJERPH, MDPI, vol. 17(16), pages 1-18, August.
    7. Chaman Verma & Zoltán Illés & Veronika Stoffová & Viktória Bakonyi, 2020. "Opinion Prediction of Hungarian Students for Real-Time E-Learning Systems: A Futuristic Sustainable Technology-Based Solution," Sustainability, MDPI, vol. 12(16), pages 1-16, August.
    8. Chen, Yanguang, 2022. "Normalizing and classifying shape indexes of cities by ideas from fractals," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    9. María Gabriela Pizarro Inostroza & Francisco Javier Navas González & Vincenzo Landi & José Manuel León Jurado & Juan Vicente Delgado Bermejo & Javier Fernández Álvarez & María del Amparo Martínez Mart, 2020. "Software-Automatized Individual Lactation Model Fitting, Peak and Persistence and Bayesian Criteria Comparison for Milk Yield Genetic Studies in Murciano-Granadina Goats," Mathematics, MDPI, vol. 8(9), pages 1-21, September.
    10. Francisco D. Guillén-Gámez & María J. Mayorga-Fernández, 2020. "Identification of Variables that Predict Teachers’ Attitudes toward ICT in Higher Education for Teaching and Research: A Study with Regression," Sustainability, MDPI, vol. 12(4), pages 1-14, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yanguang Chen, 2020. "New framework of Getis-Ord’s indexes associating spatial autocorrelation with interaction," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-25, July.
    2. Abbas Alavirad & Sanhita Athawale, 2005. "The impact of the budget deficit on inflation in the Islamic Republic of Iran," OPEC Energy Review, Organization of the Petroleum Exporting Countries, vol. 29(1), pages 37-49, March.
    3. Orçun Moralı & Neslihan Yılmaz, 2022. "An Analysis of Spatial Dependence in Real Estate Prices," The Journal of Real Estate Finance and Economics, Springer, vol. 64(1), pages 93-115, January.
    4. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2005. "Testing for Long Memory and Nonlinear Time Series: A Demand for Money Study," Trinity Economics Papers tep20021, Trinity College Dublin, Department of Economics.
    5. Huang, Wei, 2019. "Forest condition change, tenure reform, and government-funded eco-environmental programs in Northeast China," Forest Policy and Economics, Elsevier, vol. 98(C), pages 67-74.
    6. PHILIP E.T. LEWIS & GARRY A. MacDONALD, 1993. "Testing for Equilibrium in the Australian Wage Equation," The Economic Record, The Economic Society of Australia, vol. 69(3), pages 295-304, September.
    7. Baffes, John & Chambers, Robert G., 1990. "Will the Latin American Countries ever Pay their Debt?," 1990 Annual meeting, August 5-8, Vancouver, Canada 270991, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    8. Campos, Julia & Ericsson, Neil R. & Hendry, David F., 1996. "Cointegration tests in the presence of structural breaks," Journal of Econometrics, Elsevier, vol. 70(1), pages 187-220, January.
    9. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    10. Maurer, Rainer, 1995. "Is economic growth a random walk?," Kiel Working Papers 677, Kiel Institute for the World Economy (IfW Kiel).
    11. Banerjee, A.N. & Magnus, J.R., 1996. "Testing the Sensitivity of OLS when the Variance Maxtrix is (Partially) Unknown," Other publications TiSEM e942b349-586c-4201-9228-0, Tilburg University, School of Economics and Management.
    12. Jan Lemmen & Sylvester Eijffinger, 1995. "The quantity approach to financial integration: The Feldstein-Horioka criterion revisited," Open Economies Review, Springer, vol. 6(2), pages 145-165, April.
    13. Breitung, Jorg, 2001. "Rank Tests for Nonlinear Cointegration," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 331-340, July.
    14. Perevyshin, Yu. & Skrobotov, A., 2017. "The Price Convergence of Individual Goods in the Russian Regions," Journal of the New Economic Association, New Economic Association, vol. 35(3), pages 71-102.
    15. Breitung, Jörg, 1998. "Canonical correlation statistics for testing the cointegration rank in a reversed order," SFB 373 Discussion Papers 1998,105, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    16. Podivinsky, Jan M. & King, Maxwell L., 2000. "The exact power envelope of tests for a unit root," Discussion Paper Series In Economics And Econometrics 0026, Economics Division, School of Social Sciences, University of Southampton.
    17. Ffion Carney, 2021. "Linking Loyalty Card Data to Public Transport Data to Explore Mobility and Social Exclusion in the Older Population," Sustainability, MDPI, vol. 13(11), pages 1-19, May.
    18. Guerreiro, Gertrudes & Caleiro, António, 2014. "A convergência espacial do conhecimento em Portugal [The spatial convergence of knowledge in Portugal]," MPRA Paper 56176, University Library of Munich, Germany.
    19. Larraz-Iribas, Beatriz & Alfaro-Navarro, Jose-Luis & Rodriguez-Aragon, Francisco, 2008. "Asymmetric Behaviour of Spanish Regional House Prices: A Multivariate Approach," The Journal of Economic Asymmetries, Elsevier, vol. 5(2), pages 81-104.
    20. Erdogdu, Erkan, 2007. "Electricity demand analysis using cointegration and ARIMA modelling: A case study of Turkey," Energy Policy, Elsevier, vol. 35(2), pages 1129-1146, February.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0146865. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.