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Influence diagnostics in Gaussian spatial linear models

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  • Miguel Angel Uribe-Opazo
  • Joelmir Andr� Borssoi
  • Manuel Galea

Abstract

Spatial linear models have been applied in numerous fields such as agriculture, geoscience and environmental sciences, among many others. Spatial dependence structure modelling, using a geostatistical approach, is an indispensable tool to estimate the parameters that define this structure. However, this estimation may be greatly affected by the presence of atypical observations in the sampled data. The purpose of this paper is to use diagnostic techniques to assess the sensitivity of the maximum-likelihood estimators, covariance functions and linear predictor to small perturbations in the data and/or the spatial linear model assumptions. The methodology is illustrated with two real data sets. The results allowed us to conclude that the presence of atypical values in the sample data have a strong influence on thematic maps, changing the spatial dependence structure.

Suggested Citation

  • Miguel Angel Uribe-Opazo & Joelmir Andr� Borssoi & Manuel Galea, 2012. "Influence diagnostics in Gaussian spatial linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(3), pages 615-630, July.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:3:p:615-630
    DOI: 10.1080/02664763.2011.607802
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    References listed on IDEAS

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    1. Manuel Galea & Gilberto Paula & Miguel Uribe-Opazo, 2003. "On influence diagnostic in univariate elliptical linear regression models," Statistical Papers, Springer, vol. 44(1), pages 23-45, January.
    2. Bo‐Cheng Wei & Yue‐Qing Hu & Wing‐Kam Fung, 1998. "Generalized Leverage and its Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 25-37, March.
    3. Manuel Galea & Jose Diaz-Garcia & Filidor Vilca, 2008. "Influence diagnostics in the capital asset pricing model under elliptical distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(2), pages 179-192.
    4. N. G. Cadigan & P. J. Farrell, 2002. "Generalized local influence with applications to fish stock cohort analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 469-483, October.
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    1. Giron Cima, Elizabeth & Freire da Rocha-Junior, Weimar & Angel Uribe-Opazo, Miguel & Henrique Dalposso, Gustavo, 2023. "An Analysis of the Gross Domestic Product of Municipalities: a Spatial Glance into the State of Paraná-Brazil," AGRIS on-line Papers in Economics and Informatics, Czech University of Life Sciences Prague, Faculty of Economics and Management, vol. 15(2), June.
    2. Letícia Ellen Dal Canton & Luciana Pagliosa Carvalho Guedes & Miguel Angel Uribe-Opazo, 2021. "Reduction of Sample Size in the Soil Physical-Chemical Attributes Using the Multivariate Effective Sample Size," Journal of Agricultural Studies, Macrothink Institute, vol. 9(1), pages 357-376, June.
    3. Carolina Marchant & Víctor Leiva & Francisco José A. Cysneiros & Juan F. Vivanco, 2016. "Diagnostics in multivariate generalized Birnbaum-Saunders regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2829-2849, November.
    4. R. S. Fagundes & M. A. Uribe-Opazo & M. Galea & L. P. C. Guedes, 2018. "Spatial Variability in Slash Linear Modeling with Finite Second Moment," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(2), pages 276-296, June.
    5. Manuel Galea & Patricia Giménez, 2019. "Local influence diagnostics for the test of mean–variance efficiency and systematic risks in the capital asset pricing model," Statistical Papers, Springer, vol. 60(1), pages 293-312, February.
    6. R.A.B. Assumpção & M.A. Uribe-Opazo & M. Galea, 2014. "Analysis of local influence in geostatistics using Student's t -distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2323-2341, November.
    7. D. T. Nava & F. De Bastiani & M. A. Uribe-Opazo & O. Nicolis & M. Galea, 2017. "Local Influence for Spatially Correlated Binomial Data: An Application to the Spodoptera frugiperda Infestation in Corn," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 540-561, December.
    8. Fernanda De Bastiani & Audrey Mariz de Aquino Cysneiros & Miguel Uribe-Opazo & Manuel Galea, 2015. "Influence diagnostics in elliptical spatial linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 322-340, June.

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