IDEAS home Printed from https://ideas.repec.org/a/bla/istatr/v90y2022i2p237-258.html
   My bibliography  Save this article

Directions Old and New: Palaeomagnetism and Fisher (1953) Meet Modern Statistics

Author

Listed:
  • Janice L. Scealy
  • David Heslop
  • Jia Liu
  • Andrew T. A. Wood

Abstract

Most modern articles in the palaeomagnetism literature are based on statistics developed by Fisher's 1953 paper ‘Dispersion on a sphere’, which assumes independent and identically distributed (iid) spherical data. However, palaeomagnetic sample designs are usually hierarchical, where specimens are collected within sites and the data are then combined across sites to calculate an overall mean direction for a geological formation. The specimens within sites are typically more similar than specimens between different sites, and so the iid assumptions fail. This article has three principal goals. The first is to review, contrast and compare both the statistics and geophysics literature on the topic of analysis methods for clustered data on spheres. The second is to present a new hierarchical parametric model, which avoids the unrealistic assumption of rotational symmetry in Fisher's 1953 paper ‘Dispersion on a sphere’ and may be broadly useful in the analysis of many palaeomagnetic datasets. To help develop the model, we use publicly available data as a case study collected from the Golan Heights volcanic plateau. The third goal is to explore different methods for constructing confidence regions for the overall mean direction based on clustered data. Two bootstrap confidence regions that we propose perform well and will be especially useful to geophysics practitioners.

Suggested Citation

  • Janice L. Scealy & David Heslop & Jia Liu & Andrew T. A. Wood, 2022. "Directions Old and New: Palaeomagnetism and Fisher (1953) Meet Modern Statistics," International Statistical Review, International Statistical Institute, vol. 90(2), pages 237-258, August.
  • Handle: RePEc:bla:istatr:v:90:y:2022:i:2:p:237-258
    DOI: 10.1111/insr.12481
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/insr.12481
    Download Restriction: no

    File URL: https://libkey.io/10.1111/insr.12481?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. Samanta, Mayukh & Welsh, A.H., 2013. "Bootstrapping for highly unbalanced clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 70-81.
    2. Denis Larocque & Jaakko Nevalainen & Hannu Oja, 2007. "A weighted multivariate sign test for cluster-correlated data," Biometrika, Biometrika Trust, vol. 94(2), pages 267-283.
    3. J. L. Scealy & A. H. Welsh, 2017. "A Directional Mixed Effects Model for Compositional Expenditure Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 24-36, January.
    4. Jaakko Nevalainen & Denis Larocque & Hannu Oja, 2007. "A weighted spatial median for clustered data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 355-379, February.
    5. Stéphane Guerrier & Elise Dupuis-Lozeron & Yanyuan Ma & Maria-Pia Victoria-Feser, 2019. "Simulation-Based Bias Correction Methods for Complex Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 146-157, January.
    6. C. A. Field & A. H. Welsh, 2007. "Bootstrapping clustered data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 369-390, June.
    7. Janice L. Scealy & Andrew T. A. Wood, 2021. "Analogues on the Sphere of the Affine-Equivariant Spatial Median," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1457-1471, July.
    8. Jaakko Nevalainen & Denis Larocque & Hannu Oja, 2007. "A weighted spatial median for clustered data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 355-379, February.
    Full references (including those not matched with items on IDEAS)

    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. Haataja, Riina & Larocque, Denis & Nevalainen, Jaakko & Oja, Hannu, 2009. "A weighted multivariate signed-rank test for cluster-correlated data," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1107-1119, July.
    2. O’Shaughnessy, P.Y. & Welsh, A.H., 2018. "Bootstrapping longitudinal data with multiple levels of variation," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 117-131.
    3. Majumdar, Subhabrata & Chatterjee, Snigdhansu, 2022. "On weighted multivariate sign functions," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    4. Wen Shi & Xi Chen & Jennifer Shang, 2019. "An Efficient Morris Method-Based Framework for Simulation Factor Screening," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 745-770, October.
    5. David Roodman & James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2019. "Fast and wild: Bootstrap inference in Stata using boottest," Stata Journal, StataCorp LP, vol. 19(1), pages 4-60, March.
    6. María Dolores Esteban & María José Lombardía & Esther López-Vizcaíno & Domingo Morales & Agustín Pérez, 2020. "Small area estimation of proportions under area-level compositional mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 793-818, September.
    7. Jaakko Nevalainen & Somnath Datta & Hannu Oja, 2014. "Inference on the marginal distribution of clustered data with informative cluster size," Statistical Papers, Springer, vol. 55(1), pages 71-92, February.
    8. Coisnon, Thomas & Rousselière, Damien & Rousselière, Samira, 2018. "Information on biodiversity and environmental behaviors: a European study of individual and institutional drivers to adopt sustainable gardening practices," Working Papers 272611, Institut National de la recherche Agronomique (INRA), Departement Sciences Sociales, Agriculture et Alimentation, Espace et Environnement (SAE2).
    9. Robin Van Oirbeek & Emmanuel Lesaffre, 2018. "An Investigation of the Discriminatory Ability of the Clustering Effect of the Frailty Survival Model," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 6(3), pages 87-98, April.
    10. David Roodman, 2023. "Large-Scale Education Reform in General Equilibrium: Regression Discontinuity Evidence from India: Comment," Papers 2303.11956, arXiv.org, revised Sep 2023.
    11. Mathieu Bunel & Yannick L'Horty, 2011. "Les effets des aides publiques aux Hôtels Cafés Restaurants et leurs interactions," Working Papers halshs-00658460, HAL.
    12. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    13. Rainer Dyckerhoff & Christophe Ley & Davy Paindaveine, 2014. "Depth-Based Runs Tests for bivariate Central Symmetry," Working Papers ECARES ECARES 2014-03, ULB -- Universite Libre de Bruxelles.
    14. Orth, Walter, 2012. "The predictive accuracy of credit ratings: Measurement and statistical inference," International Journal of Forecasting, Elsevier, vol. 28(1), pages 288-296.
    15. Joscha Krause & Jan Pablo Burgard & Domingo Morales, 2022. "Robust prediction of domain compositions from uncertain data using isometric logratio transformations in a penalized multivariate Fay–Herriot model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(1), pages 65-96, February.
    16. Mary Ying-Fang Wang & Paul Tuss & Lihong Qi, 2019. "Augmented Weighted Estimators Dealing with Practical Positivity Violation to Causal inferences in a Random Coefficient Model," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 447-467, June.
    17. Salibian-Barrera, Matias & Van Aelst, Stefan & Yohai, Víctor J., 2016. "Robust tests for linear regression models based on τ-estimates," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 436-455.
    18. Jaakko Nevalainen & Denis Larocque & Hannu Oja, 2007. "A weighted spatial median for clustered data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 355-379, February.
    19. Damien Rousselière & Thomas Coisnon & Anne Musson & Samira Rousselière, 2023. "Following Pauline advice? A short note on moderate alcohol consumption and subjective well‐being in Europe," Agribusiness, John Wiley & Sons, Ltd., vol. 39(4), pages 1333-1351, October.
    20. Janie McDonald & Patrick D. Gerard & Christopher S. McMahan & William R. Schucany, 2016. "Exact-Permutation-Based Sign Tests for Clustered Binary Data Via Weighted and Unweighted Test Statistics," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 698-712, December.

    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:bla:istatr:v:90:y:2022:i:2:p:237-258. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/isiiinl.html .

    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.