IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v75y2021i4p482-499.html
   My bibliography  Save this article

Resolving the ambiguity of random‐effects models with singular precision matrix

Author

Listed:
  • Woojoo Lee
  • Hans‐Peter Piepho
  • Youngjo Lee

Abstract

Random walks, intrinsic autoregression, state‐space models, smoothing splines, and so on have been widely used in various areas of statistics. However, practitioners wanting to fit these models using existing packages for random‐effects models are often faced with the difficulty that their covariance matrices are not uniquely determined. Unfortunately, different specifications of the model lead to different covariance structures, giving different analyses. Even if we make a decision on specification it is not immediately obvious how to make inferences from these models. There have been various suggestions on how to overcome such difficulties. However, they differ, implying that there is as yet no agreed remedy. In this article we provide a unified view on these alternatives and show how the analysis can be made invariant with respect to the choice of covariance by inclusion of a suitable set of covariates. Several examples are used to illustrate the approach.

Suggested Citation

  • Woojoo Lee & Hans‐Peter Piepho & Youngjo Lee, 2021. "Resolving the ambiguity of random‐effects models with singular precision matrix," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(4), pages 482-499, November.
    • Handle: RePEc:bla:stanee:v:75:y:2021:i:4:p:482-499
    DOI: 10.1111/stan.12244
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/stan.12244
    Download Restriction: no
    File URL: https://libkey.io/10.1111/stan.12244?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. Ying C. MacNab & Patrick J. Farrell & Paul Gustafson & Sijin Wen, 2004. "Estimation in Bayesian Disease Mapping," Biometrics, The International Biometric Society, vol. 60(4), pages 865-873, December.
    2. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    3. Arũnas P. Verbyla & Brian R. Cullis & Michael G. Kenward & Sue J. Welham, 1999. "The Analysis of Designed Experiments and Longitudinal Data by Using Smoothing Splines," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 269-311.
    4. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    5. Youngjo Lee & Myoungjin Jang & Woojoo Lee, 2011. "Prediction interval for disease mapping using hierarchical likelihood," Computational Statistics, Springer, vol. 26(1), pages 159-179, March.
    6. M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.
    7. J. Besag & D. Higdon, 1999. "Bayesian analysis of agricultural field experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 691-746.
    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. Lee, Dae-Jin & Durbán, María, 2009. "P-spline anova-type interaction models for spatio-temporal smoothing," DES - Working Papers. Statistics and Econometrics. WS ws093312, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Guisinger, Amy Y. & Owyang, Michael T. & Soques, Daniel, 2024. "Industrial Connectedness and Business Cycle Comovements," Econometrics and Statistics, Elsevier, vol. 29(C), pages 132-149.
    3. Cabral, Celso Rômulo Barbosa & da-Silva, Cibele Queiroz & Migon, Helio S., 2014. "A dynamic linear model with extended skew-normal for the initial distribution of the state parameter," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 64-80.
    4. Antolín-Díaz, Juan & Drechsel, Thomas & Petrella, Ivan, 2024. "Advances in nowcasting economic activity: The role of heterogeneous dynamics and fat tails," Journal of Econometrics, Elsevier, vol. 238(2).
    5. Xiaojun Mao & Somak Dutta & Raymond K. W. Wong & Dan Nettleton, 2020. "Adjusting for Spatial Effects in Genomic Prediction," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(4), pages 699-718, December.
    6. Rojas, Helder & Dias, David, 2021. "Transfer of macroeconomic shocks in stress tests modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    7. Lihui Zhao & Tom Chen & Vladimir Novitsky & Rui Wang, 2021. "Joint penalized spline modeling of multivariate longitudinal data, with application to HIV‐1 RNA load levels and CD4 cell counts," Biometrics, The International Biometric Society, vol. 77(3), pages 1061-1074, September.
    8. Chiranjit Dutta & Nalini Ravishanker & Sumanta Basu, 2022. "Modeling Multivariate Positive-Valued Time Series Using R-INLA," Papers 2206.05374, arXiv.org, revised Jul 2022.
    9. Ruiz-Cárdenas, Ramiro & Krainski, Elias T. & Rue, Håvard, 2012. "Direct fitting of dynamic models using integrated nested Laplace approximations — INLA," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1808-1828.
    10. Helder Rojas & David Dias, 2018. "Transmission of Macroeconomic Shocks to Risk Parameters: Their uses in Stress Testing," Papers 1809.07401, arXiv.org, revised May 2019.
    11. Areti Boulieri & Silvia Liverani & Kees Hoogh & Marta Blangiardo, 2017. "A space–time multivariate Bayesian model to analyse road traffic accidents by severity," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(1), pages 119-139, January.
    12. Donald, Margaret & Alston, Clair L. & Young, Rick R. & Mengersen, Kerrie L., 2011. "A Bayesian analysis of an agricultural field trial with three spatial dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3320-3332, December.
    13. Iseringhausen, Martin, 2020. "The time-varying asymmetry of exchange rate returns: A stochastic volatility – stochastic skewness model," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 275-292.
    14. Lee, Dae-Jin & Durbán, María, 2008. "Smooth-car mixed models for spatial count data," DES - Working Papers. Statistics and Econometrics. WS ws085820, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Marc K. Francke & Alex Minne, 2017. "The Hierarchical Repeat Sales Model for Granular Commercial Real Estate and Residential Price Indices," The Journal of Real Estate Finance and Economics, Springer, vol. 55(4), pages 511-532, November.
    16. Dani Gamerman & Thiago Rezende Santos & Glaura C. Franco, 2013. "A Non-Gaussian Family Of State-Space Models With Exact Marginal Likelihood," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 625-645, November.
    17. Nima Nonejad, 2019. "Has the 2008 financial crisis and its aftermath changed the impact of inflation on inflation uncertainty in member states of the european monetary union?," Scottish Journal of Political Economy, Scottish Economic Society, vol. 66(2), pages 246-276, May.
    18. Nicole H. Augustin & Stefan Lang & Monica Musio & Klaus Von Wilpert, 2007. "A spatial model for the needle losses of pine‐trees in the forests of Baden‐Württemberg: an application of Bayesian structured additive regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(1), pages 29-50, January.
    19. Youngjo Lee & Myoungjin Jang & Woojoo Lee, 2011. "Prediction interval for disease mapping using hierarchical likelihood," Computational Statistics, Springer, vol. 26(1), pages 159-179, March.
    20. Oksana Bollineni‐Balabay & Jan van den Brakel & Franz Palm & Harm Jan Boonstra, 2017. "Multilevel hierarchical Bayesian versus state space approach in time series small area estimation: the Dutch Travel Survey," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1281-1308, October.

    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:stanee:v:75:y:2021:i:4:p:482-499. 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: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    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.