IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/123698.html
   My bibliography  Save this paper

Modelling correlation matrices in multivariate data, with application to reciprocity and complementarity of child-parent exchanges of support

Author

Listed:
  • Zhang, Siliang
  • Kuha, Jouni
  • Steele, Fiona

Abstract

We define a model for the joint distribution of multiple continuous latent variables, which includes a model for how their correlations depend on explanatory variables. This is motivated by and applied to social scientific research questions in the analysis of intergenerational help and support within families, where the correlations describe reciprocity of help between generations and complementarity of different kinds of help. We propose an MCMC procedure for estimating the model which maintains the positive definiteness of the implied correlation matrices and describe theoretical results which justify this approach and facilitate efficient implementation of it. The model is applied to data from the UK Household Longitudinal Study to analyse ex- changes of practical and financial support between adult individuals and their noncoresident parents.

Suggested Citation

  • Zhang, Siliang & Kuha, Jouni & Steele, Fiona, 2024. "Modelling correlation matrices in multivariate data, with application to reciprocity and complementarity of child-parent exchanges of support," LSE Research Online Documents on Economics 123698, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:123698
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/123698/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. W. R. Gilks & N. G. Best & K. K. C. Tan, 1995. "Adaptive Rejection Metropolis Sampling Within Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 455-472, December.
    2. Frederick Wong, 2003. "Efficient estimation of covariance selection models," Biometrika, Biometrika Trust, vol. 90(4), pages 809-830, December.
    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. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    2. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility (Revised in May 2007, Handbook of Financial Time Series (Published in "Handbook of Financial Time Series" (eds T.G. Andersen, R.A. Davis, Jens-Peter Kreiss," CARF F-Series CARF-F-094, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Anindya Bhadra & Arvind Rao & Veerabhadran Baladandayuthapani, 2018. "Inferring network structure in non†normal and mixed discrete†continuous genomic data," Biometrics, The International Biometric Society, vol. 74(1), pages 185-195, March.
    4. Giraud Christophe & Huet Sylvie & Verzelen Nicolas, 2012. "Graph Selection with GGMselect," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(3), pages 1-52, February.
    5. Arbia, Giuseppe & Bramante, Riccardo & Facchinetti, Silvia & Zappa, Diego, 2018. "Modeling inter-country spatial financial interactions with Graphical Lasso: An application to sovereign co-risk evaluation," Regional Science and Urban Economics, Elsevier, vol. 70(C), pages 72-79.
    6. Bo Cai & David B. Dunson, 2006. "Bayesian Covariance Selection in Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 62(2), pages 446-457, June.
    7. Li, Kan & Luo, Sheng, 2019. "Bayesian functional joint models for multivariate longitudinal and time-to-event data," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 14-29.
    8. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    9. Shao, Wei & Guo, Guangbao & Meng, Fanyu & Jia, Shuqin, 2013. "An efficient proposal distribution for Metropolis–Hastings using a B-splines technique," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 465-478.
    10. Dimitris Korobilis, 2013. "Var Forecasting Using Bayesian Variable Selection," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 204-230, March.
    11. Anzarut, Michelle & Mena, Ramsés H., 2019. "A Harris process to model stochastic volatility," Econometrics and Statistics, Elsevier, vol. 10(C), pages 151-169.
    12. Hazan, Alon & Landsman, Zinoviy & E Makov, Udi, 2003. "Robustness via a mixture of exponential power distributions," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 111-121, February.
    13. Maura Mezzetti, 2012. "Bayesian factor analysis for spatially correlated data: application to cancer incidence data in Scotland," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(1), pages 49-74, March.
    14. David Chan & Robert Kohn & Chris Kirby, 2006. "Multivariate Stochastic Volatility Models with Correlated Errors," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 245-274.
    15. Xiao Li & Michele Guindani & Chaan S. Ng & Brian P. Hobbs, 2021. "A Bayesian nonparametric model for textural pattern heterogeneity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 459-480, March.
    16. Carter, Christopher K. & Wong, Frederick & Kohn, Robert, 2011. "Constructing priors based on model size for nondecomposable Gaussian graphical models: A simulation based approach," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 871-883, May.
    17. Jelena Nikolić & Danijela Aleksić & Zoran Perić & Milan Dinčić, 2021. "Iterative Algorithm for Parameterization of Two-Region Piecewise Uniform Quantizer for the Laplacian Source," Mathematics, MDPI, vol. 9(23), pages 1-14, November.
    18. repec:jss:jstsof:43:i12 is not listed on IDEAS
    19. Chunling Wang & Xiaoyan Lin, 2022. "Bayesian Semiparametric Regression Analysis of Multivariate Panel Count Data," Stats, MDPI, vol. 5(2), pages 1-17, May.
    20. Charles Bos & Neil Shephard, 2006. "Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 219-244.
    21. Song, Xin-Yuan & Tang, Nian-Sheng & Chow, Sy-Miin, 2012. "A Bayesian approach for generalized random coefficient structural equation models for longitudinal data with adjacent time effects," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4190-4203.

    More about this item

    Keywords

    Bayesian estimation; covariance matrix modelling; item response theory models; positive definite matrices; two-step estimation;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ehl:lserod:123698. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.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.