IDEAS home Printed from https://ideas.repec.org/a/bla/jorssc/v70y2021i1p122-146.html
   My bibliography  Save this article

M‐quantile regression for multivariate longitudinal data with an application to the Millennium Cohort Study

Author

Listed:
  • Marco Alfò
  • Maria Francesca Marino
  • Maria Giovanna Ranalli
  • Nicola Salvati
  • Nikos Tzavidis

Abstract

Motivated by the analysis of data from the UK Millennium Cohort Study on emotional and behavioural disorders, we develop an M‐quantile regression model for multivariate longitudinal responses. M‐quantile regression is an appealing alternative to standard regression models; it combines features of quantile and expectile regression and it may produce a detailed picture of the conditional response variable distribution, while ensuring robustness to outlying data. As we deal with multivariate data, we need to specify what it is meant by M‐quantile in this context, and how the structure of dependence between univariate profiles may be accounted for. Here, we consider univariate (conditional) M‐quantile regression models with outcome‐specific random effects for each outcome. Dependence between outcomes is introduced by assuming that the random effects in the univariate models are dependent. The multivariate distribution of the random effects is left unspecified and estimated from the observed data. Adopting this approach, we are able to model dependence both within and between outcomes. We further discuss a suitable model parameterisation to account for potential endogeneity of the observed covariates. An extended EM algorithm is defined to derive estimates under a maximum likelihood approach.

Suggested Citation

  • Marco Alfò & Maria Francesca Marino & Maria Giovanna Ranalli & Nicola Salvati & Nikos Tzavidis, 2021. "M‐quantile regression for multivariate longitudinal data with an application to the Millennium Cohort Study," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 122-146, January.
    • Handle: RePEc:bla:jorssc:v:70:y:2021:i:1:p:122-146
    DOI: 10.1111/rssc.12452
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssc.12452
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssc.12452?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. N. Salvati & N. Tzavidis & M. Pratesi & R. Chambers, 2012. "Small area estimation via M-quantile geographically weighted regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 1-28, March.
    2. Murray Aitkin, 1999. "A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models," Biometrics, The International Biometric Society, vol. 55(1), pages 117-128, March.
    3. Annamaria Bianchi & Enrico Fabrizi & Nicola Salvati & Nikos Tzavidis, 2018. "Estimation and Testing in M‐quantile Regression with Applications to Small Area Estimation," International Statistical Review, International Statistical Institute, vol. 86(3), pages 541-570, December.
    4. Manuel Arellano & Stéphane Bonhomme, 2016. "Nonlinear panel data estimation via quantile regressions," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 61-94, October.
    5. Paolo Frumento & Matteo Bottai & Iv'an Fern'andez-Val, 2020. "Parametric Modeling of Quantile Regression Coefficient Functions with Longitudinal Data," Papers 2006.00160, arXiv.org.
    6. Nikos Tzavidis & Nicola Salvati & Timo Schmid & Eirini Flouri & Emily Midouhas, 2016. "Longitudinal analysis of the strengths and difficulties questionnaire scores of the Millennium Cohort Study children in England using M-quantile random-effects regression," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(2), pages 427-452, February.
    7. Sabine Schnabel & Paul Eilers, 2013. "Simultaneous estimation of quantile curves using quantile sheets," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(1), pages 77-87, January.
    8. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
    9. Hemant Kulkarni & Jayabrata Biswas & Kiranmoy Das, 2019. "A joint quantile regression model for multiple longitudinal outcomes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 453-473, December.
    10. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(1), pages 158-195, February.
    11. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    12. Schnabel, Sabine K. & Eilers, Paul H.C., 2009. "Optimal expectile smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4168-4177, October.
    13. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    14. Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
    15. Paolo Frumento & Nicola Salvati, 2020. "Parametric modelling of M‐quantile regression coefficient functions with application to small area estimation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 229-250, January.
    16. Annamaria Bianchi & Nicola Salvati, 2015. "Asymptotic Properties and Variance Estimators of the M-quantile Regression Coefficients Estimators," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(11), pages 2416-2429, June.
    17. Sobotka, Fabian & Kneib, Thomas, 2012. "Geoadditive expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 755-767.
    18. Petrella, Lea & Raponi, Valentina, 2019. "Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 70-84.
    19. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    20. Mu, Yunming & He, Xuming, 2007. "Power Transformation Toward a Linear Regression Quantile," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 269-279, March.
    21. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    22. Monica Pratesi & M. Ranalli & Nicola Salvati, 2009. "Nonparametric -quantile regression using penalised splines," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(3), pages 287-304.
    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. Merlo, Luca & Petrella, Lea & Salvati, Nicola & Tzavidis, Nikos, 2022. "Marginal M-quantile regression for multivariate dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    2. Luca Merlo & Lea Petrella & Nikos Tzavidis, 2022. "Quantile mixed hidden Markov models for multivariate longitudinal data: An application to children's Strengths and Difficulties Questionnaire scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(2), pages 417-448, March.
    3. Valeria Bignozzi & Luca Merlo & Lea Petrella, 2022. "Inter-order relations between moments of a Student $t$ distribution, with an application to $L_p$-quantiles," Papers 2209.12855, arXiv.org.

    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. Otto-Sobotka, Fabian & Salvati, Nicola & Ranalli, Maria Giovanna & Kneib, Thomas, 2019. "Adaptive semiparametric M-quantile regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 116-129.
    2. Merlo, Luca & Petrella, Lea & Salvati, Nicola & Tzavidis, Nikos, 2022. "Marginal M-quantile regression for multivariate dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    3. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    4. Kneib, Thomas & Silbersdorff, Alexander & Säfken, Benjamin, 2023. "Rage Against the Mean – A Review of Distributional Regression Approaches," Econometrics and Statistics, Elsevier, vol. 26(C), pages 99-123.
    5. Luca Merlo & Lea Petrella & Nikos Tzavidis, 2022. "Quantile mixed hidden Markov models for multivariate longitudinal data: An application to children's Strengths and Difficulties Questionnaire scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(2), pages 417-448, March.
    6. Francesco Schirripa Spagnolo & Nicola Salvati & Antonella D’Agostino & Ides Nicaise, 2020. "The use of sampling weights in M‐quantile random‐effects regression: an application to Programme for International Student Assessment mathematics scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 991-1012, August.
    7. Daouia, Abdelaati & Paindaveine, Davy, 2019. "Multivariate Expectiles, Expectile Depth and Multiple-Output Expectile Regression," TSE Working Papers 19-1022, Toulouse School of Economics (TSE), revised Feb 2023.
    8. Georges Bresson & Guy Lacroix & Mohammad Arshad Rahman, 2021. "Bayesian panel quantile regression for binary outcomes with correlated random effects: an application on crime recidivism in Canada," Empirical Economics, Springer, vol. 60(1), pages 227-259, January.
    9. Petrella, Lea & Raponi, Valentina, 2019. "Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 70-84.
    10. Jayabrata Biswas & Kiranmoy Das, 2021. "A Bayesian quantile regression approach to multivariate semi-continuous longitudinal data," Computational Statistics, Springer, vol. 36(1), pages 241-260, March.
    11. Taoufik Bouezmarni & Mohamed Doukali & Abderrahim Taamouti, 2023. "Testing Granger Non-Causality in Expectiles," University of East Anglia School of Economics Working Paper Series 2023-02, School of Economics, University of East Anglia, Norwich, UK..
    12. Hemant Kulkarni & Jayabrata Biswas & Kiranmoy Das, 2019. "A joint quantile regression model for multiple longitudinal outcomes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 453-473, December.
    13. Fabrizi, Enrico & Salvati, Nicola & Trivisano, Carlo, 2020. "Robust Bayesian small area estimation based on quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    14. Jose E. Gomez-Gonzalez & Jorge M. Uribe & Oscar M. Valencia, 2024. "Asymmetric Sovereign Risk: Implications for Climate Change Preparation," IREA Working Papers 202401, University of Barcelona, Research Institute of Applied Economics, revised Jan 2024.
    15. Songfeng Zheng, 2021. "KLERC: kernel Lagrangian expectile regression calculator," Computational Statistics, Springer, vol. 36(1), pages 283-311, March.
    16. Zhao, Jun & Chen, Yingyu & Zhang, Yi, 2018. "Expectile regression for analyzing heteroscedasticity in high dimension," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 304-311.
    17. Maruotti, Antonello & Petrella, Lea & Sposito, Luca, 2021. "Hidden semi-Markov-switching quantile regression for time series," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    18. Burdejova, P. & Härdle, W. & Kokoszka, P. & Xiong, Q., 2017. "Change point and trend analyses of annual expectile curves of tropical storms," Econometrics and Statistics, Elsevier, vol. 1(C), pages 101-117.
    19. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers 36/17, Institute for Fiscal Studies.
    20. Bernardi, Mauro & Bottone, Marco & Petrella, Lea, 2018. "Bayesian quantile regression using the skew exponential power distribution," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 92-111.

    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:jorssc:v:70:y:2021:i:1:p:122-146. 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/rssssea.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.