IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v74y2022i6d10.1007_s10463-022-00825-7.html
   My bibliography  Save this article

Inference of random effects for linear mixed-effects models with a fixed number of clusters

Author

Listed:
  • Chih-Hao Chang

    (National University of Kaohsiung)

  • Hsin-Cheng Huang

    (Academia Sinica)

  • Ching-Kang Ing

    (National Tsing Hua University)

Abstract

We consider a linear mixed-effects model with a clustered structure, where the parameters are estimated using maximum likelihood (ML) based on possibly unbalanced data. Inference with this model is typically done based on asymptotic theory, assuming that the number of clusters tends to infinity with the sample size. However, when the number of clusters is fixed, classical asymptotic theory developed under a divergent number of clusters is no longer valid and can lead to erroneous conclusions. In this paper, we establish the asymptotic properties of the ML estimators of random-effects parameters under a general setting, which can be applied to conduct valid statistical inference with fixed numbers of clusters. Our asymptotic theorems allow both fixed effects and random effects to be misspecified, and the dimensions of both effects to go to infinity with the sample size.

Suggested Citation

  • Chih-Hao Chang & Hsin-Cheng Huang & Ching-Kang Ing, 2022. "Inference of random effects for linear mixed-effects models with a fixed number of clusters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(6), pages 1143-1161, December.
    • Handle: RePEc:spr:aistmt:v:74:y:2022:i:6:d:10.1007_s10463-022-00825-7
    DOI: 10.1007/s10463-022-00825-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-022-00825-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10463-022-00825-7?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bates, Douglas & Mächler, Martin & Bolker, Ben & Walker, Steve, 2015. "Fitting Linear Mixed-Effects Models Using lme4," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 67(i01).
    2. Cora J. M. Maas & Joop J. Hox, 2004. "Robustness issues in multilevel regression analysis," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(2), pages 127-137, May.
    3. Peng, Heng & Lu, Ying, 2012. "Model selection in linear mixed effect models," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 109-129.
    4. Ciprian M. Crainiceanu & David Ruppert, 2004. "Likelihood ratio tests in linear mixed models with one variance component," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 165-185, February.
    5. Pu, Wenji & Niu, Xu-Feng, 2006. "Selecting mixed-effects models based on a generalized information criterion," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 733-758, March.
    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. Ping Wu & Xinchao Luo & Peirong Xu & Lixing Zhu, 2017. "New variable selection for linear mixed-effects models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 627-646, June.
    2. Sun-Joo Cho & Sarah Brown-Schmidt & Woo-yeol Lee, 2018. "Autoregressive Generalized Linear Mixed Effect Models with Crossed Random Effects: An Application to Intensive Binary Time Series Eye-Tracking Data," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 751-771, September.
    3. Simona Buscemi & Antonella Plaia, 2020. "Model selection in linear mixed-effect models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 529-575, December.
    4. Cantoni, Eva & Jacot, Nadège & Ghisletta, Paolo, 2024. "Review and comparison of measures of explained variation and model selection in linear mixed-effects models," Econometrics and Statistics, Elsevier, vol. 29(C), pages 150-168.
    5. Andrew Bell & Malcolm Fairbrother & Kelvyn Jones, 2019. "Fixed and random effects models: making an informed choice," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(2), pages 1051-1074, March.
    6. Baey, Charlotte & Cournède, Paul-Henry & Kuhn, Estelle, 2019. "Asymptotic distribution of likelihood ratio test statistics for variance components in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 107-122.
    7. Colin Griesbach & Andreas Groll & Elisabeth Bergherr, 2021. "Addressing cluster-constant covariates in mixed effects models via likelihood-based boosting techniques," PLOS ONE, Public Library of Science, vol. 16(7), pages 1-17, July.
    8. Pini, Alessia & Sørensen, Helle & Tolver, Anders & Vantini, Simone, 2023. "Local inference for functional linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    9. Ana-Maria Staicu & Yingxing Li & Ciprian M. Crainiceanu & David Ruppert, 2014. "Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 932-949, December.
    10. JANSSENS, Jochen & DE CORTE, Annelies & SÖRENSEN, Kenneth, 2016. "Water distribution network design optimisation with respect to reliability," Working Papers 2016007, University of Antwerp, Faculty of Business and Economics.
    11. Zanin, Luca & Marra, Giampiero, 2012. "Assessing the functional relationship between CO2 emissions and economic development using an additive mixed model approach," Economic Modelling, Elsevier, vol. 29(4), pages 1328-1337.
    12. D. Gunzler & W. Tang & N. Lu & P. Wu & X. Tu, 2014. "A Class of Distribution-Free Models for Longitudinal Mediation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 543-568, October.
    13. Raymond Hernandez & Elizabeth A. Pyatak & Cheryl L. P. Vigen & Haomiao Jin & Stefan Schneider & Donna Spruijt-Metz & Shawn C. Roll, 2021. "Understanding Worker Well-Being Relative to High-Workload and Recovery Activities across a Whole Day: Pilot Testing an Ecological Momentary Assessment Technique," IJERPH, MDPI, vol. 18(19), pages 1-17, October.
    14. Christopher Hassall & Michael Nisbet & Evan Norcliffe & He Wang, 2024. "The Potential Health Benefits of Urban Tree Planting Suggested through Immersive Environments," Land, MDPI, vol. 13(3), pages 1-12, February.
    15. Jie Zhao & Ji Chen & Damien Beillouin & Hans Lambers & Yadong Yang & Pete Smith & Zhaohai Zeng & Jørgen E. Olesen & Huadong Zang, 2022. "Global systematic review with meta-analysis reveals yield advantage of legume-based rotations and its drivers," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    16. Elisabeth Beckmann & Lukas Olbrich & Joseph Sakshaug, 2024. "Multivariate assessment of interviewer-related errors in a cross-national economic survey (Lukas Olbrich, Elisabeth Beckmann, Joseph W. Sakshaug)," Working Papers 253, Oesterreichische Nationalbank (Austrian Central Bank).
    17. F J Heather & D Z Childs & A M Darnaude & J L Blanchard, 2018. "Using an integral projection model to assess the effect of temperature on the growth of gilthead seabream Sparus aurata," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-19, May.
    18. Valentina Krenz & Arjen Alink & Tobias Sommer & Benno Roozendaal & Lars Schwabe, 2023. "Time-dependent memory transformation in hippocampus and neocortex is semantic in nature," Nature Communications, Nature, vol. 14(1), pages 1-17, December.
    19. Morán-Ordóñez, Alejandra & Ameztegui, Aitor & De Cáceres, Miquel & de-Miguel, Sergio & Lefèvre, François & Brotons, Lluís & Coll, Lluís, 2020. "Future trade-offs and synergies among ecosystem services in Mediterranean forests under global change scenarios," Ecosystem Services, Elsevier, vol. 45(C).
    20. Miao-Yu Tsai & Chuhsing Hsiao, 2008. "Computation of reference Bayesian inference for variance components in longitudinal studies," Computational Statistics, Springer, vol. 23(4), pages 587-604, October.

    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:spr:aistmt:v:74:y:2022:i:6:d:10.1007_s10463-022-00825-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.