IDEAS home Printed from https://ideas.repec.org/p/fir/econom/wp2019_09.html
   My bibliography  Save this paper

An F -type multiple testing approach for assessing randomness of linear mixed models

Author

Abstract

In linear mixed models the assessing of the significance of all or a subset of the random effects is often of primary interest. Many techniques have been proposed for this purpose but none of them is completely satisfactory. One of the oldest methods for testing randomness is the F -test but it is often overlooked in modern applications due to poor statistical power and non-applicability in some important situations. In this work a two-step procedure is developed for generalizing an F -test and improving its statistical power. In the first step, by comparing two covariance matrices of a least squares statistics, we obtain a "repeatable" F -type test. In the second step, by changing the projected matrix which defines the least squares statistic we apply the test repeteadly to the same data in order to have a set of correlated statistics analyzed within a multiple testing approach. The resulting test is sufficiently general, easy to compute, with an exact distribution under the null and alternative hypothesis and, perhaps more importantly, with a strong increase of statistical power with respect to the F -test.

Suggested Citation

  • Marco Barnabani, 2019. "An F -type multiple testing approach for assessing randomness of linear mixed models," Econometrics Working Papers Archive 2019_09, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    • Handle: RePEc:fir:econom:wp2019_09
    as

    Download full text from publisher

    File URL: https://labdisia.disia.unifi.it/wp_disia/2019/wp_disia_2019_09.pdf
    File Function: First version, 2019-10
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Garrett M. Fitzmaurice & Stuart R. Lipsitz & Joseph G. Ibrahim, 2007. "A Note on Permutation Tests for Variance Components in Multilevel Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 63(3), pages 942-946, September.
    2. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
    3. Hunt, Daniel L. & Cheng, Cheng & Pounds, Stanley, 2009. "The beta-binomial distribution for estimating the number of false rejections in microarray gene expression studies," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1688-1700, 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. Bijlsma Ineke & van den Brakel Jan & van der Velden Rolf & Allen Jim, 2020. "Estimating Literacy Levels at a Detailed Regional Level: an Application Using Dutch Data," Journal of Official Statistics, Sciendo, vol. 36(2), pages 251-274, June.
    2. Jie Huang & Haiming Zhou & Nader Ebrahimi, 2022. "Bayesian Bivariate Cure Rate Models Using Copula Functions," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(3), pages 1-9, May.
    3. Kubokawa, Tatsuya & Nagashima, Bui, 2012. "Parametric bootstrap methods for bias correction in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 1-16.
    4. Hasan Önder, 2017. "A Review on the Permutation Tests," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 3(3), pages 68-70, October.
    5. Myung-Jae Hwang & Jong-Hun Kim & Hae-Kwan Cheong, 2020. "Short-Term Impacts of Ambient Air Pollution on Health-Related Quality of Life: A Korea Health Panel Survey Study," IJERPH, MDPI, vol. 17(23), pages 1-11, December.
    6. J. N. K. Rao, 2015. "Inferential issues in model-based small area estimation: some new developments," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 491-510, December.
    7. 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.
    8. Masahiro Kojima & Tatsuya Kubokawa, 2013. "Bartlett Adjustments for Hypothesis Testing in Linear Models with General Error Covariance Matrices," CIRJE F-Series CIRJE-F-884, CIRJE, Faculty of Economics, University of Tokyo.
    9. Oliver E. Lee & Thomas M. Braun, 2012. "Permutation Tests for Random Effects in Linear Mixed Models," Biometrics, The International Biometric Society, vol. 68(2), pages 486-493, June.
    10. Sun-Joo Cho & Paul Boeck & Susan Embretson & Sophia Rabe-Hesketh, 2014. "Additive Multilevel Item Structure Models with Random Residuals: Item Modeling for Explanation and Item Generation," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 84-104, January.
    11. Ward, Eric J., 2008. "A review and comparison of four commonly used Bayesian and maximum likelihood model selection tools," Ecological Modelling, Elsevier, vol. 211(1), pages 1-10.
    12. María José Lombardía & Esther López‐Vizcaíno & Cristina Rueda, 2017. "Mixed generalized Akaike information criterion for small area models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1229-1252, October.
    13. Mojtaba Ganjali & Taban Baghfalaki, 2018. "Application of Penalized Mixed Model in Identification of Genes in Yeast Cell-Cycle Gene Expression Data," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 6(2), pages 38-41, April.
    14. Kauermann, Goran & Xu, Ronghui & Vaida, Florin, 2008. "Stacked Laplace-EM algorithm for duration models with time-varying and random effects," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2514-2528, January.
    15. Sanjoy Sinha & Abdus Sattar, 2015. "Inference in semi-parametric spline mixed models for longitudinal data," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 377-395, December.
    16. Philipp F. M. Baumann & Enzo Rossi & Alexander Volkmann, 2020. "What Drives Inflation and How: Evidence from Additive Mixed Models Selected by cAIC," Papers 2006.06274, arXiv.org, revised Aug 2022.
    17. Jiang, Jiming & Nguyen, Thuan & Rao, J. Sunil, 2009. "A simplified adaptive fence procedure," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 625-629, March.
    18. Kawakubo, Yuki & Kubokawa, Tatsuya, 2014. "Modified conditional AIC in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 44-56.
    19. Lizandra C. Fabio & Francisco J. A. Cysneiros & Gilberto A. Paula & Jalmar M. F. Carrasco, 2022. "Hierarchical and multivariate regression models to fit correlated asymmetric positive continuous outcomes," Computational Statistics, Springer, vol. 37(3), pages 1435-1459, July.
    20. Eric F. Lock & Nidhi Kohli & Maitreyee Bose, 2018. "Detecting Multiple Random Changepoints in Bayesian Piecewise Growth Mixture Models," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 733-750, September.

    More about this item

    Keywords

    Linear Mixed Models; Hypothesis testing; Comparison of matrices; F-distribution; Beta binomial distribution.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

    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:fir:econom:wp2019_09. 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: Fabrizio Cipollini (email available below). General contact details of provider: https://edirc.repec.org/data/dsfirit.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.