IDEAS home Printed from https://ideas.repec.org/a/bpj/ijbist/v9y2013i1p25n6.html
   My bibliography  Save this article

Efficient Analysis of Q-Level Nested Hierarchical General Linear Models Given Ignorable Missing Data

Author

Listed:
  • Shin Yongyun

    (Department of Biostatistics, Virginia Commonwealth University, 830 East Main Street, Richmond, VA 23298-0032, USA)

  • Raudenbush Stephen W.

    (Department of Sociology, University of Chicago, 1126 E. 59th Street, Chicago, IL 60637, USA)

Abstract

This article extends single-level missing data methods to efficient estimation of a Q-level nested hierarchical general linear model given ignorable missing data with a general missing pattern at any of the Q levels. The key idea is to reexpress a desired hierarchical model as the joint distribution of all variables including the outcome that are subject to missingness, conditional on all of the covariates that are completely observed and to estimate the joint model under normal theory. The unconstrained joint model, however, identifies extraneous parameters that are not of interest in subsequent analysis of the hierarchical model and that rapidly multiply as the number of levels, the number of variables subject to missingness, and the number of random coefficients grow. Therefore, the joint model may be extremely high dimensional and difficult to estimate well unless constraints are imposed to avoid the proliferation of extraneous covariance components at each level. Furthermore, the over-identified hierarchical model may produce considerably biased inferences. The challenge is to represent the constraints within the framework of the Q-level model in a way that is uniform without regard to Q; in a way that facilitates efficient computation for any number of Q levels; and also in a way that produces unbiased and efficient analysis of the hierarchical model. Our approach yields Q-step recursive estimation and imputation procedures whose qth-step computation involves only level-q data given higher-level computation components. We illustrate the approach with a study of the growth in body mass index analyzing a national sample of elementary school children.

Suggested Citation

  • Shin Yongyun & Raudenbush Stephen W., 2013. "Efficient Analysis of Q-Level Nested Hierarchical General Linear Models Given Ignorable Missing Data," The International Journal of Biostatistics, De Gruyter, vol. 9(1), pages 109-133, September.
  • Handle: RePEc:bpj:ijbist:v:9:y:2013:i:1:p:25:n:6
    DOI: 10.1515/ijb-2012-0048
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/ijb-2012-0048
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    File URL: https://libkey.io/10.1515/ijb-2012-0048?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. Datar, A. & Sturm, R., 2004. "Physical education in elementary school and body mass index: Evidence from the early childhood longitudinal study," American Journal of Public Health, American Public Health Association, vol. 94(9), pages 1501-1506.
    2. Minzhi Liu & Jeremy M. G. Taylor & Thomas R. Belin, 2000. "Multiple Imputation and Posterior Simulation for Multivariate Missing Data in Longitudinal Studies," Biometrics, The International Biometric Society, vol. 56(4), pages 1157-1163, December.
    3. Joseph L. Schafer, 2003. "Multiple Imputation in Multivariate Problems When the Imputation and Analysis Models Differ," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(1), pages 19-35, February.
    4. Harvey Goldstein & Daphne Kounali, 2009. "Multilevel multivariate modelling of childhood growth, numbers of growth measurements and adult characteristics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(3), pages 599-613, June.
    5. Bengt Muthén & David Kaplan & Michael Hollis, 1987. "On structural equation modeling with data that are not missing completely at random," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 431-462, September.
    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. Yongyun Shin & Stephen W. Raudenbush, 2007. "Just-Identified Versus Overidentified Two-Level Hierarchical Linear Models with Missing Data," Biometrics, The International Biometric Society, vol. 63(4), pages 1262-1268, December.
    2. Steven Andrew Culpepper & Herman Aguinis & Justin L. Kern & Roger Millsap, 2019. "High-Stakes Testing Case Study: A Latent Variable Approach for Assessing Measurement and Prediction Invariance," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 285-309, March.
    3. Hanrriette Carrasco-Venturelli & Javier Cachón-Zagalaz & Amador J. Lara-Sánchez & José Luis Ubago-Jiménez, 2024. "Validation and Adaptation of Questionnaires on Interest, Effort, Progression and Learning Support in Chilean Adolescents," Sustainability, MDPI, vol. 16(5), pages 1-14, February.
    4. Justina GineikienÄ—, 2013. "Consumer Nostalgia Literature Review And An Alternative Measurement Perspective," Organizations and Markets in Emerging Economies, Faculty of Economics, Vilnius University, vol. 4(2).
    5. Christopher H. Morrell & Larry J. Brant & Shan Sheng & E. Jeffrey Metter, 2012. "Screening for prostate cancer using multivariate mixed-effects models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1151-1175, November.
    6. Eldad Davidov & Stefan Thörner & Peter Schmidt & Stefanie Gosen & Carina Wolf, 2011. "Level and change of group-focused enmity in Germany: unconditional and conditional latent growth curve models with four panel waves," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(4), pages 481-500, December.
    7. Halleröd, Björn & Gustafsson, Jan-Eric, 2011. "A longitudinal analysis of the relationship between changes in socio-economic status and changes in health," Social Science & Medicine, Elsevier, vol. 72(1), pages 116-123, January.
    8. Black, Nicole & Johnston, David W. & Propper, Carol & Shields, Michael A., 2019. "The effect of school sports facilities on physical activity, health and socioeconomic status in adulthood," Social Science & Medicine, Elsevier, vol. 220(C), pages 120-128.
    9. Erik Meijer & Arie Kapteyn & Tatiana Andreyeva, 2008. "Health Indexes and Retirement Modeling in International Comparisons," Working Papers 614, RAND Corporation.
    10. Jost Reinecke & Cornelia Weins, 2013. "The development of delinquency during adolescence: a comparison of missing data techniques," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(6), pages 3319-3334, October.
    11. Grace Lordan & Debayan Pakrashi, 2015. "Do All Activities “Weigh” Equally? How Different Physical Activities Differ as Predictors of Weight," Risk Analysis, John Wiley & Sons, vol. 35(11), pages 2069-2086, November.
    12. Sarah Mustillo, 2012. "The Effects of Auxiliary Variables on Coefficient Bias and Efficiency in Multiple Imputation," Sociological Methods & Research, , vol. 41(2), pages 335-361, May.
    13. Juan Aparicio & Jose M. Cordero & Lidia Ortiz, 2021. "Efficiency Analysis with Educational Data: How to Deal with Plausible Values from International Large-Scale Assessments," Mathematics, MDPI, vol. 9(13), pages 1-16, July.
    14. Cawley, John & Frisvold, David & Meyerhoefer, Chad, 2013. "The impact of physical education on obesity among elementary school children," Journal of Health Economics, Elsevier, vol. 32(4), pages 743-755.
    15. Valentin Kvist, Ann & Gustafsson, Jan-Eric, 2007. "The relation between fluid intelligence and the general factor as a function of cultural background: a test of Cattell's investment theory," Working Paper Series 2007:23, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    16. John Cawley & Chad Meyerhoefer & David Newhouse, 2007. "The impact of state physical education requirements on youth physical activity and overweight," Health Economics, John Wiley & Sons, Ltd., vol. 16(12), pages 1287-1301, December.
    17. Stuart R. Lipsitz & Garrett M. Fitzmaurice & Roger D. Weiss, 2020. "Using Multiple Imputation with GEE with Non-monotone Missing Longitudinal Binary Outcomes," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 890-904, December.
    18. Thelma Dede Baddoo & Zhijia Li & Samuel Nii Odai & Kenneth Rodolphe Chabi Boni & Isaac Kwesi Nooni & Samuel Ato Andam-Akorful, 2021. "Comparison of Missing Data Infilling Mechanisms for Recovering a Real-World Single Station Streamflow Observation," IJERPH, MDPI, vol. 18(16), pages 1-26, August.
    19. Liu, Yuqing & Schuberth, Florian & Liu, Yide & Henseler, Jörg, 2022. "Modeling and assessing forged concepts in tourism and hospitality using confirmatory composite analysis," Journal of Business Research, Elsevier, vol. 152(C), pages 221-230.
    20. von Hippel, Paul T. & Lynch, Jamie L., 2014. "Why are educated adults slim—Causation or selection?," Social Science & Medicine, Elsevier, vol. 105(C), pages 131-139.

    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:bpj:ijbist:v:9:y:2013:i:1:p:25:n:6. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.