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

Shin Yongyun () and Raudenbush Stephen W. ()
Additional contact information
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

The International Journal of Biostatistics, 2013, vol. 9, issue 1, 109-133

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.

Keywords: child health; hierarchical general linear model; ignorable missing data; maximum likelihood; multiple imputation (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/ijb-2012-0048 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:ijbist:v:9:y:2013:i:1:p:25:n:6

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/ijb/html

DOI: 10.1515/ijb-2012-0048

Access Statistics for this article

The International Journal of Biostatistics is currently edited by Antoine Chambaz, Alan E. Hubbard and Mark J. van der Laan

More articles in The International Journal of Biostatistics from De Gruyter
Bibliographic data for series maintained by Peter Golla ().