@article{646bc9ae832f40cf8e58771c7ae2817b,
title = "Modification of the generalized quasi-likelihood model in the analysis of the Add Health study",
abstract = "The relationship between the mean and variance is an implicit assumption of parametric modeling. While many distributions in the exponential family have a theoretical mean–variance relationship, it is often the case that the data under investigation are correlated, thus varying from the relation. We present a generalized method of moments estimation technique for modeling certain correlated data by adjusting the mean–variance relationship parameters based on a canonical parameterization. The proposed mean–variance form describes overdispersion using two parameters and implements an adjusted canonical parameter which makes this approach feasible for all distributions in the exponential family. Test statistics and confidence intervals are used to measure the deviations from the mean–variance relation parameters. We use the modified relation as a means of fitting generalized quasi-likelihood models to correlated data. The performance of the proposed modified generalized quasi-likelihood model is demonstrated through a simulation study and the importance of accounting for overdispersion is highlighted through the evaluation of adolescent obesity data collected from a U.S. longitudinal study.",
keywords = "Canonical parameter, correlation, generalized linear models, generalized method of moments, overdispersion",
author = "Irimata, {Katherine E.} and Wilson, {Jeffrey R.}",
note = "Funding Information: This research uses data from Add Health, a program project directed by Kathleen Mullan Harris and designed by J. Richard Udry, Peter S. Bearman, and Kathleen Mullan Harris at the University of North Carolina at Chapel Hill, and funded by grant P01-HD31921 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development, with cooperative funding from 23 other federal agencies and foundations. Special acknowledgment is due Ronald R. Rindfuss and Barbara Entwisle for assistance in the original design. Information on how to obtain the Add Health data files is available on the Add Health website (http://www.cpc.unc.edu/addhealth). No direct support was received from grant P01-HD31921 for this analysis. The work for this paper was conducted while the first author was at Arizona State University. The findings and conclusions in this paper are those of the authors and do not necessarily represent the views of the National Center for Health Statistics, Centers for Disease Control and Prevention. Funding Information: This research uses data from Add Health, a program project directed by Kathleen Mullan Harris and designed by J. Richard Udry, Peter S. Bearman, and Kathleen Mullan Harris at the University of North Carolina at Chapel Hill, and funded by grant P01-HD31921 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development, with cooperative funding from 23 other federal agencies and foundations. Special acknowledgment is due Ronald R. Rindfuss and Barbara Entwisle for assistance in the original design. Information on how to obtain the Add Health data files is available on the Add Health website ( http://www.cpc.unc.edu/addhealth ). No direct support was received from grant P01-HD31921 for this analysis. The work for this paper was conducted while the first author was at Arizona State University. The findings and conclusions in this paper are those of the authors and do not necessarily represent the views of the National Center for Health Statistics, Centers for Disease Control and Prevention. Publisher Copyright: {\textcopyright} The Author(s) 2019.",
year = "2020",
month = aug,
day = "1",
doi = "10.1177/0962280219884980",
language = "English (US)",
volume = "29",
pages = "2087--2099",
journal = "Statistical Methods in Medical Research",
issn = "0962-2802",
publisher = "SAGE Publications Ltd",
number = "8",
}