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Reliable estimation of generalized linear mixed models using adaptive quadrature

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Author Info
Sophia Rabe-Hesketh (Institute of Psychiatry, King's College London)
Anders Skrondal (National Institute of Public Health, Oslo)
Andrew Pickles (University of Manchester)

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Abstract

Generalized linear mixed models or multilevel regression models have become increasingly popular. Several methods have been proposed for estimating such models. However,to date there is no single method that can be assumed to work well in all circumstances in terms of both parameter recovery and computational efficiency. Stata's xt commands for two-level generalized linear mixed models (e.g., xtlogit) employ Gauss-Hermite quadrature to evaluate and maximize the marginal log likelihood. The method generally works very well, and often better than common contenders such as MQL and PQL but there are cases where quadrature performs poorly.Adaptive quadrature has been suggested to overcome these problems in the two-level case. We have recently implemented a multilevel version of this method in gllamm, a program that fits a large class of multilevel latent variable models including multilevel generalized linear mixed models. As far as we know, this is the Þrst time that adaptive quadrature has been proposed for multilevel models. We show that adaptive quadrature works well in problems where ordinary quadrature fails. Furthermore,even when ordinary quadrature works, adaptive quadrature is often computationally more efficient since it requires fewer quadrature points to achieve the same precision. Copyright 2002 by Stata Corporation.

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Publisher Info
Article provided by StataCorp LP in its journal Stata Journal.

Volume (Year): 2 (2002)
Issue (Month): 1 (February)
Pages: 1-21
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Handle: RePEc:tsj:stataj:v:2:y:2002:i:1:p:1-21

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Related research
Keywords: adaptive quadrature; gllamm; generalized linear mixed models; random-effects models; panel data; numerical integration; adaptive integration; multilevel models; clustered data;

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  1. Getinet Astatike Haile, 2004. "Re-employment hazard of displaced German workers: evidence from the GSOEP," Working Papers 000284, Lancaster University Management School, Economics Department. [Downloadable!]
  2. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2003. "Maximum likelihood estimation of generalized linear models with covariate measurement error," Stata Journal, StataCorp LP, vol. 3(4), pages 386-411, December. [Downloadable!]
  3. Ellen van de Poel & Owen O'Donnell & Eddy Van Doorslaer, 2007. "What explains the Rural-Urban Gap in Infant Mortality — Household or Community Characteristics?," Tinbergen Institute Discussion Papers 07-067/3, Tinbergen Institute. [Downloadable!]
  4. Peter Haan & Arne Uhlendorff, 2006. "Estimation of Multinomial Logit Models with Unobserved Heterogeneity Using Maximum Simulated Likelihood," Discussion Papers of DIW Berlin 573, DIW Berlin, German Institute for Economic Research. [Downloadable!]
    Other versions:
  5. Jan Brenner, 2007. "Parental Impact on Attitude Formation - A Siblings Study on Worries about Immigration," Ruhr Economic Papers 0022, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen. [Downloadable!]
  6. Nicolas Sirven & Brigitte Santos-Eggimann & Jacques Spagnoli, 2008. "Comparability of Health Care Responsiveness in Europe using anchoring vignettes from SHARE," Working Papers DT15, IRDES institut for research and information in health economics, revised Sep 2008. [Downloadable!]
  7. Peter Haan, 2004. "Discrete Choice Labor Supply: Conditional Logit vs. Random Coefficient Models," Discussion Papers of DIW Berlin 394, DIW Berlin, German Institute for Economic Research. [Downloadable!]
  8. Nicholas J. Cox, 2004. "Review of Statistical Evaluation of Measurement Errors by Dunn," Stata Journal, StataCorp LP, vol. 4(4), pages 480-483, December. [Downloadable!]
  9. Alfonso Miranda & Sophia Rabe-Hesketh, 2005. "Maximum Likelihood Estimation of Endogenous Switching And Sample Selection Models for Binary, Count, And Ordinal Variables," Keele Economics Research Papers KERP 2005/14, Centre for Economic Research, Keele University. [Downloadable!]
  10. Peter Haan, . "Conditional logit versus random coefficient models: An analysis using GLLAMM," German Stata Users' Group Meetings 2004 7, Stata Users Group. [Downloadable!]
  11. David Bishai & Jody Sindelar, 2006. "Willingness to Pay for Drug Rehabilitation: Implications for Cost Recovery," NBER Working Papers 12506, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  12. Stephen Schilling & R. Bock, 2005. "High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature," Psychometrika, Springer, vol. 70(3), pages 533-555, September. [Downloadable!] (restricted)
  13. Alfonso Miranda & Massimiliano Bratti, 2006. "Non-Pecuniary Returns to Higher Education:," IZA Discussion Papers 2090, Institute for the Study of Labor (IZA). [Downloadable!]
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