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Maximum likelihood estimation of generalized linear models with covariate measurement error

Author

Listed:
  • Sophia Rabe-Hesketh

    (Graduate School of Education, University of California - Berkeley)

  • Anders Skrondal

    (Norwegian Institute of Public Health)

  • Andrew Pickles

    (School of Epidemiology and Health Science, University of Manchester)

Abstract

Generalized linear models with covariate measurement error can be estimated by maximum likelihood using gllamm, a program that fits a large class of multilevel latent variable models (Rabe-Hesketh, Skrondal, and Pickles 2004). The program uses adaptive quadrature to evaluate the log likelihood, producing more reliable results than many other methods (Rabe-Hesketh, Skrondal, and Pickles 2002). For a single covariate measured with error (assuming a classical measurement model), we describe a ÒwrapperÓ command, cme, that calls gllamm to estimate the model. The wrapper makes life easy for the user by accepting a simple syntax and data structure and producing extended and easily interpretable output. The commands for preparing the data and running gllamm can also be obtained from cme. We first discuss the case where several measurements are available and subsequently consider estimation when the measurement error variance is instead assumed known. The latter approach is useful for sensitivity analysis assessing the impact of assuming perfectly measured covariates in generalized linear models. An advantage of using gllamm directly is that the classical covariate measurement error model can be extended in various ways. For instance, we can use nonparametric maximum likelihood estimation (NPMLE) to relax the normality assumption for the true covariate. We can also specify a congeneric measurement model which relaxes the assumption that the measurements for a unit are exchangeable replicates by allowing for different measurement scales and error variances. Copyright 2003 by StataCorp LP.

Suggested Citation

  • 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.
  • Handle: RePEc:tsj:stataj:v:3:y:2003:i:4:p:386-411
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    References listed on IDEAS

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    1. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2002. "Reliable estimation of generalized linear mixed models using adaptive quadrature," Stata Journal, StataCorp LP, vol. 2(1), pages 1-21, February.
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    Citations

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    Cited by:

    1. Alberto BUCCI & Lorenzo CARBONARI & Giovanni TROVATO, 2017. "Variety, Competition, and Population in Economic Growth: Theory and Empirics," Departmental Working Papers 2017-06, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    2. Mark M. Pitt & Mark R. Rosenzweig & Mohammad Nazmul Hassan, 2012. "Human Capital Investment and the Gender Division of Labor in a Brawn-Based Economy," American Economic Review, American Economic Association, vol. 102(7), pages 3531-3560, December.
    3. Alfonso Miranda & Sophia Rabe-Hesketh, 2006. "Maximum likelihood estimation of endogenous switching and sample selection models for binary, ordinal, and count variables," Stata Journal, StataCorp LP, vol. 6(3), pages 285-308, September.
    4. Gibson, Fiona L. & Burton, Michael P., 2009. "Biased estimates in discrete choice models: the appropriate inclusion of psychometric data into the valuation of recycled wastewater," 2009 Conference (53rd), February 11-13, 2009, Cairns, Australia 47943, Australian Agricultural and Resource Economics Society.
    5. Leonardo Becchetti & Giovanni Trovato, 2011. "Corporate social responsibility and firm efficiency: a latent class stochastic frontier analysis," Journal of Productivity Analysis, Springer, vol. 36(3), pages 231-246, December.
    6. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2004. "Generalized multilevel structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 167-190, June.
    7. Anders Skrondal & Jouni Kuha, 2012. "Improved Regression Calibration," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 649-669, October.
    8. Mark M. Pitt & Mark Rosenzweig & Nazmul Hassan, 2010. "Human Capital Investment and the Gender Division of Labor," Working Papers 989, Economic Growth Center, Yale University.

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