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A two-step estimator for generalized linear models for longitudinal data with time-varying measurement error

Author

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  • Roberto Mari

    (University of Catania)

  • Antonello Maruotti

    (LUMSA University
    University of Bergen)

Abstract

We propose a novel approach for longitudinal data modeling within the Generalized Linear Models family, whenever a covariate of interest is affected by measurement error. We jointly model the response (outcome model), the covariate observed with error (measurement model) and the underlying unobserved time-varying error-free covariate (true score). This is done by assuming a first-order latent Markov chain for the true score. The estimation of the full joint model is hardly feasible when the number of covariates is large, as typical in real-data applications. Available algorithms are severely affected by numerical underflow and multiple local maxima. To overcome these problems, we propose an efficient two-step approach. With an extensive simulation study, we show that the two-step approach produces point estimates and standard errors which are almost identical to those obtained by the more time consuming, simultaneous (one-step) approach. The proposal is also illustrated by analyzing data from the Chinese Longitudinal Healthy Longevity Survey.

Suggested Citation

  • Roberto Mari & Antonello Maruotti, 2022. "A two-step estimator for generalized linear models for longitudinal data with time-varying measurement error," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 273-300, June.
    • Handle: RePEc:spr:advdac:v:16:y:2022:i:2:d:10.1007_s11634-021-00473-4
    DOI: 10.1007/s11634-021-00473-4
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    1. Florian Heiss, 2008. "Sequential numerical integration in nonlinear state space models for microeconometric panel data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(3), pages 373-389.
    2. Bakk, Zsuzsa & Kuha, Jouni, 2018. "Two-step estimation of models between latent classes and external variables," LSE Research Online Documents on Economics 85161, London School of Economics and Political Science, LSE Library.
    3. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521471626, January.
    4. G. Alexandrovich & H. Holzmann & A. Leister, 2016. "Nonparametric identification and maximum likelihood estimation for hidden Markov models," Biometrika, Biometrika Trust, vol. 103(2), pages 423-434.
    5. Vermunt, Jeroen K., 2010. "Latent Class Modeling with Covariates: Two Improved Three-Step Approaches," Political Analysis, Cambridge University Press, vol. 18(4), pages 450-469.
    6. Skrondal, Anders & Kuha, Jouni, 2012. "Improved regression calibration," LSE Research Online Documents on Economics 44135, London School of Economics and Political Science, LSE Library.
    7. Bartolucci, Francesco & Montanari, Giorgio E. & Pandolfi, Silvia, 2015. "Three-step estimation of latent Markov models with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 287-301.
    8. S. C. Noah Uhrig & Nicole Watson, 2020. "The Impact of Measurement Error on Wage Decompositions: Evidence From the British Household Panel Survey and the Household, Income and Labour Dynamics in Australia Survey," Sociological Methods & Research, , vol. 49(1), pages 43-78, February.
    9. Francesco Bartolucci & Silvia Bacci & Fulvia Pennoni, 2014. "Longitudinal analysis of self-reported health status by mixture latent auto-regressive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(2), pages 267-288, February.
    10. Anders Skrondal & Jouni Kuha, 2012. "Improved Regression Calibration," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 649-669, October.
    11. Anastasios A. Tsiatis & Yanyuan Ma, 2004. "Locally efficient semiparametric estimators for functional measurement error models," Biometrika, Biometrika Trust, vol. 91(4), pages 835-848, December.
    12. Agresti, Alan & Caffo, Brian & Ohman-Strickland, Pamela, 2004. "Examples in which misspecification of a random effects distribution reduces efficiency, and possible remedies," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 639-653, October.
    13. Antonello Maruotti, 2011. "Mixed Hidden Markov Models for Longitudinal Data: An Overview," International Statistical Review, International Statistical Institute, vol. 79(3), pages 427-454, December.
    14. Zsuzsa Bakk & Jouni Kuha, 2018. "Two-Step Estimation of Models Between Latent Classes and External Variables," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 871-892, December.
    15. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    16. F. Bartolucci & A. Farcomeni & F. Pennoni, 2014. "Rejoinder on: Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 484-486, September.
    17. Antonello Maruotti & Antonio Punzo, 2021. "Initialization of Hidden Markov and Semi‐Markov Models: A Critical Evaluation of Several Strategies," International Statistical Review, International Statistical Institute, vol. 89(3), pages 447-480, December.
    18. Li, Mengyan & Ma, Yanyuan & Li, Runze, 2019. "Semiparametric regression for measurement error model with heteroscedastic error," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 320-338.
    19. F. Bartolucci & A. Farcomeni & F. Pennoni, 2014. "Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 433-465, September.
    20. Helmut Küchenhoff & Samuel M. Mwalili & Emmanuel Lesaffre, 2006. "A General Method for Dealing with Misclassification in Regression: The Misclassification SIMEX," Biometrics, The International Biometric Society, vol. 62(1), pages 85-96, March.
    21. Antonello Maruotti, 2015. "Handling non-ignorable dropouts in longitudinal data: a conditional model based on a latent Markov heterogeneity structure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 84-109, March.
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