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Inferences in Longitudinal Count Data Models with Measurement Errors in Time Dependent Covariates

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  • Brajendra C. Sutradhar

    (Memorial University)

  • R. Prabhakar Rao

    (Sri Sathya Sai Institute of Higher Learning)

Abstract

Unlike in the independent setup, the measurement error analysis in longitudinal setup especially for discrete responses is not adequately addressed in the literature. In linear longitudinal setup, recently Fan, Sutradhar, and Rao (Sankhya B, 74, 126-148 2012) have introduced a bias corrected generalized quasi-likelihood (BCGQL) approach for the estimation of the regression effects after accommodating both measurement errors in time dependent covariates and correlations of the repeated responses. In longitudinal setup for repeated count data, a similar BCGQL estimating equation for the regression effects is provided by Sutradhar (2013) under the assumption that longitudinal correlation index parameter and measurement error variances are known. In this paper, we offer three main contributions. First, because the BCGQL estimation approach for discrete longitudinal data is complex and less familiar, we provide a complete derivation for this BCGQL estimating equation under the longitudinal count data model subject to measurement errors in time dependent covariates. Second, because the longitudinal correlation index parameter and measurement error variances involved in the model are unknown in practice, and because the main regression parameters can not be estimated without knowing them, we estimate these nuisance parameters consistently by solving appropriate unbiased estimating equations for these parameters. Next, the basic asymptotic properties of the estimators of main regression parameters are indicated.

Suggested Citation

  • Brajendra C. Sutradhar & R. Prabhakar Rao, 2016. "Inferences in Longitudinal Count Data Models with Measurement Errors in Time Dependent Covariates," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 39-65, May.
    • Handle: RePEc:spr:sankhb:v:78:y:2016:i:1:d:10.1007_s13571-015-0106-2
    DOI: 10.1007/s13571-015-0106-2
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    References listed on IDEAS

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    1. Wooldridge, Jeffrey M., 1999. "Distribution-free estimation of some nonlinear panel data models," Journal of Econometrics, Elsevier, vol. 90(1), pages 77-97, May.
    2. Wansbeek, Tom, 2001. "GMM estimation in panel data models with measurement error," Journal of Econometrics, Elsevier, vol. 104(2), pages 259-268, September.
    3. Montalvo, Jose G, 1997. "GMM Estimation of Count-Panel-Data Models with Fixed Effects and Predetermined Instruments," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 82-89, January.
    4. Staudenmayer, John & Buonaccorsi, John P., 2005. "Measurement Error in Linear Autoregressive Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 841-852, September.
    5. Taslim S. Mallick & Brajendra C. Sutradhar, 2008. "GQL Versus Conditional GQL Inferences for Non‐Stationary Time Series of Counts with Overdispersion," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 402-420, March.
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