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

Brajendra C. Sutradhar () and R. Prabhakar Rao
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Brajendra C. Sutradhar: Memorial University
R. Prabhakar Rao: Sri Sathya Sai Institute of Higher Learning

Sankhya B: The Indian Journal of Statistics, 2016, vol. 78, issue 1, No 2, 39-65

Abstract: 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.

Keywords: Bias correction; Consistency; Correlations among repeated counts; Dynamic model; Generalized quasi-likelihood estimation; Linear measurement error model for the covariates; Measurement error variances; Method of moments estimation; Primary 62F10; 62F12; Secondary 62J12 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13571-015-0106-2

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