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

• Published in: Sankhyā. Series B (2008) Vol. 78; no. 1; pp. 39 - 65
• Main Authors: Sutradhar, Brajendra C., Rao, R. Prabhakar
• Format: Journal Article
• Language: English
• Published: New Delhi Springer Science + Business Media 01.05.2016; Springer India; Indian Statistical Institute
• Subjects: Error analysis; Mathematical models; Mathematics and Statistics; Measurement errors; Responses; Statistical inference; Statistics; Variances; Bias correction; Linear measurement error model for the covariates; Correlations among repeated counts; Consistency; Generalized quasi-likelihood estimation; Primary 62F10; 62F12; Dynamic model; Measurement error variances; Secondary 62J12; Method of moments estimation
• ISSN: 0976-8386; 0976-8394
• DOI: 10.1007/s13571-015-0106-2

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.