Abstract
This chapter assumes that the observations are correlated and some of the covariates are time-independent while others are time-dependent covariate. A review of models to fit marginal models to correlated data with time-dependent covariates is conducted. Their development of a marginal regression model for longitudinal data with time-dependent covariates and with group identification of valid moments are explored.
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References
Bhargava, A. (1994). Modelling the health of Filipino children. Journal of the Royal Statistical Society, A, 157(3), 417–432.
Bickel, P. J., Klaassen, C. A. J., Ritov, Y., & Wellner, J. A. (1998). Efficient and adaptive estimation for semiparametric models. New York: Springer.
Chamberlain, G. (1987). Asymptotic efficiency in estimation with conditional moment restrictions. Journal of Econometrics, 34(3), 305–334.
Cox, D. R. (1970). Analysis of binary data. Boca Raton: Chapman and Hall.
Diggle, P., Heagerty, P., Liang, K.-Y., & Zeger, S. L. (2002). Analysis of longitudinal data. Oxford: Oxford University Press.
Eichenbaum, M., Hansen, L. P., & Singleton, K. (1988). A time series analysis of representative agent models of consumption and leisure choice under uncertainty. The Quarterly Journal of Economic, 103(1), 51–78.
Hall, A. R. (1999). Hypothesis testing in models estimated by GMM. In L. Matyas (Ed.), Generalized method of moments estimation (pp. 96–127). New York: Cambridge University Press.
Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50(4), 1029–1054.
Hu, F. (1993). A statistical methodology for analyzing the causal health effect of a time dependent exposure from longitudinal data. Boston: Harvard School of Public Health.
Lai, T. L., & Small, D. (2007). Marginal regression analysis of longitudinal data with time-dependent covariates: A generalised method of moments approach. Journal of the Royal Statistical Society, Series B, 69(1), 79–99.
Lalonde, T. L., Wilson, J. R., & Yin, J. (2014). GMM logistic regression models for longitudinal data with time-dependent covariates. Statistics in Medicine, 33(27), 4756–4769.
Leung, H.-Y., Small, D., Qin, J., & Zhu, M. (2013). Shrinkage empirical likelihood estimator in longitudinal analysis with time-dependent covariates—Application to modeling the health of Filipino children. Biometrics, 69(3), 624–632.
Liang, K.-Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73(1), 13–22.
McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (2nd ed.). Boca Raton: Chapman and Hall.
Newey, W. K. (1985). Generalized method of moments specification testing. Journal of Econometrics, 29(3), 229–256.
Newey, W. K., & Smith, R. J. (2004). Higher order properties of GMM and generalized empirical likelihood estimators. Econometrica, 72(1), 219–255.
Pan, W., & Connett, J. E. (2002). Selecting the working correlation structure in generalized estimating equations with application to the lung health study. Statistica Sinica, 12(2), 475–490.
Pepe, M., & Anderson, J. (1994). A cautionary note on inference for marginal regression models with longitudinal data and general correlated response data. Communications in Statistics: Simulation and Computation, 23(4), 939–951.
Qu, A., Lindsay, B. G., & Li, B. (2000). Improving generalised estimating equations using quadratic inference functions. Biometrika, 87(4), 823–836.
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Wilson, J.R., Vazquez-Arreola, E., Chen, (.DG. (2020). GMM Marginal Regression Models for Correlated Data with Grouped Moments. In: Marginal Models in Analysis of Correlated Binary Data with Time Dependent Covariates. Emerging Topics in Statistics and Biostatistics . Springer, Cham. https://doi.org/10.1007/978-3-030-48904-5_3
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DOI: https://doi.org/10.1007/978-3-030-48904-5_3
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