Abstract
Recall from the last chapter [eqn. (2.48)] that there exists [Verbeke and Molenberghs (2000, Chapter 3, eqn. (3.11)); Diggle, Liang, and Zeger (1994)] a random effects based longitudinal mixed model given by
where the ε it are independent errors for all t =1, …, T i for the ith (i=1, …, K) individual.
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References
Amemiya, T. (1985). Advanced Econometrics. Cambridge, MA: Harvard University Press.
Arellano, M. & Bond, S. (1991). Some tests of specification for panel data: Monte carlo evidence and an application to employment equations. Rev. Eco. Statist., 58, 277−−298.
Balestra, P. & Nerlove, M. (1966). Pooling cross-section and time series data in the estimation of a dynamic model: The demand for natural gas. Econometrica, 34, 585−612.
Bun, M. J. G. & Carree, M. A. (2005). Bias-corrected estimation in dynamic panel data models. J. Business & Econo. Statist., 23, 200−210.
Chow, S. C. & Shao, J. (1988). A new procedure for the estimation of variance components. Statist. Probab. Lett., 6, 349−355.
Diggle, P. J., Liang, K.-Y., & Zeger, S. L. (1994). Analysis of Longitudinal Data. Oxford Science, Oxford: Clarendon Press.
Hansen, L.-P. (1982). Large sample properties of generalized method of moment estimators. Econometrica, 50, 1029−1054.
Herbach, L. H. (1959). Properties of type II analysis of variance test. Ann. Math. Statist., 30, 939−959.
Hsiao, C. (2003). Analysis of Panel Data. Cambridge, U.K.: University Press.
Jiang, J. & Zhang, W. (2001). Robust estimation in generalized linear mixed models. Biometrika, 88, 753−765.
LaMotte, L. R. (1973). On non-negative quadratic unbiased estimation of variance components. J. Amer. Statist. Assoc., 68, 728−730.
McCullagh, P. (1983). Qusilikelihood functions. Ann. Statist., 11, 59-67.
Mathew, T., Sinha, B. K., & Sutradhar, B. C. (1992). Nonnegative estimation of variance components in unbalanced mixed models with two variance components. J. Multivariate Anal., 42, 77−101.
Rao, R. P., Sutradhar, B. C., & Pandit, V. N. (2010). GMM versus GQL inferences in linear dynamic panel data models. Braz. J. Probab. Statist., to appear.
Searle, S. R. (1971). Linear Models. New York: John Wiley & Sons.
Sneddon, G. & Sutradhar, B. C. (2004). On semi-parametric familial-longitudinal models. Statist. Probab. Lett., 69, 369−379.
Sutradhar, B. C. (1988). Testing linear hypothesis with t error variable. Sankhya B: Indian J. Statist., 50, 175−180.
Sutradhar, B. C. (1997). A multivariate approach for estimating the random effects variance component in one-way random effects model. Stat. Probab. Lett., 33, 333−339.
Sutradhar, B. C. (2003). An overview on regression models for discrete longitudinal responses. Statist. Sci., 18, 377−393.
Sutradhar, B. C. (2004). On exact quasilikelihood inference in generalized linear mixed models. Sankhya B: Indian J. of Statist., 66, 261−289.
Sutradhar, B. C. & Farrell, P. J. (2007). On optimal lag 1 dependence estimation for dynamic binary models with application to asthma data. Sankhya B: Indian J. Statist., 69, 448−467.
Thompson,W. A. Jr. (1962). The problem of negative estimates of variance components. Ann. Math. Statist., 33, 273−289.
Verbeke, G. & Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. New York: Springer.
Wedderburn, R. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika, 61, 439−447.
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Sutradhar, B.C. (2011). Overview of Linear Mixed Models for Longitudinal Data. In: Dynamic Mixed Models for Familial Longitudinal Data. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8342-8_3
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