Overview of Linear Fixed Models for Longitudinal Data

  • Brajendra C. SutradharEmail author
Part of the Springer Series in Statistics book series (SSS)


In a longitudinal setup, a small number of repeated responses along with certain multidimensional covariates are collected from a large number of independent individuals. Let y yi1, …,y it , …,y iT i be T i ≥ 2 repeated responses collected from the ith individual, for i = 1, …, K, where K → ∞. Furthermore, let x it = (x it 1 , …,x it p ) be the p-dimensional covariate vector corresponding to y it , and β denote the effects of the components of xit it on y it . For example, in a biomedical study, to examine the effects of two treatments and other possible covariates on blood pressure, the physician may collect blood pressure for T i = T = 10 times from K = 200 independent subjects.


Ordinary Little Square Generalize Little Square Repeated Response Ordinary Little Square Estimator Autocorrelation Structure 
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  1. 1.
    Amemiya, T. (1985). Advanced Econometrics. Cambridge, MA: Harvard University Press.Google Scholar
  2. 2.
    Box, G. E. P. & Jenkins, G. M. (1970). Time Series Analysis Forecasting and Control. San Francisco: Holden-Day.Google Scholar
  3. 3.
    Diggle, P. J., Liang, K.-Y., & Zeger, S. L. (1994). Analysis of Longitudinal Data. Oxford Science. Oxford: Clarendon Press.Google Scholar
  4. 4.
    Kendall, M., Stuart, A., & Ord, J. K. (1983). The Advanced Theory of Statistics, Vol. 3, London: Charles Griffin.Google Scholar
  5. 5.
    Mardia, K. V., Kent, J. T. & Bibby, J. M. (1979). Multivariate Analysis. London: Academic Press.Google Scholar
  6. 6.
    Pearson, J. D., Morrell, C. H., Landis, P. K., Carter, H. B., & Brant, L. J. (1994). Mixedeffects regression models for studying the natural history of prostate disease. Statist. Med., 13, 587−601.CrossRefGoogle Scholar
  7. 7.
    Rao, C. R. (1973). Linear Statistical Inference and Its Applications. New York: John Wiley & Sons.Google Scholar
  8. 8.
    Seber, G. A. F. (1984). Multivariate Observations. New York: John Wiley & Sons.Google Scholar
  9. 9.
    Sneddon, G. & Sutradhar, B. C. (2004). On semi-parametric familial-longitudinal models. Statist. Probab. Lett., 69, 369−379.CrossRefMathSciNetGoogle Scholar
  10. 10.
    Srivastava, M. S. & Carter, E. M. (1983). An Introduction to Applied Multivariate Statistics. New York: North-Holland.Google Scholar
  11. 11.
    Sutradhar, B. C. & Kumar, P. (2003). The inversion of the correlation matrix for MA(1) process. Appl. Math. Lett., 16, 317−321.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Verbeke, G. & Lesaffre, E. (1999). The effect of drop-out on the efficiency of longitudinal experiments. Appl. Statist., 48, 363−375.zbMATHGoogle Scholar
  13. 13.
    Verbeke, G. & Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. New York: Springer.Google Scholar

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMemorial UniversitySaint John’sCanada

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