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A study of effective statistical tools for longitudinal data analysis

Author Affiliations

  • 1Department of Ag. Statistics, Applied Mathematics and Computer Science, UAS, GKVK, Bengaluru, India
  • 2Department of Ag. Statistics, Applied Mathematics and Computer Science, UAS, GKVK, Bengaluru, India

Res. J. Mathematical & Statistical Sci., Volume 6, Issue (6), Pages 1-5, June,12 (2018)

Abstract

Longitudinal studies play a very important role in human life, plant science and social sciences. In such studies, data are collected from the respondents over a period of time or periodical intervals. Consequently, observations are correlated and effective statistical methods/techniques are required for the analysis of such data. Other names given to such studies are the analysis of repeated measurements and growth curves. The main focus of such data analysis is to study the changes caused by development, aging and other factors such as application of different treatments over a period of time. Such studies typically have unbalanced designs, missing data and time varying covariates and thus not tenable to standard statistical methods. This paper gives an overview of literature and important references which lead for further effective studies.

References

  1. Mauchly J.W. (1940)., Significance Test for Sphericity of a Normal n-Variate Distribution., The Ann. Math. Stat., 11(2), 204-209.
  2. Scheffe Henry (1959)., The analysis of variance., New York, Wiley.
  3. Grieve A.P. (1984)., Tests of Sphericity of normal distributions and the analysis of repeated measures designs., Psychometrika, 49(2), 257-267.
  4. Rao C.R. (1965)., The Theory of Least-Squares When the Parameters are Stochastic and Its Applications to the Analysis of Growth Curves., Biometrika, 52(3-4), 447-458.
  5. Wishart John (1938)., Growth rate determinations in nutrition studies with the bacon pig, and their analysis., Biometrika, 30, 16-28.
  6. Box G.E.P. (1950)., Problems in the analysis of growth and wear curves., Biometrics, 6, 362-389.
  7. Pottoff R.F. and Roy S.N. (1964)., A generalized multivariate analysis of variance model useful especially for growth curve problems., Biometrika, 51, 313-326.
  8. Khatri C.G. (1966)., A note on a MANOVA model applied to problems in Growth Curve., Ann. Inst. Statist. Maths., 18, 75-86.
  9. Geisser S. (1981)., Sample reuse procedures for prediction of the unobserved portion of a partially observed vector., Biometrika, 68, 243-250.
  10. Reinsel G. (1982)., Multivariate repeated measurements for growth curve models with multivariate random effects covariance structure., J. Amer. Statist. Assoc., 77, 190-210.
  11. Patel H.I. (1986)., Analysis of repeated measures designs with changing covariates in clinical trials., Biometrika, 73(3), 707-715.
  12. Khatri C.G. (1973)., Testing some covariance structures under a growth curve model., J. Multi. Anal., 3(1), 102-116.
  13. Rao C.R. (1975)., Simultaneous estimation of parameters in different linear models and applications to biometric problems., Biometrics, 31, 545-554.
  14. Rao C.R. (1967)., Least squares theory using estimated dispersion matrix and its application to measurement of signals., In Proceedings of the 5th Berkeley Symposium on Math. Statist. and Prob., L. Le Cam and J. Neyman. eds., 1, 355-372.
  15. Swamy P.A.V.B. (1971)., Statistical inference in random coefficient regression models., Springer-Verlag, Berlin.
  16. Copas J.B. (1983)., Regression, prediction and shrinkage., J. Roy. Statist. Soc., Series B, (Methodological), 45(3), 311-354.
  17. Reinsel G. (1984)., Estimation and prediction in a multivariate random effects generalized linear model., J. Amer. Statist. Assoc., 79, 406-414.
  18. Reinsel G. (1984)., A note on conditional prediction in the multivariate linear model., J. Roy. Statist. Soc., Series B, 46, 107-117.
  19. Reinsel G. (1984)., Effects of the estimation of covariance matrix parameters in the generalized multivariate linear model., Comm, Stat., (Th. and Meth.), 13(5), 639-650.
  20. Reinsel G. (1985)., Mean squared error properties of empirical Bayes’ estimators in a multivariate random effects general linear model., J. Amer. Statist. Assoc., 80, 642-650.
  21. Rao C.R. and Boudreau R. (1985)., Prediction of future observations in factor analytic type growth model., Multi. Anal., 4, 449-466.
  22. Fearn T. (1975)., A Bayesian approach to growth curves., Biometrika, 62(1), 89-100.