Skip to main content
  • 226 Accesses

Abstract

Classical methods of repeated measures analysis of variance and growth curve analysis require balanced data sets. Typically, in repeated measures analysis, a group or groups of subjects are all measured under various treatment conditions (Winer, 1971). The order of the treatments are randomized for each subject, and there should be no missing observations. In growth curve analysis, all subjects are measured at the same times, and, again, there should be no missing data (Grizzle and Allen, 1961).

This work was supported by the National Institute of General Medical Studies, Grant Number GM38519.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle, Second International Symposium on Information Theory, (B. N. Petrov and F. Csaki, Eds.), Budapest: Akademia Kaido, 267–81.

    Google Scholar 

  • Akaike, H. (1974). A new look at the statistical model identification, IEEE Transactions on Automatic Control, AC-19, 716–723.

    Article  MathSciNet  Google Scholar 

  • Dennis, J. E., Jr. and Schnabel, R. B. (1983). Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Engjewood Cliffs, New Jersey.

    MATH  Google Scholar 

  • Diggle, P. J. (1988). An approach to the analysis of repeated measurements, Biometrics, 44, 959–971.

    Article  MathSciNet  MATH  Google Scholar 

  • Grizzle, J. E. and Allen, D. M. (1969). Analysis of growth and dose response curves, Biometrics, 25, 357–82.

    Article  Google Scholar 

  • Hocking, R. R. (1985). The Analysis of Linear Models, Brooks/Cole Publishing Company, Monterey, California.

    MATH  Google Scholar 

  • Jennrich R. I. and Schluchter, M. D. (1986). Unbalanced repeated-measures models with structured covariance matrices, Biometrics, 42, 805–20.

    Article  MathSciNet  MATH  Google Scholar 

  • Jones, R. H. (1964). Predicting multivariate time series, Journal of Applied Meteorology 3, 285–289.

    Article  Google Scholar 

  • Jones, R. H. (1984). Fitting multivariate models to unequally spaced data, Time Series Analysis of Irregularly Observed Data (E. Parzen, Ed.), Lecture Notes in Statistics, 25, Springer-Verlag, 158–188.

    Chapter  Google Scholar 

  • Jones, R. H. (1993). Longitudinal Data with Serial Correlation: A State-Space Approach, Chapman & Hall, London.

    MATH  Google Scholar 

  • Jones, R. H. and Ackerson, L. M. (1990). Serial correlation in unequally spaced longitudinal data, Biometrika 77, 721–731.

    Article  MathSciNet  Google Scholar 

  • Jones, R. H. and Boadi-Boateng, F. (1991). Unequally spaced longitudinal data with AR(1) serial correlation, Biometrics, 47, 161–175.

    Article  Google Scholar 

  • Jones, R. H. and Molitoris, B. A. (1984). A statistical method for determining the breakpoint of two lines, Analytical Biochemistry, 141, 287–290.

    Article  Google Scholar 

  • Jones, R. H., Reeve, E. B. and Swanson, G. D. (1984). Statistical identification of compartmental models with applications to plasma protein kinetics, Computers and Biomedical Research, 17, 277–288.

    Article  Google Scholar 

  • Jones, R. H. and Tryon, P. V. (1987). Continuous time series models for unequally spaced data applied to modeling atomic clocks, SIAM Journal on Scientific and Statistical Computing 8, 71–81.

    Article  MathSciNet  MATH  Google Scholar 

  • Kalman, R. E. (1960) A new approach to linear filtering and prediction problems, Transactions of the ASME, Series D, Journal of Basic Engineering 82, 35–45.

    Article  Google Scholar 

  • Kalman, R. E. and Bucy, R. S. (1961). New results in linear filtering and prediction theory, Transactions of the ASME, Series D, Journal of Basic Engineering 83, 95–108.

    Article  MathSciNet  Google Scholar 

  • Laird, N. M. and Ware, J. H. (1982). Random effects models for longitudinal data Biometrics, 38, 963–74.

    Article  MATH  Google Scholar 

  • Lindstrom, M. J. and Bates, D. M. (1990). Nonlinear mixed effects models for repeated measures data, Biometrics 46, 673–687.

    Article  MathSciNet  Google Scholar 

  • Moler, C. and Van Loan, C. (1978). Nineteen dubious ways to compute the exponential of a matrix, SIAM Reviews 20, 801–836.

    Article  MATH  Google Scholar 

  • Potthoff, R. F. and Roy, S. N. (1964). A generalized multivariate analysis of variance model useful especially for growth curve problems, Biometrika, 51, 313–26.

    MathSciNet  MATH  Google Scholar 

  • Prentice, A. M. (1990). The doubly-labelled water method: Technical recommendations for use in humans, a consensus report by the IDECG working group. Conference held September, 1988, Claire College, Cambridge.

    Google Scholar 

  • Robinson, G. K. (1991). That BLUP is a good thing: the estimation of random effects, Statistical Science, 6, 15–51.

    Article  MathSciNet  MATH  Google Scholar 

  • Ruppert, D., Cressie, N. and Carroll, R. J. (1989). A transformation weighting model for estimation Michaelis-Menten parameters, Biometrics, 45, 637–56.

    Article  Google Scholar 

  • Schweppe, F. C. (1965). Evaluation of likelihood functions for Gaussian signals, IEEE Transactions on Information Theory 11, 61–70.

    Article  MathSciNet  MATH  Google Scholar 

  • Sheiner, L. B. and Beal, S. L. (1980). Evaluation of methods for estimating population pharmacokinetics parameters. I. Michaelis-Menten model: routine clinical pharmacokinetics data, J. Pharmacokin. Biopharm., 8, 553–571.

    Google Scholar 

  • Thompson, W. A. (1962). The problem of negative estimates of variance components, Ann. Math. Statist, 33, 273–89.

    Article  MathSciNet  MATH  Google Scholar 

  • Whittle, P. (1963). On the fitting of multivariate autoregressions and the approximate canonical factorization of a spectral density matrix, Biometrika 50, 129–134.

    MathSciNet  MATH  Google Scholar 

  • Winer, B. J. (1971) Statistical Principles in Experimental Design, second edition, McGraw-Hill, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Jones, R.H. (1994). Longitudinal Data Models with Fixed and Random Effects. In: Bozdogan, H., et al. Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling: An Informational Approach. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0800-3_11

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-0800-3_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4344-1

  • Online ISBN: 978-94-011-0800-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics