Skip to main content
SpringerLink
Log in
Book cover

Modelling and Prediction Honoring Seymour Geisser pp 77–103Cite as

On the Prediction of Growth Curves

  • Chapter

Abstract

The subject of this paper is generalized linear growth curve models. In the past, these types of growth curves have been studied by authors including J. Wishart, G.E.P. Box and C.R. Rao. Further attention was directed towards this subject ever since the publication of the seminal paper on the subject by R.F. Potthoff and S.N. Roy in 1964 which modeled the growth curve as a generalized multivariate linear model. However, the emphasis up until 1970 was on the estimation and testing hypothesis about parameters. In this paper we mainly review work on prediction within the context of these growth models over the last 25 years.

Work supported in part by NSC grants 82-208-M009-054 and 84-2121-M009-008 and by NIGMS grant GM-25271, respectively. The authors wish to thank the referees and professor Arnold Zellner for some constructive comments.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Anderson, T. W. (1984). An Introduction to Multivariate Statistical Analysis, 2nd edition. New York: Wiley

    MATH  Google Scholar 

  • BMDP Statistical Software Manual, Vol. 2 (1988). University of California Press, Berkeley, California.

    Google Scholar 

  • Box, G.E.P. (1950). Problems in the analysis of growth and wear curves. Biometrics, 6, 362–389

    Article  Google Scholar 

  • Chi, E.M. and Reinsel, G.C. (1989). Models for longitudinal data with random effects and AR(1) errors. Journal of the American Statistical Association, 84, 452–459

    Article  MathSciNet  Google Scholar 

  • Dawid, AP (1984). Present position and potential development: Some personal views. Journal of the Royal Statistical Society, Series A 147, 278 – 292.

    MATH  MathSciNet  Google Scholar 

  • Fearn, T (1975). A Bayesian approach to growth curves. Biometrika 62, 89–100

    Google Scholar 

  • Geary, D. N. (1989). Modeling the covariance structure of repeated measurements, Biometircs, 45, 1183 – 1195.

    Article  MATH  Google Scholar 

  • Geisser, S. and Cornfield, J. (1963). Posterior distributions for multivariate normal parameters. Journal of the Royal Statistical Society, Series B 25, 368 – 376.

    MATH  MathSciNet  Google Scholar 

  • Geisser, S. (1965). Bayesian estimation in multivariate analysis. Ann. Math. Statist. 36, 150 – 159.

    Article  MATH  MathSciNet  Google Scholar 

  • Geisser, S (1970). Bayesian analysis of growth curves. Sankhya, Series A 32, 53–64

    Google Scholar 

  • Geisser, S. (1974). A predictive approach to the random effect model. Biometrika, 61, 101 – 107.

    Article  MATH  MathSciNet  Google Scholar 

  • Geisser, S. (1975). The predictive sample reuse method with application. Journal of the American Statistical Association, 70, 320–328

    Article  MATH  Google Scholar 

  • Geisser, S. and Eddy, W.F. (1979). A predictive approach to model selection. Journal of the American Statistical Association, 74, 153–160

    Article  MATH  MathSciNet  Google Scholar 

  • Geisser, S. (1980). Growth curve analysis. In Handbook of Statistics, Vol. 1,P.R. Krishnaiah(ed.), 89–115. Amsterdam: North-Holland

    Google Scholar 

  • Geisser, S. (1981). Sample reuse procedures for prediction of the unobserved portion of a partially observed vector. Biometrika, 68, 243–250

    Article  MATH  MathSciNet  Google Scholar 

  • Geyer, C. J. and Thompson, E. A. (1992). Constrained Monte Carlo maximum likelihood for dependent data. Journal of the Royal Statistical Society, Series B 54, 657–700

    MathSciNet  Google Scholar 

  • Jenrich, R.I. and Schluchter, M.D. (1986). Unbalanced repeated-measures models with structured covariance matrices. Biometrics, 42, 805 – 820.

    Article  MathSciNet  Google Scholar 

  • Keramidas, E.M. and Lee,.1. C. (1988). Forecasting technological substitutions with concurrent short time series. Proceedings of the Business and Economic Statistics Section, American Statistical Association, 1–10

    Google Scholar 

  • Keramidas, E.M. and Lee, J. C. (1990). Forecasting technological substitutions with concurrent short time series. Journal of the American Statistical Association. 85, 625–632.

    Article  Google Scholar 

  • Keramidas, E.M. and Lee, J. C. (1995). Selection of a covariance structure for growth curves. Biometrical Journal, 37, 783–797

    Article  MATH  MathSciNet  Google Scholar 

  • Khatri, C. G. (1966). A note on MANOVA model applied to problems in growth curve. Annals of the Institute of Statistical Mathematics, 18, 75–86.

    Article  MATH  MathSciNet  Google Scholar 

  • Khatri, C. G. (1973). Testing some covariance structures under a growth curve model. Journal of Multivariate Analysis, 3, 102–116.

    Article  MATH  MathSciNet  Google Scholar 

  • Laird, N. M. and Ware, J. H. (1982). Random effects models for longitudinal data. Biometrics, 38, 963–974.

    Article  MATH  Google Scholar 

  • Lee, JC and Geisser, S (1972). Growth curve prediction. Sankhya, Series A 34, 393–412

    Google Scholar 

  • Lee, JC and Geisser, S (1975). Applications of growth curve prediction. Sankhya, Series A 37, 239–256

    Google Scholar 

  • Lee, JC and Hu, L (1995). On the distribution of linear functions of independent Fand Uvariates. Statistics and Probability Letters. (In Press)

    Google Scholar 

  • Lee, J. C. (1982). Classification of growth curves. In Handbook of Statistics, Vol. II, P. r. Krishnaiah and L. W. Kanal(eds.), 121–137. Amsteram: North- Holland

    Google Scholar 

  • Lee, JC and Tan, WY (1984). On the degree of polynomial in a general linear model. Communications in Statistics, Series A 13, 781–790

    Google Scholar 

  • Lee, J. C. (1988). Prediction and estimation of growth curves with special covariance structures. Journal of the American Statistical Association, 83, 432–440

    Article  MATH  MathSciNet  Google Scholar 

  • Lee, J. C. (1991). Test and model selection for the general growth curve model. Biometrics, 47, 147–159

    Article  MATH  MathSciNet  Google Scholar 

  • Liu, S. I. (1995). Bayesian multiperiod forecasts for ARX models. Annals of the Institute of Statistical Mathematics (In press).

    Google Scholar 

  • Lyung, G. M. and Box, G.E.P. (1980). Analysis of variance with autocorrelated observations, Scandinavian Journal of Statistics, 7, 172–180

    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, 313–326

    MATH  MathSciNet  Google Scholar 

  • Rao, C. R. (1958). Some statistical methods for comparison of growth curves. Biometrics, 14, 1–17

    Article  MATH  Google Scholar 

  • Rao, C. R. (1965). The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves. Biometrika, 52, 447–458

    MATH  MathSciNet  Google Scholar 

  • Rao, C. R. (1966). Covariance adjustment and related problems in multivariate analyses. In Multivariate Analyses, Vol. II, P. R. Krishnaish(ed.), 87 – 103. New York: Academic Press

    Google Scholar 

  • Rao, C. R. (1967). Least squares theory using an estimated dispersion matrix and its application to measurement of signals. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, 1, 355–372

    Google Scholar 

  • Rao, C. R. (1977). Prediction of future observations with special reference to linear models. In Multivariate Analysis, Vol. IV, P. R. Krishnaiah(ed.), 193–208. Amsterdam: North-Holland

    Google Scholar 

  • Rao, C. R. (1984). Prediction of future observations in polynomial growth curve models. In Proceedings of the Indian Statistical Institute Golden Jubilee International Conference on Statistics: Applications and New Directions, 512–520. Calcutta: Indian Statistical Institute

    Google Scholar 

  • Rao, C. R. (1987). Prediction of future observations in growth curve models. Statistical Science, 2, 434–471

    Article  MATH  MathSciNet  Google Scholar 

  • Reinsel, G. (1984). Estimation and prediction in a multivariate random effects generalized linear model. Journal of the American Statistical Association, 79, 06–414

    Article  MathSciNet  Google Scholar 

  • Wishart, J. (1938). Growth rate determinations in nutrition studies with the bacon pig, and their analysis. Biometrika, 30, 16–28

    Google Scholar 

  • Zellner, A., Bauwens, L and Van Dijk, H. K. (1988). Bayesian specification analysis and estimation of simultaneous equation models using Monte Carlo methods. J. of Econometrics, 38, 39–72

    Article  Google Scholar 

  • Zerbe, G. O. (1979). Randomization analysis of the completely randomized design extended to growth and response curves. Journal of the American Statistical Association, 74, 215–221

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Chiao Tung University, Taiwan

    Jack C. Lee

  2. University of Minnesota, USA

    Seymour Geisser

Authors
  1. Jack C. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seymour Geisser
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Statistics, National Chiao Tung University, 1001 Ta-Hseuh Road, Hsichu, Taiwan R.O.C

    Jack C. Lee

  2. Department of Statistics, University of California, Davis, 95616, Davis, CA, USA

    Wesley O. Johnson

  3. Graduate School of Business, University of Chicago, 1101 East 58th Street, 60637, Chicago, IL, USA

    Arnold Zellner

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer Science+Business Media New York

About this chapter

Cite this chapter

Lee, J.C., Geisser, S. (1996). On the Prediction of Growth Curves. In: Lee, J.C., Johnson, W.O., Zellner, A. (eds) Modelling and Prediction Honoring Seymour Geisser. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2414-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2414-3_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7529-9

  • Online ISBN: 978-1-4612-2414-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation