Advertisement

Review of Models Suitable for the Analysis of Longitudinal Data

  • E. Marubini
Chapter

Abstract

As pointed out previously (Marubini, 1978), it is widely accepted in growth studies that the average of the growth curves of a set of subjects is perfectly appropriate for the investigation of the distribution of various anthropometric variables (height, weight, sitting height, etc.) at different ages, for drawing the average growth curve of the population, for preparing ‘distance’ standards and for studying the relationship between some important features of growth and other important variables, e.g. social class levels and size of family. For this reason, provided that the mean growth curve does not change with time, it is immaterial whether the data is gathered by means of cross-sectional or longitudinal studies. However, the crucial requirement is that the sample dimensions are sufficiently large to evaluate pertinent statistics with predetermined reliability.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bakzalary, J.K., Corsten, L.C.A. and Kala, R., 1978, Reconciliation of two different views on estimation of growth curve parameters, Biometrika, 65: 662–665.CrossRefGoogle Scholar
  2. Bock, R.D., 1963, Multivariate analysis of variance of repeated measures, in: Problems of measuring change, C.W. Harris, ed., University of Wisconsin Press, Madison.Google Scholar
  3. Bock, R.D. and Thiessen, D.M., 1976, Fitting multicomponent models for growth in stature, in: Proceedings of the 9th International. Biometric Conference — Boston 22–27 August, The Biometric Society, Raleigh.Google Scholar
  4. Bock, R.D., Wainer, H., Petersen, A., Thiessen, D.M., Murray, J. and Roche, A., 1973, A parametrization for individual human growth curves, Hum. Biol., 45: 63.PubMedGoogle Scholar
  5. Bogin, B., 1980, Catastrophe theory model for the regulation of human growth, Hum. Bio1., 52: 215.Google Scholar
  6. Box, G.E.P., 1950, Problems in the analysis of growth and wear curves, Biometrics, 6: 362.PubMedCrossRefGoogle Scholar
  7. Church, A.Jr., 1966, Analysis of data when the response is a curve, Technometrics, 8: 229.CrossRefGoogle Scholar
  8. Danford, M.B., Hughes, H.M. and McNee, R.C., 1960, On the analysis of repeated-measurement experiments, Biometrics, 16: 547.CrossRefGoogle Scholar
  9. Deming, J., 1957, Application of the Gompertz curve to the observed pattern of growth in length of 48 individual boys and girls during the adolescents cycle of growth, Hum. Biol., 29: 83.PubMedGoogle Scholar
  10. De Molli, S., Rainisio, M. and Marubini, E., 1981, Programma per il calcolo degli standards di crescita in studi longitudinali mis-ti, Rivista di Informatica, XI: 421.Google Scholar
  11. El Lozy, M., 1978, A critical analysis of the double and triple logistic growth curves, Ann. Hum. Biol., 5: 389.PubMedCrossRefGoogle Scholar
  12. Elston, R.C. and Grizzle, J.E., 1962, Estimation of ime-response curves and their confidence bands, Biometrics, 18: 148.CrossRefGoogle Scholar
  13. Esteve, J. and Shifflers, E., 1974, Some aspect of growth in laboratory mice (statistical analysis of a family of growth curve), Ann. Zool. Ecol. Anim., 6: 449.Google Scholar
  14. Esteve, J. and Shifflers, E., 1976, Discussion et illustration de quelques méthodes d’analyse longitudinale, in: Proceedings of the 9th International Biometric Conference Boston 22–27 August, The Biometric Society, Raleigh.Google Scholar
  15. Geisser, S., 1970, Bayesian analysis of growth curves, Sankhya, Ser. A., 32: 53.Google Scholar
  16. Geisser, S., 1980, Growth curve analysis, in: Handbook of Statistics I, P.R. Krishnaiah, ed., North-Holland Publishing Company, Amsterdam.Google Scholar
  17. Goldstein, H., 1979, The design and analysis of longitudinal studies, Academic Press, London.Google Scholar
  18. Grizzle, J.E. and Allen, D.M., 1969, Analysis of growth and dose response curves, Biometrics, 25: 357.PubMedCrossRefGoogle Scholar
  19. Hauspie, R.C., Wachholder, A., Baron, G., Cantraine, F. Susanne, C. and Graffar, M., 1980, A comparative study of the fit of four different functions to longitudinal data of growth in height of Belgian girls, Ann. Hum. Biol. 7: 347.PubMedCrossRefGoogle Scholar
  20. Khatri, O.G., 1966, A note on MANOVA model applied to problems in growth curve, Annals of the Institute of Statistical Mathematics, 18: 75.CrossRefGoogle Scholar
  21. Kleinbaum, D.G., 1973, A generalization of the growth curve model. which allows missing data, J. Multiv. Anal., 3: 117.CrossRefGoogle Scholar
  22. Largo, R.H., Stützle, W., Gesser, T., Huber, P.J. and Prader, 1978, Analysis of the adolescent growth spurt using smoothing spline functions, Ann. Hum. Biol., 5: 421.PubMedCrossRefGoogle Scholar
  23. Lee, J.C. and Geisser, S., 1972, Growth curve prediction, Sankhya, Ser. A, 34: 393.Google Scholar
  24. Lee, J.C. and Geisser, S., 1975, Application of growth curve prediction, Sankhya, Ser. A, 37: 239.Google Scholar
  25. Leech, P.B. and Healy, M.J.R., 1959, The analysis of experiments on growth rate, Biometrics, 15: 98.CrossRefGoogle Scholar
  26. Marubini, E., 1978a, The fitting of longitudinal growth data of man, in: Auxology: Human growth and disorders, L. Gedda and P. Parisi, eds., Academic Press, London.Google Scholar
  27. Marubini, E., 1978b, Mathematical handling of long-term longitudinal data, in: Human growth, F. Falkner and J.M. Tanner, eds., Plenum Press, New York.Google Scholar
  28. Marubini, E. and Milani, S., 1980, Auxometria, Principi e methdi, Società Editrice La Goliardica Pavese, Pavia.Google Scholar
  29. Marubini, E., Resale, L. and Barghini, G., 1971, A comparative fitting of the Gompertz and logistic functions to longitudinal height data during adolescence in girls, Hum. Biol., 43: 237.PubMedGoogle Scholar
  30. Potthoff, R.F. and Roy, S.N., 1964, A generalized multivariate analysis of variance model useful especially for growth curve problems, Biometrika, 51: 313.Google Scholar
  31. Preece, M.A. and Baines, M.K., 1978, A new family of mathematical models describing the human growth curve, Ann. Hum. Biol., 5: 1.PubMedCrossRefGoogle Scholar
  32. Puri, M.L. and Sen, P.K., 1967, Nonparametric methods in multivariate analysis, John Wiley and Sons, New York.Google Scholar
  33. Rao, C.R., 1959, Some problems involving linear hypotheses in multivariate analysis, Biometrika, 46: 49.Google Scholar
  34. 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.PubMedGoogle Scholar
  35. Rao, C.R., 1966, Covariance adjustment and related problems in multivariate analysis, in: Multivariate analysis, P.R. Krishnaiah, ed., Academic Press, New York.Google Scholar
  36. Rao, C.R., 1967, Least squares theory using an estimated dispersion matrix and its application to measurement of signals, in: Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability — Berkeley 21 June — 18 July 1965 and 27 December 1965–7 January 1966, University of California,Press, Berkeley.Google Scholar
  37. Schwertman, M.C., Magrey, J.M. and Fridshal, D., 1981, On the analysis of incomplete growth curve data, A Monte Carlo study of two non-parametric procedures, Commun. Statist.-Simula. Computa., B, 10: 51.CrossRefGoogle Scholar
  38. Stützle, W., Gasser, T., Molinari, L., Largo, R.H., Trader, A. and Huber, P.J., 1980, Shape-invariant modelling of human growth, Ann. Hum. Biol., 7: 507.PubMedCrossRefGoogle Scholar
  39. Szczotka, F.A., 1981a, Analysis of growth curves of body height, ages 2 through 18 years, by the method of canonical decomposition, Studies in Physical Anthropology, 7: 63.Google Scholar
  40. Szczotka, F.A., 1986, Canonical decomposition of the process of simultaneous growth of body height, trunk length, biacromial diameter, biliocristal diameter and thigh circumference in boys and girls ages 9 to 18 years, Studies in Physical Anthropology, 7: 87.Google Scholar
  41. Tanner, J.M., 1963, The regulation of human growth, Child Development, 34: 817.PubMedGoogle Scholar
  42. Timm, N.H., 1975, Multivariate analysis with applications in education and psychology, Brooks/Cole Publishing Co., Monterey, California.Google Scholar
  43. Tuddenham, R.D. and Snyder, M.M. 1954, Physical growth of California boys and girls from birth to eighteen years, University of California Press, Berkeley.Google Scholar
  44. Welch, Q.B., 1970, Fitting growth and research data, Growth, 34: 293.PubMedGoogle Scholar
  45. Wishart, J., 1938, Growth rate determinations in nutrition studies with the bacon pig, and their analysis, Biometrika, 30: 16.Google Scholar
  46. Woolson, R.F., Leeper, J.D. and Clarke, W.R., 1978, Analysis of incomplete data from longitudinal and mixed longitudinal studies, J.R. Statist. Soc., A, 141: 242.Google Scholar
  47. Woolson, R.F. and Leeper, J.D., 1980, Growth curves analysis of complete and incomplete longitudinal data, Commun. Statist. Theor. Meth., A, 9: 1491.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • E. Marubini
    • 1
  1. 1.Istituto di Biometria e Statistica MedicaUniversità degli StudiMilanoItaly

Personalised recommendations