Response transformations in repeated measures and growth curve models

Communications in Statistics Part B: Simulation and Computation

Volumn 29, Issue 4, 2000, Pages 699-733

  Boik, Robert J ^a   Todd, Charles ^b   Hyde, Scott K ^a  

^a MONTANA STATE UNIVERSITY   (United States)

^b EASTERN NEW MEXICO UNIVERSITY   (United States)

Author keywords

AIC; Bartlett correction, Box Cox family; Conditional sphericity; Fisher scoring; Folded power; Likelihood ratio test, local sphericity; SAS IML; Sphericity

Indexed keywords

EID: 0006559276     PISSN: 03610918     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (82)

1. Akaike, H. (1973). Information theory as an extension of the maximum likelihood principal. In B.N. Petrov and F. Csáki (Eds), Second International Symposium on Information Theory, pp. 267-281. Budapest: Akadémiai Kiado.
2. Allison, D.B., Gorman, B.S., and Kucera, E.M. (1995). Unicorn: A program for transforming data to approximate normality. Educational and Psychological Measurement, 55, 625-629.
3. nd ed.). New York: John Wiley & Sons, Inc.
4. Andrews, D.F., Gnanadesikan, R., & Warner, J.L. (1971). Transformation of multivariate data. Biometrics, 27, 825-840.
5. Andrews, D.F., Gnanadesikan, R., & Warner, J.L. (1973). Methods for assessing multivariate normality. In P.R. Krishnaiah (Ed), Multivariate Analysis - III, pp. 95-115. New York: Academic Press.
6. Andrews, D.F., & Herzberg, A.M. (1985). Data. New York: Springer-Verlag.
7. Atkinson, A.C. (1973). Testing transformations to normality. Journal of the Royal Statistical Society, B35, 473-479.
8. Atkinson, A.C. (1985). Plots, Transformations and Regression. New York: Oxford Press.
9. Bickel, P.J., & Doksum, K.A. (1981). An analysis of transformations revisited. Journal of the American Statistical Association, 76, 296-311.
10. Boik, R.J. (1981). A priori tests in repeated measures designs: Effects of nonsphericity. Psychometrika, 46, 241-255.
11. Box, G.E.P., & Cox, D.R. (1964). An analysis of transformations (with discussion). Journal of the Royal Statistical Society, B26, 211-252.
12. Browne, M.W. (1984). Asymptotically distribution-free methods in the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62-83.
13. Bozdogan, H., & Ramirez, D.E. (1988). UTRANS and MTRANS: Marginal and joint Box-Cox transformations of multivariate data to near normality. Multivariate Behavioral Research, 23, 131-132.
14. Carroll, R.J., & Ruppert, D. (1988). Transformations and Weighting in Regression. New York: Chapman and Hall.
15. Casella, G., & Berger, R.L. (1990). Statistical Inference. Belmont, CA: Duxbury Press.
16. Cook, R.D. (1977). Detection of influential observations in linear regression. Technometrics, 19, 15-18.
17. Cook, R.D. (1979). Influential observations in linear regression. Journal of the American Statistical Association, 74, 169-174.
18. Cook, R.D., & Weisberg, S. (1982). Residuals and Influence in Regression. New York: Chapman and Hall.
19. Cook, R.D., & Weisberg, S. (1994). Transforming a response variable for linearity. Biometrika, 81, 731-737.
20. Cook, R.D., & Wang, P.C. (1983). Transformations and influential cases in regression. Technometrics, 25, 337-343.
21. Crowder, M.J., & Hand, D.J. (1990). Analysis of Repeated Measures. New York: Chapman and Hall.
22. Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, B39, 1-38.
23. Dennis, J.E., & Schnabel, R.B. (1983). Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Englewood Cliffs, NJ: Prentice-Hall.
24. Diggle, P.J., Liang, K-Y, & Zeger, S. (1994). Analysis of Longitudinal Data. New York: Oxford University Press.
25. Dunn, J.E., & Tubbs, J.D. (1980). VARSTAB: A procedure for determining homoscedastic transformations of multivariate normal populations. Communications in Statistics - Simulation and Computation, 9, 589-598.
26. Fujikoshi, Y., & Rao, C.R. (1991). Selection of covariables in the growth curve model. Biometrika, 78, 779-785.
27. Geisser, S. (1970). Bayesian analysis of growth curves. Sankhya, Ser. A, 32, 53-64.
28. Gianola, D., Im, S., Fernando, R.L., & Foulley, J.L. (1990). Mixed model methodology and the Box-Cox theory of transformations: A Bayesian approach. In D. Gianola and K. Hammond (Eds) Advances in Statistical Methods for Genetic Improvement of Livestock, pp. 15-40. New York: Springer-Verlag.
29. Grizzle, J.E., & Allen, D.M. (1969). Analysis of growth and dose response curves. Biometrics, 25, 357-381.
30. Hand, D.J., & Taylor, C.C. (1987). Multivariate Analysis of Variance and Repeated Measures. New York: Chapman and Hall.
31. Halawa, A.M. (1996). Estimating the Box-Cox transformation via an artificial regression model. Communications in Statistics - Simulation and Computation, 25, 331-350.
32. Hamilton, S.A., & Taylor, J.M.G. (1993). A comparison of the Box-Cox transformation method and nonparametric methods for estimating quantiles in clinical data with repeated measures. Journal of Statistical Computation and Simulation, 45, 185-201.
33. Hinkley, D.V. (1988). More on score tests for transformation in regression. Biometrika, 75, 366-369.
34. Hinkley, D.V., & Runger, G. (1984). The analysis of transformed data. Journal of the American Statistical Association, 79, 302-309.
35. Hinkley, D.V., & Wang, S. (1988). More about transformations and influential cases in regression. Technometrics, 30, 435-440.
36. Hooper, P.M., & Yang, Z. (1997). Confidence intervals following Box-Cox transformation. The Canadian Journal of Statistics, 25, 401-416.
37. Hoyle, M.H. (1973). Transformations - An introduction and a bibliography. International Statistical Review, 41, 203-223.
38. Huang, C.L., Moon, L.C., & Chang, H.S. (1978). A computer program using the Box-Cox transformation technique for the specification of functional form. The American Statistician, 32, 144.
39. Huynh, H., & Feldt, L.S. (1970). Conditions under which mean square ratios in repeated measures designs have exact F-distributions. Journal of the American Statistical Association, 65, 1582-1589.
40. Khatri, C.G. (1966). A note on a MANOVA model applied to problems in growth curve. Annals of the Institute of Statistical Mathematics, 18, 75-86.
41. Khatri, C.G. (1973). Testing some covariance structures under a growth curve model. Journal of Multivariate Analysis, 3, 102-116.
42. Kim, C., Storer, B.E., & Jeong, M. (1996). A note on Box-Cox transformation diagnostics. Technometrics, 38, 178-180.
43. Kim, M.G. (1996). Local influence in Box-Cox transformation for multivariate regression data. Communications in Statistics - Theory and Methods, 25, 2955-2969.
44. rd ed.), Pacific Grove, CA: Brooks/Cole Publishing Co.
45. Kshirsagar, A.M., & Smith, W.B. (1995). Growth Curves. New York: Marcel Dekker.
46. Lawrance, A.J. (1987). The score statistic for regression transformation. Biometrika, 74, 275-279.
47. Lawrance, A.J. (1988). Regression transformation diagnostics using local influence. Journal of the American Statistical Association, 83, 1067-1072.
48. Lee, J.C. (1988). Prediction and estimation of growth curves with special covariance structures. Journal of the American statistical Association, 83, 432-440.
49. Lindsey, J.K. (1993). Models for Repeated Measures. New York: Oxford University Press.
50. Longford, N.T. (1993). Random Coefficient Models. New York: Oxford University Press.
51. McLachlan, G.J., & Krishnan, T. (1997). The EM Algorithm and Extensions. New York: John Wiley & Sons, Inc.
52. Mendoza, J.L., Toothaker, L.E., & Crain, B.R. (1976). Necessary and sufficient conditions for F ratios in the L x J x K factorial design with two repeated factors. Journal of the American Statistical Association, 71, 992-993.
53. Mikulich, S.K., Zerbe, G.O., Jones, R.H., & Crowley, T.J. (1999). Relating the classical covariance adjustment techniques of multivariate growth curve models to modern univariate mixed effects models. Biometrics, 55, 957-964.
54. Mosteller, F., & Tukey, J.W. (1977). Data Analysis and Regression. Reading, MA: Addison-Wesley.
55. O'Sullivan, J.B., & Mahan, C.M. (1966). Glucose tolerance test: Variability in pregnant and non-pregnant women. American Journal of Clinical Nutrition, 19, 345-351.
56. Potthoff, R.F., & Roy, S.N. (1964). A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika, 51, 313-326.
57. Quiroz, A.F., Nakamura, M., Pérez, F.J. (1996). Estimation of a multivariate Box-Cox transformation to elliptical symmetry via the empirical characteristic function. Annals of the Institute of Statistical Mathematics, 48, 687-709.
58. Redfern, D., & Campbell, C. (1998). The Matlab 5 Handbook. New York: Springer-Verlag.
59. Rao, C.R. (1965). The theory of least squares when parameters are stochastic and its application to the analysis of growth curves. Biometrika, 52, 447-458.
60. Rao, C.R. (1966). Covariance adjustment and related problems in multivariate analysis. In P.R. Krishnaiah (Ed) Multivariate Analysis, pp. 87-103. New York: Academic Press.
61. Rao, C.R. (1967). Least squares theory using an estimated dispersion matrix and its application to measurement of signals. In L.M. LeCam & J. Neyman (Eds) Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, pp. 355-372. Berkeley: University of California Press.
62. Rouanet, H., & Lépine, D. (1970). Comparison between treatments in a repeated-measurement design: ANOVA and multivariate methods. British Journal of Mathematical & Statistical Psychology, 23, 147-163.
63. Sakia, R.M. (1988). Application of the Box-Cox transformation technique to linear balanced mixed ANOVA models with a multi-error structure. Unpublished doctoral dissertation, Universität Hohenheim, FRG.
64. Sakia, R.M. (1990). Retransformation bias: A look at the Box-Cox transformation to linear balanced mixed ANOVA models. Metrika, 37, 345-351.
65. Sakia, R.M. (1992). The Box-Cox transformation technique: A review. The Statistician, 41, 169-178.
66. SAS Institute Inc. (1990). SAS/IML Software: Usage and Reference, Version 6, First Edition. Cary, NC: SAS Institute Inc.
67. SAS Institute Inc. (1995). SAS/IML Software: Changes and Enhancements Through Release 6.11. Cary, NC: SAS Institute Inc.
68. SAS Institute Inc. (1997). SAS/STAT Software: Changes and Enhancements through Release 6.12. Cary, NC: SAS Institute Inc.
69. Searle, S.R. (1982). Matrix Algebra Useful for Statistics. New York: John Wiley & Sons, Inc.
70. Shi, P., & Fung, W-K. (1998). A note on transforming a response variable for linearity. Biometrika, 85, 749-754.
71. Schoenfield, L.J., Lachin, J.M., the Steering Committee, & the NCGS Group. (1981). Chonodiol (chenadeoxycholic acid) for dissolution of gallstones: The National Cooperative Gallstone Study. Annals of Internal Medicine, 95, 257-282.
72. Solomon, P.J. (1985). Transformations for components of variance and covariance. Biometrika, 72, 233-239.
73. Srivastava, M.S., & Khatri, C.G. (1979). An Introduction to Multivariate Statistics. New York: Elsevier North Holland Inc.
74. Srivastava, M.S., & von Rosen, D. (1999). Growth curve models. In S. Ghosh (Ed), Multivariate Analysis, Design of Experiments, and Survey Sampling: A Tribute to Jagdish N. Srivastava, pp. 547-578. New York: Marcel Dekker, Inc.
75. Tsai, C-L., & Wu, X. (1990). Diagnostics in transformation and weighted regression. Technometrics, 32, 315-322.
76. Velilla, S. (1993). A note on the multivariate Box-Cox transformation to normality. Statistics & Probability Letters, 17, 259-263.
77. Velilla, S. (1995). Diagnostics and robust estimation in multivariate data transformations. Journal of the American Statistical Association, 90, 945-951.
78. von Rosen, D. (1991). The growth curve model: A review. Communications in Statistics - Theory and Methods, 20, 2791-2822.
79. Weerahandi, S., & Berger, V.W. (1999). Exact inference for growth curves with intraclass structure. Biometrics, 55, 921-924.
80. Wei, L.J., & Lachin, J.M. (1984). Two-sample asymptotically distribution-free tests for incomplete multivariate observations. Journal of the American Statistical Association, 79, 653-661.
81. Yang, Z. (1997). More on the estimation of Box-Cox transformation. Communications in Statistics - Simulation and Computation, 26, 1063-1074.
82. Yang, Z. (1996). Some asymptotic results on Box-Cox Transformation methodology. Communications in Statistics - Theory and Methods, 25, 403-414.