Mixed Models

Essential Statistical Methods for Medical Statistics

Volumn 27, Issue , 2011, Pages 146-173

  Gurka, Matthew J ^a   Edwards, Lloyd J ^b  

^a UNIVERSITY OF VIRGINIA   (United States)

^b IL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MIXED MODELS;

STATISTICS;

EID: 84944528211     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-0-444-53737-9.50008-6     Document Type: Chapter

References (87)

1. Agresti A. Categorical Data Analysis 2002, Wiley InterScience, New Jersey. 2nd ed.
2. Ahn C.H. Score tests for detecting non-constant variances in linear mixed models. ASA Proceedings of the Biopharmaceutical Section 2000, 0:33-38.
3. Akaike H. A new look at the statistical model identification. IEEE Transaction on Automatic Control 1974, AC-19:716-723.
4. Allen, D. M. (1971). The Prediction Sum of Squares as a Criterion for Selecting Predictor Variables, Technical Report 23, Department of Statistics, University of Kentucky.
5. Bozdogan H. Model selection and Akaike's information criterion: The general theory and its analytical extensions. Psychometrika 1987, 52:345-370.
6. Burnham K.P., Anderson D.R. Model selection and multimodel inference: A practical information-theoretic approach 2002, Springer, New York.
7. Butler S.M., Louis T.A. Random effects models with non-parametric priors. Statistics in Medicine 1992, 11:1981-2000.
8. Cantoni E., Mills Flemming J., Ronchetti E. Variable selection for marginal longitudinal generalized linear models. Biometrics 2005, 61:507-514.
9. Carroll R.J., Ruppert D. Power transformations when fitting theoretical models to data. Journal of the American Statistical Association 1984, 79:321-328.
10. Catellier D.J., Muller K.E. Tests for Gaussian repeated measures with missing data in small samples. Statistics in Medicine 2000, 19:1101-1114.
11. Chi E.M., Reinsel G.C. Models for longitudinal data with random effects and AR(1) errors. Journal of the American Statistical Association 1989, 84:452-459.
12. Claeskens G., Hjort N.L. The focused information criterion. Journal of the American Statistical Association 2003, 98:900-916.
13. Davidian M., Giltinan D.M. Nonlinear Models for Repeated Measures Data 1995, Chapman & Hall, London.
14. Demidenko E. Mixed Models: Theory and Application 2004, Wiley, New York.
15. Dempster A.P., Laird N.M., Rubin R.B. Maximum likelihood with incomplete data via the E-M algorithm. Journal of the Royal Statistical Society, Series B 1977, 39:1-38.
16. Dempster A.P., Rubin R.B., Tsutakawa R.K. Estimation in covariance components models. Journal of the American Statistical Association 1981, 76:341-353.
17. Diggle P.J., Heagerty P., Liang K.Y., Zeger S.L. Analysis of Longitudinal Data 2002, Oxford University Press, Oxford.
18. Fellner W.H. Robust estimation of variance components. Technometrics 1986, 28:51-60.
19. Flegal K.M., Carroll M.D., Ogden C.L., Johnson C.L. Prevalence and trends in obesity among US adults, 1999-2000. Journal of the American Medical Association 2002, 288(14):1723-1727.
20. Geisser S. The predictive sample reuse method with applications. Journal of the American Statistical Association 1975, 70:320-328.
21. Geisser S., Eddy W.F. A predictive approach to model selection. Journal of the American Statistical Association 1979, 74:153-160.
22. Gelman A., Pardoe I. Bayesian measures of explained variance and pooling in multilevel (hierarchical) models. Technometrics 2005, 48:241-251.
23. Goldstein H. Multilevel Statistical Models 2003, Arnold, London. 3rd ed.
24. Gomez E.V., Schaalje G.B., Fellingham G.W. Performance of the Kenward-Roger method when the covariance structure is selected using AIC and BIC. Communications in Statistics-Simulation and Computation 2005, 34:377-392.
25. Grady J.J., Helms R.W. Model selection techniques for the covariance matrix for incomplete longitudinal data. Statistics in Medicine 1995, 14:1397-1416.
26. Gurka M.J. Selecting the best linear mixed model under REML. The American Statistician 2006, 60:19-26.
27. Gurka M.J., Edwards L.J., Muller K.E., Kupper L.L. Extending the Box-Cox transformation to the linear mixed model. Journal of the Royal Statistical Society, Series A 2006, 169:273-288.
28. Harville D.A. Bayesian inference for variance components using only error contrasts. Biometrika 1974, 61:383-385.
29. Harville D.A. Extension of the Gauss-Markov theorem to include the estimation of random effects. Annals of Statistics 1976, 4:384-395.
30. Harville D.A. Maximum likelihood approaches to variance component estimation and to related problems. Journal of the American Statistical Association 1977, 72:320-338.
31. Helms R.W. Intentionally incomplete longitudinal designs: I. Methodology and comparison of some full span designs. Statistics in Medicine 1992, 11:1889-1913.
32. Hjort N.L., Claeskens G. Frequentist model average estimator. Journal of the American Statistical Association 2003, 98:879-899.
33. Huber P.J. Robust Statistics 1981, John Wiley, New York.
34. Hurvich C.M., Tsai C.L. Regression and time series model selection in small samples. Biometrika 1989, 76:297-307.
35. Jiang J., Rao J.S. Consistent procedures for mixed linear model selection. The Indian Journal of Statistics 2003, 65:23-42.
36. Kackar R.N., Harville D.A. Approximations for standard errors of estimators of fixed and random effect in mixed linear models. Journal of the American Statistical Association 1984, 79:853-862.
37. Kenward M.G., Roger J.H. Small sample inference for fixed effects from restricted maximum likelihood. Biometrics 1997, 53:983-997.
38. Knowler, W.C., Barrett-Connor, E., Fowler, S.E., Hamman, R.F., Lachin, J.M., Walker, E.A., Nathan, D.M. (Diabetes Prevention Program Research Group) (2002). Reduction in the incidence of type 2 diabetes with lifestyle intervention or metformin. New England Journal of Medicine346(6), 393-403.
39. Laird N.M., Ware J.H. Random-effects models for longitudinal data. Biometrics 1982, 38:963-974.
40. Laird N.M., Lange N., Stram D. Maximum likelihood computations with repeated measures: Application of the EM algorithm. Journal of the American Statistical Association 1987, 82:97-105.
41. Lange N., Ryan L. Assessing normality in random effects models. Annals of Statistics 1989, 17:624-642.
42. Lin L.I. A concordance correlation coefficient to evaluate reproducibility. Biometrics 1989, 45:255-268.
43. Lindstrom M.J., Bates D.M. Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data. Journal of the American Statistical Association 1988, 83:1014-1022.
44. Lipsitz S.R., Ibrahim J., Molenberghs G. Using a Box-Cox transformation in the analysis of longitudinal data with incomplete responses. Applied Statistics 2000, 49:287-296.
45. Littell R., Milliken G., Stroup W., Wolfinger R., Schabenberger O. SAS for Mixed Models 2006, SAS Institute Inc., Cary, NC, Chapter 12. 2nd ed.
46. Little R.J.A., Rubin D.B. Statistical Analysis with Missing Data 1987, John Wiley and Sons, New York.
47. Liu H., Weiss R.E., Jennrich R.I., Wenger N.S. PRESS model selection in repeated measures data. Computational Statistics and Data Analysis 1999, 30:169-184.
48. p. Technometrics 1973, 15:661-675.
49. MathSoft Inc. S-Plus Release 6) 2002, MathSoft Inc., Seattle.
50. McCarroll, K.A., Helms, R.W. (1987). An evaluation of some approximate F statistics and their small sample distributions for the mixed model with linear covariance structure. The Institute of Statistics Mimeo Series. Department of Biostatistics, University of North Carolina, Chapel Hill, NC.
51. McCullagh P., Nelder J.A. Generalized Linear Models 1989, Chapman & Hall, New York. 2nd ed.
52. McCulloch C.E., Searle S.R. Generalized, Linear and Mixed Models 2001, Wiley, New York.
53. Mokdad A.H., Bowman B.A., Ford E.S., Vinicor F., Marks J.S., Koplan J.P. The continuing epidemics of obesity and diabetes in the United States. Journal of the American Medical Association 2001, 286(10):1195-1200.
54. Molenberghs G., Verbeke G. Models for Discrete Longitudinal Data 2005, Springer, New York, .
55. Muller K.E., Stewart P.W. Linear Model Theory: Univariate, Multivariate, and Mixed Models 2006, Wiley, New York.
56. Oberg A., Davidian M. Estimating data transformations in nonlinear mixed effects models. Biometrics 2000, 56:65-72.
57. Overall J.E., Doyle S.R. Estimating sample sizes for repeated measurement designs. Controlled Clinical Trials 1994, 15:100-123.
58. Palta M., Qu R.P. Testing lack of fit in mixed effect models for longitudinal data. New Trends in Probability and Statistics Volume 3: Multivariate Statistics and Matrices in Statistics (Proceedings of the 5th Tartu Conference) 1995, 93-106. VSP International Science Publishers, Zeist, The Netherlands.
59. Patterson H.D., Thompson R. Recovery of inter-block information when block sizes are equal. Biometrika 1971, 58:545-554.
60. Pinheiro J.C., Bates D.M. Approximations to the log-likelihood function in the nonlinear mixed-effects model. Journal of Computational and Graphical Statistics 1995, 4:12-35.
61. Pinheiro J.C., Bates D.M. Mixed Effects Models in S and S-Plus 2000, Springer, New York.
62. R: A Language and Environment for Statistical Computing 2006, R Development Core Team, R Foundation for Statistical Computing, Vienna.
63. Richardson A.M., Welsh A.H. Robust restricted maximum likelihood in mixed linear models. Biometrics 1995, 51:1429-1439.
64. ® 9.1 2003, SAS Institute Inc, SAS Institute Inc., Cary, NC.
65. SAS/Stat User's Guide, Version 9.1 2003, SAS Institute Inc, 2003b, SAS Institute Inc, Cary, NC.
66. Schwarz G. Estimating the dimension of a model. Annuals of Statistics 1978, 6:461-464.
67. Shao J. Linear model selection by cross-validation. Journal of the American Statistical Association 1993, 88:486-494.
68. Shi P., Tsai C.L. Regression model selectiona residual likelihood approach. Journal of the Royal Statistical Society B 2002, 64(2):237-252.
69. Shen X., Dougherty D.P. Discussion: Inference and interpretability considerations in frequentist model averaging and selection. Journal of the American Statistical Association 2003, 98:917-919.
70. Rel. 14.0.1 2006, SPSS for Windows, SPSS Inc., Chicago.
71. Stata Statistical Software: Release 9 2005, StataCorp, StataCorp LP., College Station, TX.
72. Stone M. Cross-validatory choice and assessment of statistical predictions (with discussion). Journal of the Royal Statistical Society, Series B 1974, 36:111-147.
73. Stone M. An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion. Journal of the Royal Statistical Society, Series B 1977, 39:44-47.
74. Stroup W.W. Mixed model procedures to assess power, precision, and sample size in the design of experiments 1999, American Statistical Association, Alexandria, VA, (pp. 15-24).
75. Verbeke G., Lesaffre E. A linear mixed-effects model with heterogeneity in the random-effects population. Journal of the American Statistical Association 1996, 91:217-221.
76. Verbeke G., Lesaffre E. The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data. Computational Statistics and Data Analysis 1997, 23:541-556.
77. Verbeke G., Molenberghs G. Linear Mixed Models for Longitudinal Data 2000, Springer, New York.
78. Verbeke G., Molenberghs G. The use of score tests for inference on variance components. Biometrics 2003, 59:254-262.
79. Vonesh, E.F. (2004). Hypothesis testing in mixed-effects models. Presented in Session 12: Estimation and Inference in Mixed-Effects Models. 2004 International Biometric Society Eastern North American Region Meetings, Pittsburgh, PA.
80. Vonesh E.F., Chinchilli V.M. Linear and Nonlinear Models for the Analysis of Repeated Measurements 1997, Marcel Dekker, New York.
81. Vonesh E.F., Chinchilli V.M., Pu K. Goodness-of-fit in generalized nonlinear mixed-effects models. Biometrics 1996, 52:572-587.
82. Weiss R.E., Wang Y., Ibrahim J.G. Predictive model selection for repeated measures random effects models using Bayes factors. Biometrics 1997, 53:592-602.
83. Welham S.J., Thompson R. A likelihood ratio test for fixed model terms using residual maximum likelihood. Journal of the Royal Statistical Society, Series B 1997, 59:701-714.
84. Wolf A.M., Conaway M.R., Crowther J.Q., Hazen K.Y., Nadler J.L., Oneida B., Bovbjerg V.E. Translating lifestyle intervention to practice in obese patients with type 2 diabetes: Improving control with activity and nutrition (ICAN) study. Diabetes Care 2004, 27(7):1570-1576.
85. Xu R. Measuring explained variation in linear mixed effects models. Statistics in Medicine 2003, 22:3527-3541.
86. Zeger S.L., Liang K.-Y., Albert P.S. Models for longitudinal data: A generalized estimating equation approach. Biometrics 1988, 44(4):1049-1060.
87. Zucker D.M., Lieberman O., Manor O. Improved small sample inference in the mixed linear model. Journal of the Royal Statistical Society, Series B 2000, 62:827-838.