Model-based clustering for longitudinal data

Computational Statistics and Data Analysis

Volumn 52, Issue 3, 2008, Pages 1441-1457

  De la Cruz Mesía, Rolando ^a   Quintana, Fernando A ^b   Marshall, Guillermo ^b  

^a PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

^b PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

Author keywords

Cluster analysis; EM algorithm; Markov chain Monte Carlo; Mixture model; Non linear models; Random effects

Indexed keywords

BAYESIAN NETWORKS; ESTIMATION; HIERARCHICAL SYSTEMS; HORMONES; MARKOV PROCESSES; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; MONTE CARLO METHODS;

BAYESIAN ESTIMATION PROCEDURES; DATA VARIABILITY; EM ALGORITHM; LONGITUDINAL DATA; MARKOV CHAIN MONTE CARLO (MCMC) SAMPLING SCHEMES;

CLUSTERING ALGORITHMS;

EID: 35548932932     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.04.005     Document Type: Article

References (55)

1. Booth, J.G., Casella, G., Hobert, J.P., 2007. Clustering using objective functions and stochastic search, submitted for publication.
2. Breiman L., Fridman J.H., Olshen R.A., and Stone C.J. Classification and Regression Trees (1984), Wadsworth, Belmont, CA
3. Celeux G. Bayesian inference for mixtures: the label switching problem. In: Payne R., and Green P. (Eds). COMPSTAT 98 (1998), Physica-Verlag, Wurzburg 227-232
4. Celeux G., Hurn M., and Robert C.P. Computational and inferential difficulties with mixture posterior distribution. J. Amer. Statist. Assoc. 95 (2000) 957-970
5. Celeux G., Lavergne C., and Martin O. Mixture of linear mixed models for clustering gene expression profiles from repeated microarray experiments. Statist. Model. 5 (2005) 243-267
6. Chib S. Marginal likelihood from the Gibbs output. J. Amer. Statist. Assoc. 90 (1995) 1313-1321
7. Dasgupta A., and Raftery A.E. Detecting features in spatial point processes with clutter via model-based clustering. J. Amer. Statist. Assoc. 93 (1998) 294-302
8. Davidian M., and Giltinan D.M. Nonlinear Models for Repeated Measurement Data (1995), Chapman & Hall, London
9. De la Cruz-Mesía R., and Marshall G. A Bayesian approach for nonlinear regression model with continuous errors. Comm. Statist. Theory Methods 32 8 (2003) 1631-1646
10. De la Cruz-Mesía R., and Marshall G. Nonlinear random effects models with continuous time autoregressive errors: a Bayesian approach. Statist. in Medicine 25 9 (2006) 1471-1484
11. Dempster A.E., Laird N.M., and Rubin D.B. Maximum likelihood with incomplete data via the E-M algorithm. J. Roy. Statist. Soc. Ser. B 39 (1977) 1-38
12. DeSarbo W.S., and Cron W.L. A maximum likelihood methodology for clusterwise linear regression. J. Classification 5 1 (1988) 249-282
13. Diebolt J., and Robert C.P. Estimation of finite mixture distributions through bayesian samplings. J. Roy. Statist. Soc. Ser. B 56 (1994) 363-375
14. Escobar M.D., and West M. Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90 (1995) 577-588
15. Fitzmaurice G.M., Laird N.M., and Ware J.H. Applied Longitudinal Analysis (2004), Wiley, New York
16. Fraley C., and Raftery A.E. How many clusters? which clustering method? answers via model-based cluster analysis. Comput. J. 41 (1998) 578-588
17. Fraley C., and Raftery A.E. MCLUST: software for model-based cluster analysis. J. Classification 16 (1999) 297-306
18. Fraley C., and Raftery A.E. Model-based clustering discriminant analysis and density estimation. J. Amer. Statist. Assoc. 97 (2002) 611-631
19. Frits M.A., and Guo S.M. Doubling time of human chorionic gonadotropin (hCG) in early normal pregnancy: relationship to hCG concentration and gestational age. Fertil. Steril. 47 (1987) 584-589
20. Frühwirth-Schnatter S. Markov chain Monte Carlo estimation of classical and dynamic switching and mixture models. J. Amer. Statist. Assoc. 96 (2001) 194-209
21. Gaffney, S.J., Smyth, P., 2003. Curve clustering with random effects regression mixtures. In: Bishop, C.M., Frey, B.J. (Eds.), Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics, Key West, FL.
22. Gelman A., Roberts G.O., and Gilks W.R. Efficient Metropolis jumping rules. In: Bernardo J.M., Berger J.O., Dawid A.P., and Smith A.F.M. (Eds). Bayesian Statistics vol. 5 (1996), Oxford University Press, Oxford 599-607
23. Geweke J. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In: Bernardo J.M., Berger J.O., Dawid A.P., and Smith A.F.M. (Eds). Bayesian Statistics vol. 4 (1992), Oxford University Press, Oxford 169-194
24. Guo S.W., and Thompson E.A. Monte Carlo estimation of mixed models for large complex pedigrees. Biometrics 50 (1994) 417-432
25. Hartigan J.A. Clustering Algorithms (1975), Wiley, New York
26. Hosmer D. Maximum likelihood estimates of the parameters of a mixture of two regression lines. Comm. Statist. 3 10 (1974) 995-1006
27. Hosmer D.W., and Lemeshow S. Applied Logistic Regression. second ed (2000), Wiley, New York
28. Hurn M., Justel A., and Robert C.P. Estimating mixtures of regressions. J. Comput. and Graphical Statist. 12 1 (2003) 55-79
29. James G., and Sugar C. Clustering for sparsely sampled functional data. J. Amer. Statist. Assoc. 98 (2003) 397-408
30. Jasra A., Holmes C.C., and Stephens D.A. Markov chain Monte Carlo and the label switching problem in Bayesian mixture modelling. Statist. Sci. 20 1 (2005) 50-67
31. Jennrich R.I., and Schluchter M.D. Unbalanced repeated-measures models with structured covariance matrices. Biometrics 42 4 (1986) 805-820
32. Jones P.N., and McLachlan G.J. Fitting finite mixture models in a regression context. Austral. J. Statist. 34 2 (1992) 233-240
33. Kass R.E., and Raftery A.E. Bayes factors. J. Amer. Statist. Assoc. 90 (1995) 773-795
34. Li B. A new approach to cluster analysis: the clustering-function-based method. J. Roy. Statist. Soc. Ser. B 68 (2006) 457-476
35. Marshall G., and Barón A.E. Linear discriminant models for unbalanced longitudinal data. Statist. in Medicine 19 (2000) 1969-1981
36. McLachlan G.J., and Basford K.E. Mixture Models: Inference and Applications to Clustering (1988), Marcel Dekker, New York
37. McLachlan G.J., and Peel D. Finite Mixture Models (2000), Wiley, New York
38. Pauler D.K., and Laird N.M. A mixture model for longitudinal data with application to assessment of noncompliance. Biometrics 56 (2000) 464-472
39. Peng F., Jacobs R.A., and Tanner M.A. Bayesian inference in mixtures-of-experts and hierarchical mixtures-of-experts with an application to speech recognition. J. Amer. Statist. Assoc. 91 (1996) 953-960
40. Pfeifer C. Classification of longitudinal profiles based on semi-parametric regression with mixed effects. Statist. Model. 4 (2004) 314-323
41. Pinheiro J.C., and Bates D.M. Mixed-Effects Models in S and S-PLUS (2000), Springer, New York
42. Quandt R.E. A new approach to estimating switching regressions. J. Amer. Statist. Assoc. 57 (1972) 306-310
43. Quandt R.E., and Ramsey J.B. Estimating mixtures of normal distributions and switching regressions. J. Amer. Statist. Assoc. 73 (1978) 730-738
44. Ramsay J.O., and Silverman B.W. Functional Data Analysis (1997), Springer, New York
45. Richardson S., and Green P.J. On Bayesian analysis of mixture models with an unknown number of components. J. Roy Statist. Soc. Ser. B 59 4 (1997) 731-792
46. Roeder K., and Wasserman L. Practical Bayesian density estimation using mixtures of normals. J. Amer. Statist. Assoc. 92 (1997) 894-902
47. Schwarz G. Estimating the dimension of a model. Ann. Statist. 6 (1978) 461-464
48. Segal M.R. Tree-structured methods for longitudinal data. J. Amer. Statist. Assoc. 87 (1992) 407-418
49. Smith, B.J., 2004. Bayesian Output Analysis Program (BOA). Version 1.1.2 for S-PLUS and R. Available at: 〈http://www.public-health.uiowa.edu/boa〉.
50. Stephens M. Dealing with label switching in mixture models. J. Roy. Statist. Soc. Ser. B 62 (2000) 795-809
51. Verbeke G., and Molenberghs G. Linear Mixed Models for Longitudinal Data (2000), Springer, New York
52. Viele K., and Tong B. Modeling with mixtures of linear regressions. Ann. Statist. 27 (2002) 439-460
53. Vonesh E.F., and Chinchilli V.M. Linear and Nonlinear Models for the Analysis of Repeated Measurements (1997), Marcel Dekker, New York
54. Wu C.F.J. On the convergence properties of the EM algorithm. Ann. Statist. 11 1 (1983) 95-103
55. Zhang H. Multivariate adaptive splines for analysis of longitudinal data. J. Comput. Graphical Statist. 6 (1997) 74-91