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A semiparametric mixture regression model for longitudinal data. (English) Zbl 1425.62084

Summary: A normal semiparametric mixture regression model is proposed for longitudinal data. The proposed model contains one smooth term and a set of possible linear predictors. Model terms are estimated using the penalized likelihood method with the EM algorithm. A computationally feasible alternative method that provides an approximate solution is also introduced. Simulation experiments and a real data example are used to illustrate the methods.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62G08 Nonparametric regression and quantile regression
62J07 Ridge regression; shrinkage estimators (Lasso)
62P10 Applications of statistics to biology and medical sciences; meta analysis
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[1] Basford, Κ. Ε.; McLachlan, G. J., Likelihood estimation with normal mixture models, Applied Statistics, 34, 282-89 (1985) · doi:10.2307/2347474
[2] Dempster, Α.; Laird, Ν.; Rubin, D., Maximum likelihood estimation for incomplete data via the EM algorithm, Journal of the Royal Statistical Society Β, 39, 1-38 (1977) · Zbl 0364.62022
[3] Diggle, P., P. Heagerty, K.-Y. Liang, and S. Zeger. 2013. Analysis of longitudinal data, 2nd ed. Oxford, UK: Oxford University Press. · Zbl 1268.62001
[4] Fariaa, S.; Soromenho, G., Fitting mixtures of linear regressions, Journal of Statistical Computation and Simulation, 80, 201-25 (2010) · Zbl 1184.62118 · doi:10.1080/00949650802590261
[5] Fitzmaurize, G. M., N. M. Laird, and J. H. Ware. 2011. Applied longitudinal analysis, 2nd ed. Hoboken, NJ: Wiley. · Zbl 1226.62069 · doi:10.1002/9781119513469
[6] Gasser, T.; Muller, H. G.; Kohler, W.; Molinari, L.; Prader, A., Nonparametric Regression analysis of growth curves, Annals of Statistics, 12, 210-29 (1984) · Zbl 0535.62088 · doi:10.1214/aos/1176346402
[7] Green, P., and B. Silverman. 1994. Nonparametric regression and generalized linear models. A roughness penalty approach. Monographs on Statistics and Applied Probability, 58. Boca Raton, FL: Chapman Hall/CRC. · Zbl 0832.62032 · doi:10.1007/978-1-4899-4473-3
[8] Huang, M.; Yao, W., Mixture regression models with varying mixing proportions: A semiparametric approach, Journal of the American Statistical Association, 107, 711-24 (2012) · Zbl 1261.62036 · doi:10.1080/01621459.2012.682541
[9] Huang, M.; Li, R.; Wang, S., Nonparametric mixture regression models, Journal of the American Statistical Association, 108, 929-41 (2013) · Zbl 06224977 · doi:10.1080/01621459.2013.772897
[10] Johnson, W., Human biology toolkit: Analytical strategies in human growth research, American Journal of Human Biology, 27, 69-83 (2015) · doi:10.1002/ajhb.22589
[11] Jones, B.; Nagin, D.; Roeder, K., A SAS procedure based on mixture models for estimating developmental trajectories, Sociological Methods & Research, 29, 374-393 (2001) · doi:10.1177/0049124101029003005
[12] Karlberg, J., On the modeling of human growth, Statistics in Medicine, 6, 185-92 (1987) · doi:10.1002/sim.4780060210
[13] Leisch, F., FlexMix: A general framework for finite mixture models and latent class regression in R, Journal of Statistical Software, 11, 1-18 (2004) · doi:10.18637/jss.v011.i08
[14] Leng, C.; Zhang, W.; Pan, J., Semiparametric mean-covariance regression analysis for longitudinal data, Journal of the American Statistical Association, 105, 181-93 (2010) · Zbl 1397.62130 · doi:10.1198/jasa.2009.tm08485
[15] McLachlan, G., and D. Peel. 2000. Finite mixture models. New York, NY: John Wiley and Sons. · Zbl 0963.62061 · doi:10.1002/0471721182
[16] McLachlan, G.; Rathnayake, S., On the Number of Components in a Gaussion mixture, WIREs Data Mining and Knowledge Discovery, 4, 341-55 (2014) · doi:10.1002/widm.1135
[17] Muthen, B.; Khoo, S. T., Longitudinal studies of achievement growth using latent variable modeling, Learning and Individual Differences, 10, 73-101 (1998) · doi:10.1016/S1041-6080(99)80135-6
[18] Muthen, L., and B. Muthen. 2007. Mplus user’s guide, 6th ed. Los Angeles, CA: Muthen & Muthen.
[19] Nagin, D., Analyzing developmental trajectories: Semiparametric, group-based approach, Psychological Methods, 4, 39-177 (1999) · doi:10.1037/1082-989X.4.2.139
[20] Nagin, D. 2005. Group-based modeling of development. Cambridge, MA: Harvard University Press. · doi:10.4159/9780674041318
[21] Nummi, T.; Pan, J.; Siren, T.; Liu, K., Testing for cubic smoothing splines under dependent data, Biometrics, 67, 871-75 (2011) · Zbl 1226.62049 · doi:10.1111/j.1541-0420.2010.01537.x
[22] Nummi, T.; Pan, J.; Mesue, N., Testing linearity in semiparametric regression models, Statistics and Its Interface, 6, 3-8 (2013) · Zbl 1327.62026 · doi:10.4310/SII.2013.v6.n1.a1
[23] Nummi, T.; Hakanen, T.; Lipiäinen, L.; Harjunmaa, U.; Salo, M.; Saha, M.-T.; Vuorela, N., A trajectory analysis of body mass index for Finnish children, Journal of Applied Statistics, 41, 1422-35 (2014) · Zbl 1514.62785 · doi:10.1080/02664763.2013.872232
[24] Poortema, K. 1984. On the statistical analysis of growth. PhD thesis, Groningen University, Groningen, The Netherlands. · Zbl 0946.62035
[25] Ruppert, D., M. P. Wand, and R. J. Carrol. 2005. Semiparametric regression. New York, NY: Cambridge University Press.
[26] Titterington, D. M., A. F. M. Smith, and U. E. Makov. 1985. Statistical analysis of finite mixture distribution. Wiley, New York. · Zbl 0646.62013
[27] Verbeke, G.; Lesaffre, E., A linear mixed-effects model with heterogeneity in the random-effects population, Journal of the American Statistical Association, 91, 217-21 (1996) · Zbl 0870.62057 · doi:10.1080/01621459.1996.10476679
[28] Vuorela, N. 2011. Body mass index, overweight and obesity among children in Finland — A retrospective epidemilogical study in Pirkanmaa District spanning over four decades. Acta Universitatis Tamperensis 1611, Tampere University Press, Tampere.
[29] Ye, H.; Pan, J., Modelling covariance structures in generalized estimating equations for longitudinal data, Biometrika, 93, 927-41 (2006) · Zbl 1436.62348 · doi:10.1093/biomet/93.4.927
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